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Introductory Electricity & Magnetism Lab Manual, 2 nd Ed.

1. 4 1 Charge a flat sheet of plastic insulator by rubbing vigorously with fake fur Set a flat conductor on top of it using an insulated handle i e don t touch the conductor yet Sketch a labeled diagram of how the charge is vertically separated in the conductor while neutral overall net charge equal to zero 56 4 2 Pull the conductor from the charged insulator still without touching the conductor and see that the conductor is still neutral Test this using the electroscope or Faraday cage You may detect some small amount of charge transfer to the conductor itself or the plastic handle the conductor or even your hand because there are such enormous electrostatic fields at work Write your observations amp 43 Recharge your flat sheet of plastic insulator and again place the flat conductor on the plate without touching it This time momentarily place your finger on the metal Remove your finger and then lift the conductor disc from the plate You may hear electrical crackling during this if your insulator was initially highly charged DO NOT LET THIS TOUCH THE ELECTROSCOPE See that your conductor now has net charge and determine the sign of the excess charge with the electroscope or Faraday cage Make a cartoon that shows how this process of induction works and what the net charge of the conductor is positive or negative Cartoon Frames use more frames if necessary 57 Section 5 faraday ice pail Becaus
2. 107 This page intentionally left blank 108 Week 4 Take Home Quiz Score 5 THQ 1 5 points Derive the CRT deflection equation Clearly explain every step of the derivation in words i e explain why one step of the equation is equal to the next which might be mathematical or based on physics concepts You will not get credit for simply copying equations without demonstrating you understand the math and physics that connect all the steps 109 keep going 110 Unit 3 Lab Report Instructions Unit Lab Report 40 points Use the following section titles in your report Images text or equations plagiarized from the internet are not allowed Remember to write your report alone as collaborating with a lab partner will make you both guilty of plagiarism Please label your lab report sections Title 0 points A catchy title worth zero points so make it unique and fun Mini Report 10 points 4 6 paragraphs 2 double spaced pages Choose one of the following sections about which to write your mini report Week 5 Section 3 or Week 6 Section 3 Write a mini report for one particular section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable Please label your mini report sections o Ab
3. amp 4 7 Now use two channel observations to simultaneously measure the resistor voltage and the source voltage to determine their respective phase shift in seconds 248 48 Theoretical calculations Use the labeled values for inductance capacitance and resistance that you have in your circuit as well as your actual driving frequency to calculate the following RLC circuit parameters in SI units XC XL resonance fiesoiance amp 49 Comparing theory and observation Use your results from the previous question along with your observed source voltage amplitude should still be 5 V to theoretically calculate the voltage amplitudes of the resistor inductor and capacitor in SI units Then compare each of these theoretically computed amplitudes to your previous observations 249 ees 7T resistor Power Since Pees mad 2V2 resistor R the power converted to heat by the resistor oscillates in time as a squared sine function 2 2 V t E Voie P t sin i Osivet The average value of a squared sine function over a complete oscillation cycle is 0 5 average insist F 5 This means that the power consumed by the resistor averaged over time is 2 R amplitude Trasee IR 4 10 Use this formula to find the average power loss of your circuit in SI units 411 When the driving frequency is at resonance the voltages of the source and resistor are equal and in phase Use this
4. _ V raies 27 A you may use Ohm s law to find the total current I patey a B e Since charge cannot pile up anywhere in a circuit this is also the same current as in R3 27 4 I F A You can now find the voltage across Rs V R I V e Now note that R and R2 are in parallel so that V V2 remember conservation of energy in circuit loops Subtract V3 from the total voltage to find the voltage across these 4 ae parallel resistors V V 9 V Now you can easily find the current in V V each component I 2 A and Z 2 A Check your parallel currents R 7 R 14 as they must add up to the total J 7 gt z A which is the total current coming into the parallel components Also note that since R32 has twice the resistance of R only half as much current flows through that resistor The logic is beautiful but it takes a good amount of practice to learn how to work inward then back outward on these kinds of problems 121 2 7 The following compound circuit shows a 10 V battery discharging through two parallel 2 ohm resistors and two 8 ohm resistors in parallel The two parallel pairs of resistors are themselves in series You need to find all the unknown component voltages and currents as well as the total circuit resistance and current You may assume the battery is ideal has no internal resistance The answers are given so that you can check your work Hint t
5. b If the positive DMM lead is placed at point a and the negative DMM lead placed at point b what reading will the DMM yield THQ 2 1 point i fl AMSLLVE g AMSLLVE 4 il AuaLive Ad ESENTE There are four identical 1 5 V batteries in series with ten identical light bulbs What is the voltage drop across any single light bulb 41 THQ 3 2 points In the following circuits all four light bulbs are identical A B 6 0V a Which circuit has the larger voltage drop across each bulb b Which circuit has the lower equivalent resistance c Which circuit draws the greater current from the voltage sources d Which circuit has brighter bulbs based on your answers to a and c 42 Week 2 Pre Lab Magnetism and Electrostatics Read the following short pre lab upon which you will take a quiz at the beginning of lab Magnetic materials create a magnetic field around them that can be represented using lines that start on the magnetic north pole s and end on the magnetic south pole s These magnetic field lines may never intersect one another Example 1 Example 2 The earth s north geographic pole is really a south magnetic pole which attracts the north magnetic pole of a compass The arrow tip of a compass is a north magnetic pole which is always attracted to the south magnetic pole of another magnet S MAGNETIC Nwacnetic 43 If net charge is placed on a conductor
6. 2 3 On graph paper plot your four voltage phasors at t 0 on the complex plane Be sure to label magnitudes and phase shifts for each of the phasors Your graph must be planned ahead to fill the entire page have labeled and hash marked axes and a descriptive title d 2 4 Calculate and write the time dependent current as a complex exponential phasor 286 Section 3 measuring the phasors Construct a sinusoidally driven RLC circuit using the following values N ounce amplitude 5 VY farive 700 Hz R 1000 Q C 10 uF L 100 mH 3 1 Measure the voltage amplitudes of each of the four circuit component voltages and compare these to your calculations in the previous section The measured values should be approximately equal to your calculated values 3 2 Measure the time shift between the source voltage and resistor voltage and use this to calculate the measured phase shift Remember that z 27 tein Desires T irive snit T 287 Section 4 authentic assessment Perhaps the most critical feature of a sinusoidally driven RLC circuit is the fact that there exists a resonant frequency at which the circuit s current amplitude is maximized or alternatively when the circuit s total impedence Z is minimized For the following circuit parameters V source amplitude 5 V R 1000 Q C 10 pF and L 100 mH use the oscilloscope in XY mode measuring the voltages of the corr
7. In this section you will make predictions about different circuits then build and test them Always use SI units A B 44 D E ni f 15 15 f 1 5 1 5 V 1511 5 I 3 15 r eal 2 3 1 For the previous figure showing various arrangements of batteries predict the voltages that would be measured Explain your predictions Write both your predictions and explanations amp 3 2 Now set up each of the circuits and test your predictions What are the actual voltages of the battery arrangements Be sure to apply the positive and negative leads of your DMM correctly as indicated to obtain the correct sign of the voltage compare the sign of the voltage in circuits a and b If some of your predictions are wrong ask around and figure out why then explain why you were mistaken 28 B G D 19y 15 VY 1 5 V 15V 15V Ej 15 WV Eh 3 3 For the previous figure predict the order of brightness of the bulbs from least to most bright and then explain why you think this will be the case Write both your predictions and explanations Always make the circuit first before you approach it with your DMM amp 3 4 Now set up each of the above circuits and test your predictions What is the actual order of the bulbs from least to most bright If some of your predictions are wrong ask around and figure out why then explain why you were mistaken 29 B G D 15y 15 VY 1 5 V qJ 15V 15V Ej 15 WV Eh 3 5
8. Unit 2 e Electric Field Mapping e Cathode Ray Tube This unit emphasizes the concept of the electric field and its relation to voltage Students continue to practice using the DMM and gain skills with equipment needed to operate a CRT Unit 3 e Vulture Iguana Rabbit e Oscilloscope This unit emphasizes the concepts of Ohm s law and oscillating voltages AC Students begin developing the most important skill of oscilloscope concepts and mastery Unit 4 e RC Circuits DC Source e RC Circuits AC Source This unit emphasizes the concepts of differential equations and circuit capacitance Students practice the skill of measuring a working circuit s properties with an oscilloscope Unit 5 e Motors e Solenoids This unit emphasizes the concepts of induction and changing magnetic flux Students continue to practice wiring and measuring multiple circuits with an oscilloscope Unit 6 e RLC Circuit AC Driven e RLC Radios This unit emphasizes the concepts of inductance phase shifts and resonance Students continue to practice wiring novel devices and measuring novel circuits with an oscilloscope Tentative Lab Schedule Before printing the lab manual replace this page with a Tentative Lab Schedule as two single sided pages Otherwise students should receive a tentative lab schedule as a handout or be able to view one online This page intentionally left blank Physics 241 Lab Policies Before printing the lab manu
9. Wires bared to act as brushes Wires bared to act as leads See the next page for power line hints Note on testing your motor Always start with low voltage 2 Volts when connecting your motor to the DC power supply Then start the motor by spinning it with your fingers You should be able to feel with your fingers which way the motor is being pushed to rotate This will tell you which way to spin it You may have to keep increasing the supply voltage to keep your motor spinning Never let your motor stay connected to the source with current running through it when it is not spinning because the insulation will rapidly melt away You will hear the TA shouting from time to time during this lab Unhook it Unhook it 200 Other power line configurations have shown improvement over the original design One idea is to double up the power lines so that they make better contact and are more durable J These power lines are doubled up to allow better connectivity with the axle leads as well as to strengthen the power lines so that they are less quickly j deformed by the operation 4 of the motor Another idea is to change the location of the power lines so that they hug the axle more than in the original positioning This doubled power line starts and ends near the l bottom of the motor enclosure box and contacts BE the axle leads from the top This doubled power line starts and en
10. _ SY inductor erm resistor term capacitor term 0 243 Notice that the second two terms on the right hand side show that the time dependence of the capacitor voltage is related to the antiderivative of the resistor voltage LTO RO QO V ua dt dt l The capacitor voltage is proportioml to theantiderivaive of theresistor voltage 0 V stag amplitude capacitor voltage must be described by a negative cosine function the antiderivative of the sin function But the negative cosine function is also phase shifted from the sine function by 7 2 COS yivet sil ac z Since the resistor voltage is described by a sine function V t sin iv lt the resistor 2 1 2 Use the fact that dn av An and use calculus explain in a different way why the inductor voltage is phase shifted from the resistor voltage by 1 2 Begin with d O g deo _ 2 V ource t PUS ge dt dt C 0 and O t gt s COS Ogivet pte a 2 2 Use calculus to explain why the capacitor voltage is phase shifted from the inductor voltages by n 244 Section 3 extra lab techniques An RLC circuit has a resonant driving frequency fesonance that maximizes the circuit current amplitude Therefore a plot of the current amplitude vs driving frequency will show peak current amplitude at the resonant driving frequency However this graph can appear different depending on whether a large or small resistance is used
11. a units 102 y You will now experimentally test the vertical CRT deflection equation D k T that you have derived by adjusting Vay and observing Dy in order to estimate the y geometrical factor The y geometrical constant in this other direction is different from z because the geometry of the deflecting plates is different in the z direction from the y direction i e one set of plates is closer to the screen than the other 2 5 Use tape on screen to mark position of electron beam when there is NO DEFLECTION Vay set to zero to find the origin of the CRT Be sure to record V and keep this value constant for the rest of this section V is the sum of Vg and Vc on the CRT power module and should be set as high as possible while the scintillation dot is still in focus Record your constant accelerating voltage d 2 6 Adjust Va on the horizontal plates and mark D on the tape for several values of Vay make a data table with at least 5 data points Record your data table of Vay and D G 2 7 Create graph of D vs Va by hand Graph D vs Va on graph paper Your data should give you a straight line 2 8 Measure the slope of the line of best fit Since D lt Vas y a the slope will equal fes so multiply by V to obtain k Record your result for k here in SI a units 103 You will now experimentally test in another way the horizontal CRT deflection equation D k a by a
12. ae EE ee ae Sa ee eS 74 1 3 In the following picture depicting equipotential lines dashed lines of constant voltage label in the picture where the two regions are located that have the strongest electric field and the two regions that have the weakest electric field Use the letter S for the region of strongest electric field and W for the region of weakest electric field Below the picture explain how you made your decision Draw on the picture below and write an explanation below the picture ae EE ie a a a 2a ws sV 1 jee a OUT 7 ime 4 e BiT in 7 Pa r Ri I 7 rr omnm NN I r e A 7S e gt 1 i P I I YASS N l lO i my 3 i i l I l l 1 oy IN 1 l d oN S Pod Z4 lt a Nig P aif Er S o Mn Nas a Pa Nx Na ania ae gt Pe jg T Sis cee gel Ps n E a ga Pa wie ee OO 75 Perhaps the simplest system to study is the conducting parallel plates Two parallel walls of a conductor are separated with each wall electrified with a different voltage In the example below the conducting plates are separated by 10 cm and given electric potentials of 10 V for the plate on the left and 0 V for the plate on the right Note that since the voltage is constant throughout any part of a conductor setting one part of the plate to 10 V means that any point on the conductor is at 10 V and similarly fo
13. d THQ 1 2 point Practice the math for an example of a sinusoidally driven series RLC circuit Wecana amplitude 15V drive 790 Hz R 2 000 Q C 15 uF L 75 mH Calculate each of the basic RLC circuit parameters in SI units though not necessarily in the order given SI units Xc XL y R amplitude Vi C amplitude y L amplitude Psource I amplitude 257 THQ 2 2 point Next write a time dependent equation for each quantity below using the numerical results from the previous question V ee source V t Ve V0 I t Qa t THQ 3 1 point What is the resonant driving frequency fp of this circuit sonant 258 Week 12 Pre Lab RLC Radios Audio Frequency 1500 Hz V 4 t Modulating High Frequency Waves with Low Frequency Waves Imagine that you want to transmit a 1 500 Hz sound wave from one place to another Clearly you could play the sound and have its vibrations be carried in the air as compression rarefaction waves But for long distance transport you may want to turn the sound into an electronic signal which can be transported with less energy loss along a wire But if we need to transport the sound to many people radio or someone at a changing location walkie talkie we can take advantage of our knowledge of electromagnetism and turn the sound wave into an electromagnetic wave and send the electromagnetic wave through the
14. and also we need to use SVa e V usually to substitute for v Check here if you read that sentence twice ____ First we need to find Ay You will need to justify each step below in your lab report 99 Next we need to find Ay You will need to justify each step below in your lab report Ay v At L eaf Finally this gives our equation for the total deflection on the oscilloscope screen Dy 2 w w L Vis Di 4d 2d V might as well replace all these geometric factors with a single unknown geometric constant Kgy y D Sky THIS IS OUR FINAL CRT DEFLECTION EQUATION Note that by a However we cannot open up the CRT to measure d w or L so we 100 symmetry we get the same derivation for the total deflection in the horizontal x direction V D k a THEREFORE THERE IS A CRT DEFLECTION EQUATION FOR EACH DEFLECTION DIRECTION EACH WITH ITS OWN GEOMETRIC CONSTANT 1 15 Explain how we have we achieved the goal set out in 1 14 Subsection D Now you need to answer some questions about the CRT deflection equations 1 16 Given the CRT deflection equation in the vertical direction D k Vas what a you would see on the CRT screen if the deflection voltage was increased Explain why this would happen using a physical argument i e not using math Your answer and explanation 4in7 Viy Given the CRT deflection equation i
15. magnetic field is created nearby the CRT Then check your prediction For this you will need to remember what the cross product means in the Lorenz force equation better ask around if you don t F q7 xB and how to use the right hand rule Circle your predictions then check them experimentally while showing a student in a different group Assessment 2 magnet Assessment 1 ou magnet magnet 1 LLCO ATOS PanGF 4 nS B Yes I have seen this student determine how magnetic fields affect moving electrons They will be able to protect themselves from dangerous ions on their trip to Mars if they take a magnet If you are uncomfortable having another student check your work please ask your TA Student Signature 105 Section 4 open ended If you were able to see inside a CRT you would see that one set of deflection plates is closer to the scintillation screen than the other set of deflection plates If both pairs of deflection plates were identically shaped then the pair closer to the screen would have a smaller L and therefore a smaller geometric constant kg Your job is to determine whether the vertical plates or the horizontal plates inside your CRT are closer to the scintillation screen assuming both pairs of plates are identically shaped This is equivalent to finding which geometric constant is larger kgx or Kgy You might say that you already know the answer to this based on your pre
16. C Qeap 0 Q Qeap 0 If the capacitor begins with Q 9 0x10 coul C 1 0x10 farad and R 10 Q then Y 2 9 0 V and RC 1 0x10 seconds Notice that resistance times capacitance equals time since RC must be dimensionless This circuit will discharge as shown Qcaplt 9x10 C 6x10 3 C 3x10 C t t RC 0 01 s Note that when t RC EEE so that Q RC Qe 250 Thus when t RC the RC RC en as a capacitor s charge has fallen to approximately 1 3 of its initial value Since the resistor is ohmic we can always find the current moving through it I Te But in this simple circuit the voltage across the resistor is equal to the voltage across the capacitor which in t turn is Q C Thus the magnitude of the current through the resistor is given by Ike t Lre RG 156 Week 7 Lab RC Circuits DC Source Students Absolutely Must Learn e The properties of exponential functions e How to describe the time dependence of charging and discharging capacitors with exponential functions e What differential equations are and how to check their function solutions e Advanced features of oscilloscopes Section 1 examining slow RC circuits with a stopwatch A large capacitance C and large resistance R translate into a slow time constant t RC so that you may easily measure the rate of decay with a stopwatch You are supplied with a 1000 uF electrolytic capacitor Electrolytic capacitors are one way capac
17. For the previous figure predict the order of the magnitude of current through the light bulb from least to greatest and then explain why you think this will be the case Write both your predictions and explanations 3 6 Now set up each of the above circuits and test your predictions What is the actual order of the magnitude of bulb current from least to most If some of your predictions are wrong ask around and figure out why then explain why you were mistaken 30 Section 4 more circuit behavior The following circuit uses two 1 5 V batteries in series to power three identical light bulbs Marbles are shown to represent the unit charge carriers that produce the current in the circuit Thus each marble represents 1 coul For every second of time that passes 9 marbles flow from the top of the battery so we say that Irorat 9 amp The marbles are pushed through the circuit by the battery and must push each other out of the way to proceed through the The marbles must return to the bottom of the batteries to replenish the batteries reservoir rota AMALLVE i z z 3 4 1 Calculate the current of marbles for each of the five delineated parts of the wire Ia Ip Ic Ip Ir 4 2 Explain what is meant when an electrical engineer says that they will lower the total resistance of a circuit by adding a component in parallel 31 In the following simple circuit four locations along
18. Your predictions in SI units amp 4 7 Now set this circuit up and test your predictions Record each of your results and if some of your predictions were wrong explain the mental misconceptions you held Your observations in SI units and any explanations of misconceptions amp 4 8 Why doesn t placing the DMM between points c and d complete the circuit and cause current to flow thus lighting the bulb Hint there may be some current flowing but 33 Section 5 comparing circuit behaviors Below are three light bulb configurations made with identical bulbs Imagine that each light bulb carries 1 Q of resistance regardless of its temperature unrealistic Answer all the following questions without making observations Note drawing energy circuit diagrams like those of the previous section is sometimes helpful A B C 3V 3V 3V 5 1 Calculate the total resistance equivalent resistance for each circuit Your answers in SI units You don t need any fancy equations to do this so long as you remember that to push the electrons through twice as many resistors requires more effort while providing the electrons twice as many paths reduces the effort needed 5 2 Calculate the voltage across each light bulb Your answers in SI units 5 3 If circuit A is known to produce 3 A of current through the battery find the currents through the batteries in circuits B and C Your answers in SI units 3
19. a battery to a circuit a current can be induced in a circuit without any other voltage source present An interesting example of this is when a magnet approaches a solenoid in series with a resistor becomes Since the presence of a induced voltage is effectively like dB Inside the solenoid T gt 0 velocity F VA R Here the magnet s north pole is approaching the solenoid from the left The magnetic field strength is growing inside the inductor coils as the magnet approaches gt 0 This causes current to flow in the coil which creates its own magnetic field Welociy Lenz s Law states that the induced magnetic field must cause the moving magnet to slow down Think of this in terms of conservation of energy we expect the resistor to absorb energy from the current in the solenoid This energy has to come from somewhere it comes from the kinetic energy of the moving magnet which must slow down to turn some of its own kinetic energy into the heating of the resistor Once you figure out which direction the induced magnetic field must be to slow the moving magnet you use the right hand rule to figure out the direction of the current in the solenoid coils 218 velocity It is a little tricky to see but if you follow how your fingers wrap around the coils you find the direction of the current Ask other students or get your TA if you don t see why the current is flowing to the right in the previous picture Be
20. air Of course an electromagnetic wave traveling through the air moves at the speed of light because an electromagnetic wave is light We can turn our sound wave into light to transport it First investigate transporting sound as oscillating magnetic fields in solenoids from one solenoid the transmitter to another solenoid the receiver The two solenoids are not connected in any way so that the oscillating magnetic field inside one solenoid must be made to j Saw 3 os d oscillate within the other solenoid to utilize Faraday s Law of inductance aera a process called mutual inductance Unfortunately this wave is alternating much too slowly to induce a large voltage in the receiving solenoid Remember the equation for mutual inductance GI cit 1 _ gt circuit f induced 1 to 2 where M is a constant that describes how much the solenoids in circuit 2 dt overlap If the current doesn t oscillate rapidly enough then V induced is very small 1n circuit You might say gee I wish this wave oscillated more quickly to cause a bigger induced voltage in the receiving solenoid But then it wouldn t be the same sound pitch that you wanted to hear in the first place Still it sounds like something you might say since you understand that to utilize Faraday s law you need rapidly changing magnetic fields Next examine a wave that oscillates quickly at radio wave frequency or slightly sub radio frequency 259 Sub Radio Freq
21. are at the same voltage height Therefore V se O V As the current travels through the light bulb the voltage decreases from 1 5 V to O V so that Vwa 1 5 V Points d and e are at the same voltage height so there is no voltage change between them If you put the positive lead of the DMM at point b and the negative lead at point d the DMM display would show a voltage of Vi tob 1 5 V 1 1 For the previous circuit if you put the positive lead of the DMM at point e and the negative lead at point c what value would the DMM display Hint what is V Introductory students are often confused by negative DMM readings The negative lead is the starting point and the positive is the final the DMM tells the voltage going from negative lead to positive 22 Now imagine adding another identical light bulb in series with the first as shown in the following picture Charge flowing through this circuit will lose half of its electrical potential energy traversing the first light bulb and the other half of its electrical potential energy traversing the second light bulb a Reulb b Reutb G 4 4 4 Which one may think of using the following picture voltage height 1 50 V 0 75 V 0 V C As the current travels from the voltage source at a through the first bulb to b the voltage drops 0 75 V and from b to c the voltage drops again by 0 75 V A DMM would measure the voltage of either light bu
22. battery a light bulb in the above picture The SI unit that describes how much friction the resistive component has is the ohm or Q where Q is the capital Greek letter omega Circuit diagrams are simple ways to represent actual physical circuits Below three unique pictures are shown to represent a certain battery light bulb circuit the third picture is called a circuit diagram Note that the positive terminal of the battery is represented by a wider line than the negative terminal and the resistive component the bulb is represented by zig zag lines lt lt Reuts 17 A digital multimeter DMM is a device used to measure voltage current and resistance A DMM may measure the voltage of a circuit component by applying its two leads in parallel on either side of the component and setting the DMM to DC voltage Note that most DMMs have three or more terminals for attaching leads even though you only use two at any given time Your TA will help you choose the correct terminals A DMM may also measure the current through a component by being wired in series next to the component and setting the DMM to amps or miliamps mA A DMM can also measure the resistance of a component once it has been disconnected from the circuit 18 Week 1 Lab Elementary Circuits Students Absolutely Must Learn To relate the concept of voltage very closely with electrical potential energy using voltage height
23. be done with some consideration of which components you will measure with your oscilloscope since you only have two channels to measure with The three circuit configuration examples below and the questions that follow are used to illustrate this point A B C 1 1 In circuit A which pairs of components can be separately measured on the oscilloscope with a middle ground technique You are free to choose the location of the oscilloscope ground 241 1 2 In circuit B which pairs of components cannot be separately measured on the oscilloscope with a middle ground technique You are free to choose the location of the oscilloscope ground 1 3 In circuit C which pairs of components can be separately measured on the oscilloscope with a middle ground technique You are free to choose the location of the oscilloscope ground Depending on which two components you wish to measure you often have to rearrange the actual components 1 4 Sketch a circuit configuration along with the proper placement of the three oscilloscope leads red 1 red 2 and ground in order to be able to separately measure the time dependence of the solenoid and resistor simultaneously 1 5 Sketch a circuit configuration along with the proper placement of the three oscilloscope leads red 1 red 2 and ground in order to be able to separately measure the time dependence of the source and resistor simultaneously 242 Section 2 calculus expl
24. before setting the source voltage on the function generator Why not just hook the function generator directly to the oscilloscope and set its properties first You must keep this driving frequency the same as you are answering different questions until told otherwise because the properties of the circuit change with driving frequency 4 2 It is often the case that components in a circuit become disconnected at bad solder joints even though you cannot see this with the unaided eye What can you do experimentally to make sure that your RLC circuit is still conducting current through all its connections without disconnecting the circuit Hint what information can the ohmic component give you 43 Quickly measure the voltage amplitudes of each component separately using a single channel of your oscilloscope Double check that your source voltage amplitude is 5 V first 247 a 4 4 Now use two channel observations to simultaneously measure the resistor voltage and the inductor voltage to determine their respective phase shift Don t forget that one channel should be inverted when using a middle ground configuration a 45 Now use two channel observations to simultaneously measure the resistor voltage and the capacitor voltage to determine their respective phase shift da 4 6 Now use two channel observations to simultaneously measure the inductor voltage and the capacitor voltage to determine their respective phase shift
25. begins charging the capacitor until the capacitor is fully charged The charging up equation that describes the time dependence of the charge on the capacitor is t Qcap t Omnax l e The final charge on the capacitor Qmax 1s determined by the internal structure of the capacitor i e its capacitance Qx C V source V soured C Qcap 0 0 Qeap 0 Quax As an example imagine V axe 9 V and C 1 0x10 farad with the initial charge Qca 0 0 then the final charge Q on the capacitor can be found using Q C V 9 0x10 coul A sketch of how the capacitor will charge up is given by Qeap t 9x10 C where the time to charge is larger when there is more resistance Of course you could charge the capacitor without the resistor and then it will charge very quickly since there will be only a minute resistance in the circuit The voltage across the capacitor rises similarly Vcap t 9 V 155 The discharging of the capacitor in an RC circuit occurs when the capacitor begins with some initial charge Q and is wired in series with a resistor The capacitor begins discharging through the resistor until no charge remains on the capacitor plates The discharging equation that describes the time t dependence of the charge on the capacitor is Q t Ove FC It helps to think of an RC circuit with a charged capacitor that has a switch that is about to be closed so that the capacitor can discharge R
26. can successfully measure the current through a resistor using an ammeter Once you are successful have them sign below Note if someone is stuck please give them advice Yes I have seen this successfully use make an ammeter measurement They have not forgotten the major difference between measuring voltage and measuring current with a DMM Student Signature 128 Section 5 open ended At each lab station is a long board with Nichrome wire nickel chromium of various thickness Nichrome wire has a moderately high resistance and is often used in simple heating elements Imagine you work for a company that produces resistive wire You need to determine some basic technical specifications for the resistive wire for use in your sales catalog Reporting the total resistance is useless since this depends on how thick and long a particular wire is Instead you should report resistivity p with units of 2m which is a microscopic description of resistance This will allow an engineer designing a coffee maker the ability to calculate the size and shape of the Nichrome heating element that they need to order from your company The total resistance of a wire increases linearly with the length of the wire Roc L However the total resistance of a wire is inversely proportional to the cross sectional area of a wire R a This is because increasing the thickness of the wire gives the electrons more surface to flow through so that they encounter les
27. capacitor voltages equal 2 3 Set up a 3 volts 400 Hz sinusoidally driven RC circuit with R 10 000 Q and C 1x10 farads Set up a middle ground to view the voltage across both the resistor and the capacitor simultaneously making sure to invert the correct channel Adjust the driving frequency until the resistor and capacitor voltages are equal Then use your formula from 2 2 to find your experimentally determined value for capacitor s capacitance Remember that the function generator reads the linear frequency 180 The multiple measurements method for finding an unknown capacitance is more involved but more accurate as it involves multiple measurements The voltage amplitudes of the sinusoidally driven RC are a resistor source amplitude Z amplitude and X Se Vapa z source amplitude Z amplitude Dividing these two equations gives X c Voins amplitude capacitor Z xX amplitude _ C Vasto R Vaie R amplitude amplitude Z Therefore capacitor _ amplitude resistor amplitude In order to experimentally determine C for your capacitor simply combine the last equation with the definition v7 and rearrange V 1 resistor amplitude Soc NE i R Vona amplitude Dative 181 V 1 resistor amplitude S iy R Va amplitude looks like a weird arrangement for this equation but if you think of y mx then you see that if 1 resistor amplitude you graph VSH you should obtain
28. careful if the solenoid had been wound differently the current direction would have been reversed more practice examples are next to check your understanding a 2 1 Draw the correct current direction in the resistor a 8 Velocity Direction of I 2 2 Draw the charged plates on the capacitor Q and Q ea a V F velocity er 219 2 3 Draw the correct current direction in the resistor V velocity Direction of I 2 4 Draw the correct current direction in the resistor eae V velocity Direction of I 2 5 Draw the correct current direction in the resistor LL V velocity co Direction of I d 2 6 Explain why a strong magnet dropped down a copper pipe would fall much more slowly than you would naively expect 220 Section 3 induced solenoid voltage by external magnetic fields Now you will experimentally observe how a changing magnetic field induces a voltage in an unpowered solenoid Check your bar magnet with your compass to see that it is labeled correctly Remember that the compass s needle labeled north should point to south magnetic poles like the north geographic pole of the earth Hook up your unpowered solenoid directly to the oscilloscope by itself so you can measure the electric potential difference between both ends Don t bother placing a resistor in series Instead you will just examine the direction of the back EMF by checking the si
29. collaborating with a lab partner will make you both guilty of plagiarism Please label your lab report sections Title 0 points A catchy title worth zero points so make it unique and fun Mini Report 10 points 4 6 paragraphs 2 double spaced pages Choose one of the following sections about which to write your mini report Week 1 Section 4 or Week 2 Section 3 Write a mini report for one particular section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable Please label your mini report sections o Abstract Write 2 3 sentences about the goals of this section Describe the concepts you were investigating and how the experimentation you performed allowed you to investigate these concepts Write 2 3 sentences summarizing the procedure Write 2 3 sentences summarizing the results and what the results mean with regard to the concepts you were investigating It is best to write the abstract last o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Provide a description of the data you obtained such as data tables Restate any measured values calculated slopes of lines of best f
30. competitive world To this end these students should e Understand the role of science in our society O O There is electronic circuitry all around us in the walls of our buildings in the gadgets we carry in our transportation amp communication in life saving medical equipment and even within our own bodies How charges flow through metals freely or become deposited on objects is the basis for the majority of our technology An elementary understanding of charge separation is essential for modern chemistry and biology and many other fields How charged conductors produce electric fields or equivalently how they produce electric potential landscapes helps students understand how the electric field actually permeates the space we live in How charged plates can accelerate and steer moving charges a concept widely used in older technologies How Ohm s law allows one to quickly unravel the nature of common circuitry that live in our gadgets and machines How the quantum mechanics of semiconductors has given us personal electronics and high speed computing How a capacitor can store energy for later use in an electric field How a sinusoidal alternating current works to power circuit components and causes sinusoidal responses in the components of the circuit How motors function how they are designed and how to measure their properties How a solenoid affects an AC circuit allowing electrical energy to be stored in a magnetic
31. computation table graph etc Please read all warnings indicated by exclamation marks TYPOS should be a nuisance only once Please record any typos or poorly worded sentences and send them in an email so they can be fixed forever Thank you bunches if you do this Matt Leone MattLeone gmail com 13 Lab Report General Guidelines USE THE FOLLOWING SECTION TITLES AND LABEL THEM IN YOUR REPORT e Title 0 points A catchy title worth zero points so make it unique and fun e Mini Report 10 points 3 5 paragraphs 1 2 double spaced pages Check each unit s grading guidelines to find which section to write about Write a mini report for one particular section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Provide a description of the data you obtained such as data tables Restate any measured values calculated slopes of lines of best fit etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of
32. estimate electric fields from electric potential measurements How positive charges lower their electrical potential energy by moving to lower voltages e How negative charges lower their electrical potential energy by moving to higher voltages Section 1 sketching electric fields V x y dotted lines show constant electric potential y solid lines show electric field 71 If you examine a two dimensional electric potential landscape first picture from above you will see an aerial view second picture that obscures the third dimension height or voltage X Nevertheless if you know that the middle is supposed to have a higher electric potential voltage then you can imagine that each sequentially outward dotted ring represents a lower step down the voltage mountain The solid lines show the direction of electric field but without arrowheads so that you must figure out the direction yourself That is not hard because electric fields always point in the direction of lower electric potential down the voltage hill Also note that electric field lines are always perpendicular to equipotential lines where they intersect What is not obvious is where the electric field and thus forces on test charges would be the strongest A good rule of thumb is that the strength of the electric field is largest where the density of electric field lines is greatest This would imply that the electric field magnitude is great
33. field The resonance behavior of an RLC circuit that allows devices to be tuned to specific frequencies The mutual inductance of transformers that carry energy across the world e Have a firm grasp of the theories that form the basis of electricity and magnetism O O Use Gauss s Law to understand electric potential in circuits as conservation of energy Use Gauss s Law to understand how charges are transported in physical systems Relating a stationary vector field to its corresponding scalar potential field Relating voltage differences to electric fields forces and accelerations of charged particles Using Ohm s Law to predict total circuit properties and individual component properties Experimentally testing Ohm s law to solidify conceptual understanding and to be exposed to the interplay of electricity amp magnetism and quantum mechanics 294 OoO00 0 Use differential equations and their solutions to model and understand circuit behavior Use differential equations and their solutions to model and understand circuit behavior Use concepts of magnetism to understand motors Use of Faraday s Law Ampere s Law and Lenz s Law Use trigonometric functions to model a complex circuit Use of Faraday s law e Be able to apply the principles of physics to solve real world problems O O oOoo0o0o0o O Design an experiment to find how resistance adds in series vs parallel Design an experiment to
34. geographic south pole This causes the local magnetic field to point toward the north geographic pole The compass aligns with this magnetic field and thus points toward the north geographic pole If your compass has been flipped fix it with a strong magnet or tell your TA so they can fix it Examine the direction of the windings of your solenoid You can tell which way the current circulates by how the wire enters the solenoid Then you can use the right handed screw rule to determine the direction of the magnetic field inside the solenoid which side is north and which is south 1 1 Even though the solenoid is made of wire wound into a coil it is so long that it actually has some sizeable resistance Use a DMM to measure the resistance of the solenoid so this is a real solenoid not an ideal solenoid 214 Gq 1 2 Apply constant current using the constant voltage supply a few volts should be good to your solenoid Find the current in the solenoid using Ohm s law 1 3 Use the right handed screw rule to predict the positive direction north pole of the magnetic field produced within the solenoid and the magnetic field surrounding the solenoid in general Test your prediction using the compass and sketch the magnetic field surrounding the solenoid below Be sure to draw your solenoid in such a way as to show the reader how the current flows through the solenoid Next you will experimentally observe the process of self inducta
35. group as you show them your solution Yes I have seen this student determine the north pole of an unlabeled magnet and their verbal explanation of the process is correct They are well prepared for owning a refrigerator Student Signature 61 Section 8 open ended If one conducting sphere is charged to a constant positive electric potential voltage and another neutral ungrounded conducting sphere is brought near to it then the charge on the neutral sphere will separate On the second sphere a certain amount of negative charge will be attracted to the sphere held at the constant positive potential and an equal amount will be repelled It is extremely difficult to calculate the arrangement of charge on the neutral sphere Sometimes a mathematical theory is of little use in a complex system and you just have to experiment to get answers Figure out a way to determine the arrangement of the separated charged on the ungrounded neutral sphere constant voltage charge separation evenly clustered clustered arranged positive negative You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the ev
36. is actually applied to the resistor So if your 12 V car battery dies unexpectedly you can t substitute your car battery with eight 1 5 V batteries in series even though they provide 12 V in series because their internal resistance will not allow them to deliver such a large current to move the engine s heavy parts 113 When two resistors are put into series it is often useful to treat them as a single composite resistor and find the Daa resistance of this single resistor The a for this is equivalent ny Eo When two resistors are put into parallel the equivalent resistance is given by RR Reguivalent R R i a _ Solving compound circuits is a very important skill Here is an example where you must solve for the current through the battery Ipattery the total resistance Rota as well as the voltages across and currents through each of the components R equiv alent Ro 4 Q R 12 Lar Ve The strategy is to pretend taat the two series resistors are equivalent to a sone resistor E First collapse the two series components R R R 5 Q Since this is actually the total resistance of the circuit assuming an ideal battery which has zero internal resistance you may V use Ohm s law to find the total current Ipaey 2 A Since charge cannot pile up A anywhere in a circuit this is also the same current as in R and Ry 7 Z 2 A You can now find the voltage across Ry V
37. it spreads out uniformly along the conductor surface Excess positive charge on the Excess negative charge on surface of a spherical conductor the surface of a cubic conductor Excess charges always repel each other to the surface If a neutral conductor comes into the presence of an electric field say from another charged object the charges of the conductor will redistribute so that there is macroscopic charge separation across the entire conductor The charges that redistribute will lie on the conductor surface while the inside of the conductor will be neutral next picture Negatively charged attracts positive charge and repels negative charges on the surface of a conductor Some dielectric insulators are made of polar molecules that can rotate at their position in the material when placed in the presence of an electric field This leads to microscopic charge separation Positively charged object creates an electric field that rotates polar molecules in insulator insulator dielectric material 44 Week 2 Lab Magnetism and Electrostatics Students Absolutely Must Learn e How different materials with excess charge behave conductors vs insulators e How different materials with net neutral charge behave conductors vs insulators containing polar molecules How to draw magnetic field lines so that they don t intersect How to measure the direction of a magnetic field using a compass How like cha
38. left might be at 7 volts while all points on the dotted line on the right might be at 3 volts as 10 volts decreases to 0 volts A charge would not raise or lower its potential energy if it moved along a given dotted line because there would be no change in its potential energy This means that there would be no force on the charge in the direction parallel to the dotted line However the charge would definitely change its electric potential and thus its potential energy if it moved off a dotted line This means it feels an electric force pushing it away from and perpendicular to the dotted equipotential lines The solid lines represent electric field lines They also show the direction of electric force that a charge would feel since F gE Note they are perpendicular to the equipotential lines where they intersect 80 Do not write on the conductive paper 2 1 Electrify the dipole conductive paper two dots of silver paint with AV 10 volts Use a DMM to measure the locations of at least seven dashed equipotential lines and sketch them on special graph paper which matches the conductive paper Be sure to use the physical symmetry of the system to reduce your work by 75 Make a copy for both lab partners answer on separate graph paper G 2 2 Sketch at least 8 electric field lines using solid lines on top of the dashed equipotential lines you just graphed Each partner should use their own copy for this answer on sep
39. of the capacitor 3s At very high driving frequency Xc becomes very small so that the amplitude of the capacitor voltage becomes very small 174 Week 8 Lab RC Circuit AC Source Students Absolutely Must Learn e The behavior of a sinusoidally driven system including phase shifts e How to use the solutions to the RC circuit driven by a sinusoidal voltage source and what they mean e Advanced features of oscilloscopes Section 1 examining the components Set up the sinusoidally driven RC circuit with R 10 000 Q and C 1x10 F Set your function generator to create a sine wave with a voltage amplitude of a nice round number like 3 V You may want to adjust your frequency later but start at about 400 Hz Set up a middle ground to view the voltages across the resistor and the capacitor simultaneously making sure to invert one of the channels a necessary step when using a middle ground Check your setup with other students in the lab i ground red 2 175 1 1 Make a sketch of the oscillating resistor and capacitor voltages on the oscilloscope screen below Label the signals V and V on your sketch EITT kdd bht be tet db le of of Measure the amplitudes of each signal by measuring the peak to peak voltage of each signal 1 3 Use the labeled values to calculate the impedance of your circuit for this driving frequency Remember Za JR X 176 Gq 1 4 Use your previous answer to c
40. order to measure the frequencies of these signals 230 Section 7 authentic assessment 7 1 Transformers in power lines use metal contained inside their solenoid coils to help increase the mutual inductance Investigate what kinds of metals and shapes thereof help increase the mutual inductance in a transformer Use two large solenoids for this the function generator and your oscilloscope Various test metal pieces of different geometrical shapes are available in the lab brass stainless steel galvanized steel and aluminum Take only one or two at a time and put them back immediately when you are done i e share Sinusoidal electromagnetic waves light transmitted from one solenoid to another can be blocked by highly conducting objects This is for the same reason that good conductors metals are shiny they reflect light so it cannot pass Investigate what kinds of metals are good or poor conductors using this effect Use two large solenoids with a gap between them for this the function generator and your oscilloscope Metallic sheets are in one part of the room Take only one or two at a time and put them back immediately when you are done Determine what shapes and metals placed inside solenoids maximize mutual inductance Determine if stainless steel is a good or bad conductor If you are uncomfortable having another student check your work please ask your TA Yes I have seen this student explore the effects of differ
41. page intentionally left blank 238 Week 11 Pre Lab RLC Circuit AC Source R ohm V wines C fa rad L henry Just as the RC circuit with a sinusoidal source had sinusoidal voltages containing phase shifts so too does the RLC circuit with sinusoidal source You will need to understand the following underived time dependent formulae for RLC component voltages R V t source Vione SiN givel Perit T z V esistor a Voire sin 4 amplitude Z amplitude X mT X m C 4 a L V C eapacitor z Voue sin Orive Een V inductor Sy V nauer s n Orive te Z amplitude 2 Z amplitude 2 Vit This graph shows that the resistor voltage has no phase shift as its graph goes through the origin The capacitor voltage is phase shifted by 7 2 from the resistor voltage while the inductor voltage is phase shifted by 2 2 from the resistor voltage in the opposite direction from the capacitor voltage Finally the source voltage is the negative sum of the other components V Vg t V t V t due to conservation of energy The phase shift of the source is more complicated depending on the parameters of the circuit inductance L and capacitance C This formula is provided later The voltage across each component oscillates at the same frequency as the driving frequency of the source arivee The properties of inductor and capacitor are frequency dependent which makes the circuit respond differently to different
42. ranges of hearing loss Do these frequencies correspond to the kinds of music you listen to too loudly 265 Speakers create sound waves in the air by mechanically oscillating a solid object that strikes air molecules For a given constant output voltage cheaper speakers will not respond to all frequencies with the same intensity Really cheap speakers may even have a few resonant frequencies where they mechanically rattle 1 4 Does your simple speaker have any resonant frequencies probably Find and record the frequencies that make the speaker the loudest There may be more than one resonant frequency for your speaker since it is a complex mechanical system only very simple systems have one resonant frequency 266 Section 2 the modulated wave The radio frequency RF modulator takes an input envelope wave and modulates it with a rapidly oscillating carrier wave If you do not input any envelope wave only the pure carrier wave will be output Hook your RF modulator directly to the oscilloscope without the input envelope wave from the function generator Use a carrier RF wave of 500 000 Hz 2 1 Use the oscilloscope to determine the period of the 500 kHz RF carrier wave 3 1 Does this make sense since T z z Now input an audio frequency signal of 1 000 Hz from your function generator into your RF modulator shown below Use a carrier radio frequency wave of 500 000 Hz to create a modulated output wave of 1 0
43. size of the vectors representing the strength of the field at that point in space Note that the strength of the electric field decreases as you move away from the charge The electric field points away from positive charges and toward negative 69 A positively charged object creates a mountain of voltage that positive charges will be forced to roll downward and negative charges will attracted upward V x y dotted lines show constant electric potential y solid lines show electric field arrow shows force on test charge Similarly a negatively charged object creates a valley of voltage that a positive charge will be forced to roll downward and negative charges will be repelled upward Thus positive charges move from areas of high voltage to low voltage while negative charges move from low voltage to high voltage 70 Week 3 Lab Electric Field Mapping Students Absolutely Must Learn e The relationship between potential energy and force visually and mathematically e The relationship between electric potential and electric field visually and mathematically How to calculate partial derivatives The difference between vector fields and scalar fields How to visualize a vector field with arrow graphs How to visualize a vector field with field lines How electric fields cause electric forces on charged particles How to draw equipotential lines and electric field lines How to
44. the leads are not in the plane of the armature box the coil will receive current when the coil is 90 rotated away from the magnet not good tape insulation baredin amp out current wires 197 9 Wherever good electrical contact is desired the colored insulation must be burned and sanded off that part of the wire so that clean bright copper can be seen To bare the wire you must burn off the insulation along the part of the wire you wish to bare Burn the insulation thoroughly it will appear blackened Then use sandpaper to clean the charred wire insulation and leave a nice bright bared length of copper wire Do not sand the finish off the EWR tops _ 198 10 Place the axle into the motor enclosure box You may eventually need to add tape to other parts of the axle in order to keep the axle from shifting around too much in the motor enclosure box during operation WPL 199 11 Finally you must insert two bared wires to act as brushes for your motor These power lines are the most difficult part of the motor to get correct The axle leads must make precise contact with these power lines as the motor turns Motors that work best tend to have very straight brushes that lie tightly against the axle Note that the location of the power lines the punched holes in the sides of the motor enclosure box may need to be changed depending on the final position of your axle leads These wires not connected
45. the next page 88 6 1 hypothesizing planning 6 2 observations data 6 3 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 89 Week 3 Take Home Quiz Score ___ 5 THQ 1 1 point Above is a sketch of some equipotential lines dashed and some electric field lines solid The points where these intersect are labeled If an electron is released from rest at point e which intersection will it reach some time later d THQ 2 4 points Now calculate the velocity of the electron when it reaches that point Hint use energy conservation with AK AU q4AV e AV where K sm Note m 9 1x10 kg 90 Week 4 Pre Lab Cathode Ray Tube Read the following short pre lab upon which you will take a quiz at the beginning of lab A cathode ray tube works by boiling electrons off a cathode heating element and accelerating them with a large voltage difference Then the high speed electrons pass between a pair of charged deflection plates so that the path of the electron is altered There are two pairs of deflection plates for vertical deflection and then horizontal deflection see below figure Finally the electrons strike a screen coated with a fluorescent material and you see a scintillation take place i e you see light emitted All of this is done in a vacuum so that
46. to tell you on its screen the wave s amplitude Remember that the peak to peak voltage value is twice the amplitude Record your measurement here 161 2 5 Adjust the amplitude of the wave on the function generator until you see that the wave spends more of its time being negative than positive using the DC offset feature on the function generator This will change your average value for the voltage Use a two cursor measurement of time and get the oscilloscope to tell you on its screen how much time the sine wave spends being positive Then do the same thing to find out how much time the wave spends being negative Record your measurement here 2 6 Now use a two cursor measurement in voltage and get the oscilloscope to tell you on its screen the voltage drop of the wave from its maximum positive value to zero Record your measurement here G 2 7 Change your sine wave to a triangle wave of 500 000 Hz and use the DC offset so that the minimum of the triangle wave is zero volts Examine a part of the triangle wave that is decreasing Use a two cursor measurement to find how long it takes for the triangle wave to decrease from its highest value to one half of that value Record your measurement here Initially many students become confused about the cause and effect relationship between function generator and the oscilloscope The function generator is creating the oscillating voltage while the oscilloscope is merely observi
47. xc gt Xc gt Xi Oirivel gt Z Orive tan Z ze Peource R The above equations show that the capacitor voltage lags behind the resistor voltage by 90 while the inductor voltage leads the resistor voltage by 90 Note that in the above equations we take the resistor as the reference point because it is Ohmic and thus also describes the circuit current hence we must use a phase shift to describe the source voltage time 283 1 1 If R 20 O L 15 H C 10 F Vsource amplitude 10 V and farive 50 Hz find the voltage amplitudes of the inductor and capacitor in SI units 1 2 Use the following values to calculate each of the RLC circuit parameters below N cures amplitude 5 V farive 700 Hz R 1000 Q C 10 uF L 100 mH Write the numerical value with correct SI unit for each listed parameter Xc XL Z Vp anplitude Vo amplitude V amp litude Osource L mplitude 284 Section 2 practice calculating phasors Use the following values in the following questions V source amplitude 5 VY farive 700 Hz R 1000 Q C 10 uF L 100 mH 2 1 Calculate the time dependent phasors and write them in complex exponential notation for each of the four voltages of the RLC circuit 2 2 Compute the real and imaginary components of each of the four voltage phasors at t 10 ms and make sure both the real and the imaginary components sum to zero 285
48. 00 Hz envelope waves surrounding a 500 kHz high frequency wave 123 Calculate the period of the envelope wave using T 7 Examine the output of this signal on your oscilloscope using two different time ranges so that you can see the audio frequency signal and then separately the radio frequency signal To do this choose a seconds per division setting for the time axis that is appropriate for the time scale of the wave you wish to examine i e use the wave s period to select the seconds per division You may need to press the run stop button to view the wave packets if they appear smeared out on the oscilloscope 267 2 3 Sketch the appearance of the modulated wave at both the audio frequency scale and then the radio frequency scale and record the time scales used to observe the waves Notice that the RF generator does not necessarily produce a clean RF output as was discussed earlier in this handout Also be sure you can hear the envelope waves of the modulated signal in your speaker Radio Frequency AEN ee ee PT ey Td a oa a ia PEP re rt oe a A E Pe a Ee eal ae ed E aa E T CP NEEL EPP ttt Ey Audio Frequency ECLELLCLELCLES opal let oh A le fel ol le de Lo ae et Tt ttt ty et tT tT a hd Ed ay dl ep ol to eh A de bet ol fe be al TT ttt ty ett Tt TT Tt ttt ty Pe tT tT a at fd ae ol Heap al le Lesh te fe at ol Ie de a Le ee E Tt ttt ty ee T SF Rae eae Ree Mot bf lel by 268 S
49. 16 Week 1 Pre Lab Elementary Circuits Read the following short pre lab upon which you will take a quiz at the beginning of lab In a circuit a battery pushes electrons along wires and through resistive components that absorb electrical potential energy Voltage is a quantity that measures how much electrical potential energy each unit of charge is given as it moves through the circuit The SI unit of voltage is the volt which is written inside brackets in this manual volts or V The battery is like a pump moving water through pipes handle spinning paddle wheel AYALLVE The current describes the amount of charge moving through the wires and components of the circuit in coulombs per second which defines the SI unit ampere also written as amp or just A Current is analogous to how much water is moving through a plumbing system If a circuit is a single loop then the current must be the same at any point in the circuit to prevent the accumulation of charge in part of the circuit Of course if a circuit branches into two wires then the current will be divided between the two paths These concepts explain why current cannot flow unless the circuit forms a loop so that electrons can get back to where they began The battery is expending energy and due to conservation of energy this energy must be absorbed somewhere The resistor is the circuit component that has electrical friction which removes energy from the
50. 4 5 4 Use your previous answer to find the current through each single light bulb in the three circuits Your answers in SI units The power supplied by the battery is equal to the current emanating from the battery times the voltage of the battery Puppies Z Viae The power dissipated by a resistive circuit component is found by multiplying the voltage drop across the component and the current flowing through the component P I Viomponent Lhe SI unit of power is watts or W If you have ever imbibed the soft drink Mr Pibb then you can remember the power formula by thinking of Mr PIV battery i issipated component i 5 5 Use your previous answers to find the power dissipated as heat and light by each light bulb in the three circuits Your answers in SI units d 5 6 Use your previous answer to compare the brightness of each light bulb in the three circuits Your answers amp 5 7 Finally use your previous answers to calculate the total power output by the batteries in each circuit Your answers in SI units 35 5 8 An electric field always points from high voltages toward low voltages Electrons are negatively charged and so flow from low to high voltages In the following circuit diagram draw the direction of the electric filed inside the resistor label it and then draw the direction the electron moves through the resistor label it Electrons are negatively charged so flow in the opposite directi
51. 5 195 5 At this point examine what a finished motor should look like Two non touching bared 1 Y wires power lines that F bring current into and out of the motor Unbared wire looped to ae doo u interact with magnet _ gD a Bared wire resting on tape to connect to power lines 6 Tape your magnet into your box and add tape to the axle rod The tape in the axle rod serves the dual purpose of insulating wires from the metal rod as well as keeping the rod positioned correctly in the motor enclosure box so the armature box stays above the magnet Pay careful attention to locate the insulating tape on the correct location of the rod by repeatedly placing the rod into the motor enclosure box and spinning it with your fingers 1 j Tape t insulate bared wire from conductive axle ae i 196 7 Add some tape as neatly as possible to affix the axle rod to the armature box or before closing the armature box tape it to the axle tape axle armature box 8 Take 2 meters of wire and wrap the armature box Both ends of the wire should protrude from the winding box along the axle insulation You will eventually bare the two ends and tape them down to the axle but leave them free until you learn how to bare the wires Notice that the two ends of the winding protrude to the left of the armature box and are taped down flat against the axle and in the place of the armature box If
52. Course Information Page Student Name Student Email Lab Room Lab Section Weekday Time Office Office Hours Course Lecturer _ i ns Email Office Office Hours Lab Director Dr Roger Haar Email haar physics arizona edu Office PAS 324 Free tutoring Consultation Room PAS 372 Mon Fri Administrative help Academic Support Office PAS 260 This page intentionally left blank Introductory Electricity and Magnetism Laboratory Manual 2 Edition By R Matt Leone M S M Ed M S Dr Roger Haar Ph D June 2011 Based in part on previous University of Arizona Physics Department Laboratory Manuals Copyright 2011 All rights reserved Arizona Board of Regents Contents Course Information Page Introductory Electricity and Magnetism Laboratory Manual 2 Edition Unit Summaries Tentative Lab Schedule Physics 241 Lab Policies Strategies for Success How to Use this Manual Lab Report General Guidelines Rules for Excused Absences Unit 1 Lab Report Instructions Week 1 Pre Lab Elementary Circuits Week 1 Lab Section 1 Section 2 Section 3 Section 4 Section 6 Section 7 Elementary Circuits thinking about voltage circuit basics circuit behavior more circuit behavior authentic assessment open ended Week 1 Take Home Quiz Week 2 Pre Lab Magnetism and Electrostatics Week 2 Lab Sect
53. Home Quiz Unit 6 Lab Report Instructions Week 11 Pre Lab RLC Circuit AC Source Week 11 Lab RLC Circuit AC Source Section 1 measuring with two oscilloscope channels Section 2 calculus explains 1 2 phase shifts Section 3 extra lab techniques Section 4 specific oscilloscope measurements Section 5 authentic assessment Section 6 open ended Week 11 Take Home Quiz Week 12 Pre Lab RLC Radios Week 12 Lab RLC Radios Section 1 introducing the equipment Section 2 the modulated wave Section 3 mutual inductance radio Section 4 authentic assessment real radio wave reception Section 5 open ended Week 12 Fake HomeQuiz Repeated Rules for Excused Absences Makeup Lab Report Instructions Makeup Pre Lab RLC Circuit using Phasors Pre Lab Practice Questions Section 1 review sinusoidally driven RLC circuits Section 2 practice calculating phasors Section 3 measuring the phasors Section 4 authentic assessment Section 5 open ended creative design Assessment Learning Outcomes Other 218 221 223 225 230 231 232 235 237 239 241 241 243 245 247 253 254 257 259 261 261 267 269 273 274 276 277 278 279 281 283 285 287 288 289 294 298 Unit Summaries Unit 1 e Elementary Circuits e Magnetism and Electrostatics This unit emphasizes the concept of the electrostatic potential voltage and introduces the concept of vector fields Students develop the practical skills of wiring circuits and using a DMM
54. RZ 2 V and Rz V R 8 V Due to the conservation of energy you expect the voltages across the components to add to the total supplied by the battery and indeed 2 8 10 114 Week 5 Lab Vulture Iguana Rabbit Students Absolutely Must Learn How resistance R is defined whether or not a component is ohmic How R V and I are related in ohmic devices How to find equivalent resistances in series and parallel How to find equivalent resistances of complex compound circuits How to use ohms law to find voltages and currents for all parts of a circuit How to make an ammeter measurement Section 1 experimentally determining resistance 1 1 Make a sketch of the small board of resistors provided to you and use your DMM to measure the resistance of each do this quickly please Label the values on your sketch The picture below is provided to remind you that to measure current you must divert the charges flowing in the circuit through the DMM so that it may count them as pass through mA 115 Never apply such a large voltage that the resistor becomes very hot dangerous and non ohmic Gq 1 2 Experimentally verify that the 100 Q resistor on your resistor board is ohmic at room temperature Do this by gathering voltage current data and making the appropriate graph Your graph of your data should quite nicely show the linear behavior of your ohmic resistor The correct choice of V vs I or I vs V s
55. a or formulae for the total resistance of two resistors combined in parallel A Riga XR B Row R Ry RxR C Rota A i A 1 2 D Rot Vy R 55 R 1 E Rota 2 R R 1 F Rotal 1 1 ee ee Ri R G Roa R tR R xR R R H Rota e You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the next page 38 7 1 hypothesizing planning 7 2 observations data 7 3 calculations conclusion I the physics 241 laboratory TA have examined this student s worksheet pages and found them to be thoroughly completed TA signature 39 This page intentionally left blank 40 Week 1 Take Home Quiz Score 5 THQ 1 2 points 6 0V b a What are the voltages at points a and b
56. a linear graph with a slope equal to C R capacitor amplitude 2 4 Find C by collecting data for multiple driving frequencies making a graph on separate graph paper and finding the slope 182 Section 3 authentic assessment 3 1 Quickly set up a working circuit that simultaneously uses a random capacitor and a 1000 Q resistor in series powered by a sinusoidal source voltage on your function generator Then make the necessary measurements to determine the capacitance of the capacitor Be sure your experimentally determined measurements give the correct capacitance Show your results to a student in a different group If you are uncomfortable having another student check your work please ask your TA Yes I have seen this student find an unknown capacitance the easy way Student Signature _ re 183 Section 4 open ended Make a capacitor from the square cardboard pieces covered in conductive aluminum foil Sandwich a non foil square of cardboard between the foiled boards and be sure your makeshift capacitor is not shorted out by accident Measure the capacitance of your homemade capacitor The equation for the capacitance of two parallel plates is given by C eA Use this equation to report the dielectric constant x of the sandwiched cardboard between the plates with correct 2 units Note 8 85x10 Design an experiment to determine the capacitance of your 7 cardboard capacitor and the dielectric con
57. a useful formula relating Rpmm to other variables and then measuring the other variables experimentally Theoretically examine the circuit with R placed in series with the DMM You won t be asked to set up the circuit and make measurements until a later problem 3 1 Predict the total resistance of this circuit from the two component resistances 126 3 2 Calculate the total current I in the circuit in terms of V R and Rpmm 3 3 Since the total current is also the current through Rpmm you may also calculate I in terms of Romm and Vpmm amp 3 4 Equate I in your previous two answers in order to find an equation relating V Ri Romm and Vpmm 3 5 Rearrange your previous answer in order to obtain Rom oo R DMM 3 6 With the aid of your derived formula given in 3 5 use your DMM and the 10 MQ resistor to find the internal resistance of your DMM 10 kQ for the internal resistance of the analog voltmeter if one is provided 127 Section 4 authentic assessment Set up a working circuit that simultaneously uses three resistors not all in series and measure the current through each resistor separately using an ammeter Be sure not to apply too large of a voltage Sketch your circuit and label the resistances and measured currents of each resistor If you are uncomfortable having another student check your work please ask your TA 4 1 Show a student in a different group that you
58. ach consecutive halving of its value occurs in the same amount of time Thus the half life is an important feature in exponentially decaying systems because no matter when you begin measuring you know that each half life of time that passes the value will have decreased by half 3 13 Using this knowledge predict how long it should take for your capacitor to discharge to 1 128 of its initial value which is approximately 1 of its initial value 166 3 14 A more accurate estimate of C can be made by taking many measurements similar to that done in 1 3 to 1 7 Use the cursors to collect voltage vs time data for your decaying capacitor Then linearize your data graph it on regular graph paper and compute to the capacitance C from the slope Be sure your value is close to the labeled value Record your data below linearize your data record below make your linearized graph on separate graph paper find the slope and calculate C below 167 Section 4 authentic assessment Quickly set up a working circuit that simultaneously uses a capacitor and resistor in series powered by a function generator Use the concept of a half life and a single measurement to determine the capacitance of the capacitor Note using thar 0 69 RC is much quicker than finding the slope of a linearized graph with several data points though much less accurate Sketch your circuit and label the resistance of the resistor If you are uncomfortable havin
59. ains 1 2 phase shifts The explanation of the 90 phase shifts of the inductor and capacitor voltages from the resistor voltage can be explained using calculus Conservation of energy the sinusoidally driven RLC circuit gives t V O V O4 V t 0 Substituting Ohm s Law V t J t R the definition of inductance V t L Ve Ses d and the definition of capacitance V t i gives ZU QE Vo TF L R I t 0 o4 resistor term inductor erm capacitor term First notice that the time dependence of the inductor is related to the resistor by a time derivative dI t Q t C Voa dN 0 source R I t The inductor wltage is proportioral to the time derivativeof theresistor voltage All time dependent quantities of the circuit are oscillating sinusoidally including Q t and I t V sin ive the resistor amplitude Since the resistor voltage is described by a sine function V t resistor current is as well t Z a sin Since dl t i a ae ea oa aon COS O givet drive so the inductor voltage must be described by a cosine function But the cosine function is shifted from the sine function by 7 2 mT L Oarive Liy COS Oarivet Sin Dative Taig iy t z Thus calculus has explained the 90 phase shift of the inductor voltage relative to the resistor voltage Aen Next remember the definition of current t to find that Cet ak doco 2 dt dt C
60. al replace this page with the Physics 241 Lab Policies as three single sided pages Otherwise students should receive the Physics 241 Lab Policies as a handout or be able to view them online 10 This page intentionally left blank 11 This page intentionally left blank 12 Strategies for Success Take the lab activities seriously complete them conscientiously discuss ideas fully with your lab partner check answers with neighboring groups discuss misconceptions with your teaching assistant TA etc After you have tried to figure some concept out and realize that you are stuck ask for help from students around you the TA the lecturer etc Form study groups and meet as often as possible Be sure to be inclusive in creating your study groups Use the free tutoring resources available on campus especially the Physics Department consultation room PAS 372 open weekdays How to Use this Manual This manual has been written as if the author was standing beside you talking to you and asking probing questions This manual often attempts to create a Socratic dialogue in written form to help students master difficult concepts The lab activities are often demanding and require the full amount of time allotted for the lab Be prepared when you arrive and do not waste time while you work i In this manual the upside down question mark is provided to indicate where the student must provide an answer explanation numerical
61. alculate the amplitudes of the resistor and capacitor voltages then compare to your measurements to make sure things are as they should be if not get help 1 5 Be sure you are able to use the oscilloscope cursors to double check the driving frequency given by the function generator 1 6 Use your answers to the previous questions to write equations for V t V t and V t entirely with numerical values no free parameters Don t forget the phase shifts 177 1 7 Set your oscilloscope to plot V on the x axis and V on the y axis an XY plot Sketch the result on the oscilloscope screen below d E E ni W I LS i L mE E E 178 Section 2 experimentally finding the capacitance Next you will test the relationship X by observing a sinusoidally driven RC circuit Mp using many different driving frequencies Use the same circuit set up as in the previous part of the lab 2 1 As you increase the driving frequency the amplitude of the resistor voltage will increase because the total circuit impedance is decreasing i e R V vcctor houe Work through this logic so that you are sure you amplitude Z amplitude understand it Meanwhile as the driving frequency increases the capacitor amplitude decreases This makes sense because the resistor and the capacitor are the only two components in the circuit other than the source Since the voltages across both must add up to the sou
62. arate graph paper 2 3 Label the part s of your sketch where the electric field appears to be the strongest Each partner should use their own copy for this answer on separate graph paper G 2 4 Calculate the electric field at the point that is 2 cm to the left and 3 cm above the center of the dipoles using the derivative approximation Be sure to express your answer for the electric field in vector notation 81 2 5 Draw both electric field components for the point in the previous problem as arrows on your field mapping paper and label the strength of the field in each direction At this point your field mapping paper should look something like this only with many more lines i a answer on separate graph paper d 2 6 Discuss where the electric field should be the strongest for the dipole system based upon the spacing of the equipotential lines 82 line of symmetry is x axis where y 0 Place an x y coordinate system on your graph paper as shown above On another sheet of regular graph paper graph voltage versus the x coordinate V x 0 vs x along the line of symmetry that goes through both poles of the dipole conducting paper using your previous results Your voltage axis and distance axis should be in SI units An example is shown below answers on separate graph papers y where the equipotential line intersects the line of symmetry 3 V ane 83 2 8 On anothe
63. asurements V vs t o frequency o period o voltage amplitude o current amplitude via resistor voltage amplitude e Oscilloscope measurements V vs Vy o RLC resonance e Tricky oscilloscope measurements o capacitance o inductance O00 0 0 276 Repeated Rules for Excused Absences You should always email your TA as soon as you know that you will be missing a lab You are not permitted to attend a different lab than the one for which you are registered If you have a valid excuse with documentation then you may complete the Makeup Lab near the end of the semester Therefore you may only makeup lab at most If you are writing your biweekly lab report and you have been absent 1 week then you may only earn 75 of the possible lab report points 30 out of the total possible 40 If you have a valid and documented excused absence completing the makeup lab and writing the report for it will allow you to earn the remaining 10 points for the unit during which you were absent When you are writing your biweekly lab report and you have been absent 1 week then e Write the Mini Report using the section for which you were present e Write the Open Ended Discussion using the open ended activity for which you were present e Attach the graphs you created for the week you were present e Attach the Post Lab Quiz for the week you were present e Attach the Selected Worksheet Pages you completed for the week you were present For the makeup
64. charged glass rod near but don t touch the electroscope You will have attraced negative charges to the top of the electroscope Now touch the electroscope with your hand Negative charges from your body will also be attracted to the rod and will be deposited on the electroscope Remove your hand THEN remove the glass rod and see that the electroscope has a net charge because the gold leaf is still raised Use the picture template provided below to show how the charges on the metallic bar gold leaf are arranged after you touch the electroscope in the presence of the glass rod 55 Section 4 charging by induction With a little ingenuity you can charge a conductor with either positive or negative charge by using the process of induction If you bring a neutral conductor near a positively charged object but without touching the conductor to the charged object and then touch the conductor with your finger then negative charge will rush from your body onto the conductor in order to be near the positively charged object Then remove your finger so that the negative charge remains on the conductor If you then pull the conductor away from the positively charged object your conductor will be negatively charged To induce positive charge on a conductor simply place the conductor near a negatively charged object and touch it with your finger then remove Of course you can always charge an insulator by rubbing it with wool or imitation fur etc
65. ct electrons How to complete and explain a long physics derivation Section 1 cathode ray tube derivations The operation of a cathode ray tube is described by just a few simple physics concepts However the chain of logic math that relates the plate voltages to where the electron strikes the scintillation screen is quite cumbersome Many student become confused in the derivation that calculates this deflection distance of the electron Much of the theoretical work that follows is designed to help the students understand each part of this long derivation upward and outward describe which way the electron is deflected 1 1 In the cathode ray tube an electron is initially at rest approximately and is accelerated by a force produced by an electric field However in lab you will only know the positive change in voltage V really AV of the plates through which the electron is accelerated What simple formula using V q and W work can you write to relate the work done on the electron to the change in voltage of the apparatus Note the V is used for voltage and y for velocity Check your answer with other students or your TA Your formula 93 1 2 Now slightly extend this formula using the work energy theorem The work energy theorem states that the change in kinetic energy is equal to the work done on the object Using this concept write a formula relating the change in the electron
66. cy is easily found because you will see an ellipse when Va t and Vogource t are out of phase and a diagonal line when they are in phase You see a straight line when they are in phase because both voltages must reach zero simultaneously Ve t Va t 45 V t Vs t out of phase in phase Note that if R is chosen small enough the resistance of the very long wire of the solenoid may become an appreciable resistance of the circuit When this occurs the amplitude of the resistor voltage will be smaller than the source voltage amplitude so that you will see a different angle of tilt not 45 of the in phase resonance line shown above This is because V V BV ite V Ve 0 source real solenoid 246 Section 4 specific oscilloscope measurements Construct an RLC circuit driven by a sinusoidal driving voltage of V source amplitude faie 10 000 Hz R 1 KQ C 0 1 WF and L 50 mH The frequency and resistance values were not randomly selected but were determined so that R vy and y are of V and V C amp L amp 5 V with the same order of magnitude check if you like This means that V will amp also be of the same order of magnitude This cheat is only for this your first time so you learn the measurement techniques better Later you will need to be able to analyze two components on your oscilloscope when their voltages are drastically different 4 1 Why must you hook up the entire circuit
67. data calculations recorded observations random ideas etc Write at the prompts on the next page 169 5 1 hypothesizing planning 5 2 observations data 5 3 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 170 Week 7 Take Home Quiz Score ___ 5 THQ 1 5 points An initially charged capacitor is discharged through a resistor R a Will the capacitor discharge faster or slower if the resistance is increased using the same amount of initial charge b Will the capacitor discharge faster or slower if the capacitance is increased using the same amount of initial charge c As the capacitor discharges does the magnitude of the current through the resistor increase or decrease d As the capacitor discharges what is the magnitude of the current in the space between the plates e As the capacitor discharges through the resistor energy is being deposited in the resistor as it is heated Where was this energy stored initially Note your answer must be more explicit than simply stating the capacitor 171 This page intentionally left blank 172 Week 8 Pre Lab RC Circuit AC Source Last week you studied RC circuits examining the exponential time dependence of the capacitor voltage as you charged and discharged the capacitor with a constant source voltag
68. de the coils A cross sectional picture is provided along with an actual solenoid a compass inside its coils can be seen interacting with the magnetic field Ideal Solenoid found using the Biot Savart Law dB However this law can be difficult to use totalenclosedby Amperian loop Boutside 0 Q E Q OOOOOOO U uniform magnetic field inside i fi In the laboratory an experimenter may easily control the current through a solenoid and so it is desirable to determine the strength of the magnetic field inside the solenoid as a function of the current Because of the high degree of symmetry in the ideal solenoid Ampere s Law may be used to find the magnetic field inside the solenoid Vy b Q l a 5 R LHS f Beds Beds B dy B dy B L 8 O NGS wholeloop inside B Q REIS Hol wat MoNT HoNI Q Q 4 NI RON LHS RHS B pnl Sen soon amp i Q A 211 Two very important concepts in the study of electricity and magnetism are Ampere s Law and Faraday s Law Ampere s Law states that a current in a wire creates a magnetic field Faraday s Law states that if the magnetic field changes oscillates the changing magnetic field will create a voltage in the wire with the strange choice of epsilon as the variable to represent this db dt area If a magnetic field is uniform over a certain area A then the magnetic flux is easy to calculate B A r
69. diagrams To think of current as marbles or water flowing in a garden hose and how current must be behave so as to prevent charges from piling up in any part of the circuit To understand how components in parallel series affect equivalent resistance To understand how components in parallel series affect current drawn from the battery To understand how components in parallel series affect the voltage delivered to a circuit component To understand how the three previous concepts conspire to affect the power used by a component as observed with bulb brightness How to compare the currents and resistances of different circuits To use a DMM to measure current voltage and resistance all have a different procedure To make a real circuit from viewing a circuit diagram How to design and conduct an experiment to address an open ended question 19 Section 1 thinking about voltage 1 5 V Reus The circuit diagram of a battery powering a light bulb is shown above Introductory students sometimes confuse the new concepts of voltage current resistance etc Where voltage is concerned a good way to think about what is happening is to think of voltage as a kind of height The battery lifts the electrons to a height of 1 5 V at the positive terminal of the battery Then as the current flows through the light bulb the electrons fall back to a height of 0 V Current flows from high voltage to low voltage One could equival
70. djusting Va and observing Dx amp 29 Set V to about 2 to 3 4 its maximum value and adjust Va to the largest value possible that still enables you to see the scintillation dot it may be fuzzy but you should measure deflections using the center of the dot Be sure to record Vax and to keep this value constant for the remainder of this section Record your constant deflecting voltage Vax 2 10 Adjust V to larger and larger values and record the corresponding horizontal screen displacement D for several values of V make a data table with at least 5 data points Record your data table of V and D 2 11 Linearize your data by making a graph of D vs 1 V by hand Graph D vs 1 V on graph paper Your data should give you a straight line 2 12 Measure the slope of the line of best fit Since D k a the slope will equal a k V So divide by Vax to obtain k Record your result for k here in SI units 104 Section 3 authentic assessment 3 1 You will learn later that the magnetic force is given by F q7 x B but usually the speed of the charged particle is too slow to be able to visually see the effects of the magnetic force However electrons in CRTs move so fast you can actually see them being deflected by a magnetic field In fact this is how old fashioned television first worked You must correctly predict whether the scintillation dot will be deflected horizontally or vertically when a
71. driving frequencies This causes there to be a specific frequency where the circuit has the largest possible current This is the resonant frequency resonant 239 The total circuit impedance the circuit s total resistance is Z JR X x Q The capacitive reactance the capacitor s resistance is time dependent Xo QO If Oniive you increase the driving frequency X will decrease inversely proportional The inductive 66 reactance the inductor s resistance is time dependent also X _ If you increase the driving frequency X will increase linearly proportional Since increasing the driving frequency causes Xo to decrease while X increases then there is a specific driving frequency when they are equal Xo X When this happens the total circuit impedance is a minimum Lwin 4 R x ees y R and this particular driving frequency therefore allows the most current to flow through the circuit This is called the resonant frequency X X The phase shift formula for the source voltage is u tar A Xe Also note that the source familiar Ohm s law I V R can be used as a pneumonic for the formula for the current in the RLC V circuit T or _amplimde amplitude Z As an example imagine an RLC circuits sinusoidally driven with the following parameters IfR 0 5 Q L 0 010 H C 0 10 F V source amplitude 3 V and Pie 10 Hz Then Onive 27
72. ds near the top of the motor enclosure box and contacts the axle leads from the bottom amework 201 Section 2 making measurements Power amp Efficiency At some time as the motor rotation rate speeds up the angular speed reaches an equilibrium value where the opposing torques balance the torque caused by the magnetic force T fom De T These opposing torques come from friction and any load you place on the B field motor work you make the perform In this experiment it will be difficult to directly analyze the magnetic force being applied to the motor so that the force torque perspective will not be useful Therefore it is better to examine the energy perspective of the motor Conservation of energy indicates that power in must equal power out ae T aot Pii power power ction Thinking of the motor as any other circuit component we know that the electrical power being used by the component is P IV So the input electrical power can be measured in the lab as FeS input through across power motor motor The output power is equal to the rate of work energy that the motor performs per second TON YY eit At f power onenvironmert Since work is given by e W ina Tora d object r onenvironmert travels this is easy to calculate if the motor were to be lifting an object vertically upward since in this case gt gt onobject aca onobject TM obvject8 by motor by gravity so that by motor M
73. dwich each component with both channel leads WRONG red 1 black 1 100 2009 black 2 red 2 The problem with using both channel grounds is that 1 it is not necessary since they connected internally and 2 if they end up being connected to different parts of the circuit they short the circuit out because they are connected internally Sometimes students use an external wire to connect both black leads of the oscilloscope channels to remind themselves of this so they don t end up making mistakes on their lab practicals Never use both channel grounds Only use one of them either will do 141 Set up the function generator to output a 200 Hz sine wave with a 3 Volt amplitude through a 100 Q and a 200 Q resistor in series see figure below Use the two oscilloscope channels to measure the voltage across each resistor simultaneously on both channels by setting up a bottom ground set up as shown in the figure below The voltage between red 1 and ground will tell you the potential difference across both resistors while the voltage between red 2 and ground will tell you the voltage across the 200 Q resistor red 1 black bottom red 2 ground 200 Q 2 5 What must you do mathematically to find the voltage across the 100 Q resistor d 2 6 Are the two oscillating voltages across the resistors in phase with each other G 2 7 Determine the amplitudes of the voltage differences across each resi
74. e R VS Varive resistor amplitude you should obtain a linear graph with a slope equal to L 5 4 Find L by collecting data for multiple driving frequencies making a graph on separate graph paper and finding the slope Make your observations and graph now Then write your work and result for L 229 Section 6 fast Fourier transform FFT detection of frequencies This is the perfect opportunity to learn the use of your oscilloscopes FFT fast Fourier transfer math function The FFT math operation changes the time axis to a frequency axis You may then adjust the frequency scale using the seconds div knob zoom in using the math gt FFT zoom function horizontally scan using the horizontal shift knob A mathematical description of electromagnetic waves in the air is as follows A sawas A Sin t A sin t A sin t in air An EM wave is made of many components of different frequencies Each frequency has its own amplitude A1 Ao A Fourier transform is a mathematical technique that gives the amplitudes of the various components of wave Your oscilloscope has this fast algorithm programmed into it 6 1 Use your solenoid to search for stray alternating magnetic fields in the lab There are many strange high frequency electromagnetic oscillations radio waves permeating the laboratory Use a large unpowered solenoid to detect the oscillating magnetic fields of these radio waves in
75. e To do this you used a square wave with a DC offset Now you will examine the behavior of a capacitor when a sinusoidal source voltage is applied V t V sin t where p is source source amplitude called the angular driving frequency of the circuit R V source t C The capacitor voltage will no longer exhibit exponential time behavior Instead the capacitor voltage will oscillate sinusoidally with the same frequency as the source driving frequency The following formulae can be found by solving the appropriate differential equation not here The results of that calculation are provided the time dependent voltages across each component Thus you are not required to be able to derive the solutions to the AC driven RC circuit but you must understand and be able to use these results Each component of the sinusoidally driven RC circuit has a sinusoidally varying voltage across it but each peaks at a different time determined by a phase shift Different components reach their maximum voltages at different times than other components V ouret Poara amplitude sin pt pi 7 R Vaesistor 2 Va sin pt Z amplitude X Vcapacitor t e Vanu snost z Z amplitude There are several new parameters to discuss The reactive capacitance Xc Greek letter chi is like the resistance of the capacitor and is measured in SI units of QO But unlike a resistor s sak 1 resistance Xc depends on t
76. e a resonant frequency nearer to the audio frequency or the carrier frequency 3 5 Calculate the resonant frequency fresonance Of the secondary circuit amp 3 6 Adjust the carrier frequency until a maximum output voltage is determined on the oscilloscope If it does not match your previous answer get help Explain why the carrier wave needs to be at the resonance frequency of the secondary circuit to maximize transmission of the modulated wave Now use your earphone to determine that maximum broadcast transmission occurs when the carrier wave is at the resonance of the secondary circuit 270 amp 3 7 Write directly onto the figure below to completely explain how this compound circuit s works You can use labels text and arrows and you do not need to write in complete sentences a Ss T ammi SECONDARY SOLENOID PRIMARY SOLENOID he s S 8 m X envelope Hz 271 This page intentionally left blank 272 Section 4 authentic assessment real radio wave reception Now replace the function generator and RF modulator with a real antenna as shown Change the secondary solenoid inductance 4 options and the capacitance continuous adjustment to find radio stations which cause the secondary circuit to have a maximum current large voltage on the oscilloscope ground PRIMARY SECONDARY SOLENOID SOLENOID If you are uncomfortable having another student check your w
77. e electrons are negatively charged an electron always moves toward regions of higher electric potential higher voltage If you see an electron move from point A to point B then you can be sure that V gt V A Faraday ice pail made of two concentric cylindrical cages detects the presence of excess charge that is placed in the center of the pail without touching the inner cage If an object with positive excess charge is held inside the pail electrons are attracted to the inner cage This means that the outer cage must have a lower voltage than the inner wall Since the grounding lead of the electroscope is attached to the outer cage and the positive lead is attached to the inner cage the electroscope registers a positive voltage If a negatively charged object is placed inside the pail then the electrons will be repelled to the outer cage and the electroscope will register a negative voltage 5 1 Use the Faraday cage and electrometer to check the signs of the excess charge on several classroom objects Make a table of your observations Be sure to see what happens when scotch tape is placed on the table then removed Do electrons stick to the tape 58 5 2 Find two different non conducting insulators blue and white paddles if equipped and place the uncharged insulators into the pail Rub them against each other Since they are made of different materials it is likely that the difference in electronegativi
78. e prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the following page Be sure to read the take home quiz before you leave 274 5 1 hypothesizing planning 5 2 observations data 5 3 calculations conclusion Be sure to read the take home quiz right now I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 275 Week 12 Fake Home Quiz Score D 5 THQ 1 5 points if you have finished the lab and have time remaining you should review lab techniques for the lab practical e Using the DMM to measure o voltage o current o resistance e Building circuits from schematics o series o parallel e Operation of a DC power supply e Operation of a function generator o square and sin waves o output frequency o output voltage amplitude o DC offset e Oscilloscope general usage o middle ground vs bottom ground setups time scale voltage scale where V 0 is on screen triggering screen capture o how to get it off French if done so by accident e Oscilloscope me
79. e resistor increase or decrease What about the inductor Explain your reasoning 226 When you measure VR amplitude EL amplitude then you know that that X L7 R If you find the frequency where this happens you can use X Ojivel to find L by substituting R for X pe Orive 5 2 Use this single measurement method to find L for your solenoid 5 3 Use the XY setting of your oscilloscope to observe the 90 phase shift between the resistor and inductor voltage by viewing the subsequent Lissajous figure 227 There is a second multi measurement method to find L The voltage amplitudes of the sinusoidally driven RL circuit are very similar to those for the sinusoidally driven RC circuit you encountered a few weeks ago R VE ese V sities SIN O givet Z amplitude and IT L V t inductor Vane s n Darvel Poe Z amplitude 2 This gives the following relationships for the amplitudes R X ae ae F ine and Vadio E are amplitude Z amplitude amplitude Z amplitude Dividing these two equations gives X Y source amplitude V aii Z amplitude _ a X resistor R Venice R amplitude amplitude Therefore Vadias amplitude s E e resistor amplitude In order to test the relationship lt and experimentally determine L for your solenoid simply combine the last two equations inductor amplitude Oprivel R V resistor amplitude 228 Therefore if you graph y inductor amplitud
80. e your report alone as collaborating with a lab partner will make you both guilty of plagiarism Please label your lab report sections Title 0 points A catchy title worth zero points so make it unique and fun Mini Report 10 points 4 5 paragraphs 2 double spaced pages Choose one of the following sections about which to write your mini report Week 11 Section 4 or Week 12 Section 3 Write a mini report for one particular section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable Please label your mini report sections o Abstract Write 2 3 sentences about the goals of this section Describe the concepts you were investigating and how the experimentation you performed allowed you to investigate these concepts Write 2 3 sentences summarizing the procedure Write 2 3 sentences summarizing the results and what the results mean with regard to the concepts you were investigating It is best to write the abstract last o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Provide a description of the data you obtained such as data tables Restate any measured values calculated s
81. eatures in addition to your own intense emotional attachment to your motor Design a way to calculate the minimum source voltage required to operate your motor Voource min and the RPMs at this minimum voltage Also find and the power loss due to frictional torque Pmotor on Note that you cannot obtain an accurate measure of voltage or current with the built in source meters so must use the oscilloscope to find these values as shown in section 2 Also you should report the maximum safe source operating voltage Vosourcemax and corresponding RPMs your motor can operate safely at but don t find RPM otorFaiture You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the next page 207 4 1 hypothesizing planning 4 2 observations data 43 calculatio
82. ect two components to find the resonant frequency Be sure to use the fact that theoretically w sie to check your work resonance JLC If you are uncomfortable having another student check your work please ask your TA 4 1 Show a student in a different group that you can successfully measure the resonance frequency of an RLC circuit four circuits compare your data with theirs Once you are successful have them sign below Note if someone is stuck please give them advice Yes I have seen this student successfully the resonance frequencies of four RLC circuits Their results match mine Either they are doing it right or we are both wrong in the same way Student Signature _ a 288 Section 5 open ended creative design THEORY gt REALITY R ohm Veouree C farad Veoures C farad R ohm L henry L henry In real life we often deal with non ideal circuit components For this open ended you will investigate a non ideal solenoid If the solenoid is made from a very long wire it can have a sizeable resistance This means that the oscilloscope when measuring the voltage across the inductor is composed of two components Vea f Vigeu Viaex t But these two inductor inductor resistor components are mixed together so that the oscilloscope is unable to separate them Use a 5 555 uF capacitor using the capacitor box in series with a large unknown solenoid sinusoidally driven and the concept of p
83. ection 3 mutual inductance radio Now you will use a sound wave to modulate a radio frequency wave then use mutual inductance to transmit the radio frequency wave to a separate RLC circuit and finally listen to the broadcast sound wave Set the capacitor to its maximum setting 3 1 First determine the inductances Lprimary and Lsecondary Of your solenoids using the methods from previous labs In other words for each solenoid create an RL circuit driven sinusoidally and monitor the voltage across the resistor and inductor as you vary the driving frequency Use the appropriate equation to solve for the inductance L Even with the 10 Q resistor you will need to use large driving frequencies as these inductances are very small 3 2 Determine the capacitance of the capacitor using methods from a previous lab Choose your favorite audio frequency wave to broadcast and a carrier wave initially 550 kHz Instead of trying to hear the broadcast wave in the secondary circuit send the output to your oscilloscope so you can see the broadcast wave RF Modulator envelope Hz EAR Q RS A Sit 269 3 3 The secondary circuit is supposed to be an RLC circuit with a resonance frequency Where is the resistance and why would you want the resistance to be as low as possible amp 3 4 Do you expect the secondary circuit to hav
84. effectively act like a resistor with some special features 212 Week 10 Lab Solenoids Students Absolutely Must Learn How to use Ampere s law Phase lag of inductors How to use Faraday s law How induction works external self and mutual How to use Lenz s law Advanced features of oscilloscopes Section 1 creating magnetic fields inside the solenoid Magnetic fields are created by moving charges A revolving charge produces a magnetic field parallel to the plane of its motion The right hand wrap rule indicated the direction of that magnetic field t Thumb shows direction of A magnetic field t Wrap fingers in direction of current If charge q is negative reverse B field direction 213 When currents flow through coils of wire many charges are moving simultaneously in circular paths These create a magnetic field inside the wire coils The right hand wrap rule again indicates the direction of this magnetic field t Thumb shows direction of magnetic field D t X Now you will experimentally examine the magnetic field produced by a solenoid with current flowing through it Note that a real solenoid produces a magnetic field qualitatively similar to a bar magnet of the same dimensions First check that your compass has not been flipped The compass arrow should align itself with the local magnetic field produced by the Earth Remember that the Earth s north magnetic pole is at the
85. electron once it has reached the other side of the deflection plates Write your answer for Ay using W vr e m and Ey Your work and answer in SI units 1 13 Use the kinematics equation v a At to determine the final y velocity vty when the electron has reached the other side of the deflection plates Write your answer for vs using W Vrz me and Ey Your work and answer 98 The following is not a problem but you must read through it in lab This is where all the analysis you have done from the previous section is synthesized together to derive the cathode ray tube equation You will need to understand the following work in order to write your lab report The derivation will use the following figure to find Dy Z o coordinates nunnnnnnnnnnnnnnnnnnnnnnn g massgopttll nnnnunnnnnnnnnnnanannnnnnabnnnnnnnnnnnnnnnnnnnnnnnnnn I J V L acceleration acceleration constant motion in z direction in y direction while crossing while crossing remaining distance deflection plates to screen 1 14 READ THE FOLLOWING SENTENCE TWICE Our goal here is to derive a final equation that relates D to the only things we can control in the lab V and Vay as well as the things we can t control the geometric parameters of the CRT d w and L Note that capital V will always represent a voltage while a lower case v will always represent a velocity In the derivation ignore directional negative signs for simplicity
86. ent materials and geometries on mutual inductance Student Signature 231 Section 8 open ended You wake as if in a dream All is white all is cold It comes back slowly the plans the plane the explosion You were on an expedition to the Earth s polar region But which one north or south You can t remember You find the debris field of the plane Your oscilloscope luckily in one piece as well as your portable power supply From the wrecked engine you take a large solenoid In your pocket of course some wires and alligator clips You rescue some cheap unlabeled ceramic magnets from the icy ground before they are covered by the falling snow and lost A magnet could be used to make a compass if only you knew which end was the north magnetic pole A compass is your only chance to figure out where on earth you are and then how to proceed Use your oscilloscope and solenoid and wires to devise a way to determine the north magnetic pole of an unlabeled magnet You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you shou
87. ent that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort 62 Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the next page 8 1 hypothesizing planning 8 2 observations data 8 3 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 63 This page intentionally left blank 64 Week 2 Take Home Quiz Score 5 THQ 1 1 point The following picture shows a neutral conducting disc in the presence of a positively charged conductor Choose which would happen to total charge of the conducting disc if it was momentarily touched by the positively charged object a become negatively charged b stay neutral c become positively charged THQ 2 1 point Choose the best explanation for why the gold leaf is raised in the below picture a It has been touched by a negatively charged conductor b It has been touched by a positively charged conductor c There is a negatively charged object nearby d There is a positively charged object nearby 65 amp THQ 3 3 points Use the following figure of a dipole in the presence of a si
88. ently say that the electrical potential energy of the charge carriers is increased by the battery and then the charge carriers lose that potential energy as they flow through the light bulb voltage height 1 5 V _ z To I o V GE lt S Note that the wires of the circuit are drawn nearly horizontal This is because wires are highly conductive very low resistance and so there is no appreciable drop in electrical potential along a wire will blow the fuse in your DMM Always use some resistance in your circuit when measuring amps or you 20 The following pictures attempt to make this concept very clear by providing different ways to visualize the previous situation at various points of the circuit The circuit with labeled points b ow R 1 5 V BULB TC Which one may think of using the following picture d voltage height o V 21 One can examine the change of voltage for the current moving from point to point through the circuit voltage 1 5 V a b c d e a position on circuit Examine the labeled points on the pictures above Both pictures represent that same circuit labeled at the same points Moving from point a to point b the voltage increases by 1 5 V V tob 1 5 V The DMM actually measures voltage differences Placing the positive lead at b and the ground lead at a would give the measurement V b V V 1 5 V Points b and c
89. entz force law for wires o Brush contacts How generators work Skill working with wire How to measure power being consumed by a motor Advanced features of oscilloscopes Section 1 constructing the motor The wire s insulation melts at approximately 5 amps of intermittent current depending on applied voltage Once the insulation melts all the motor loops are shorted out so that you only have one loop to drive the motor i e the motor is ruined e Do not use too large of an input power e Do not let the motor get stuck with current flowing through its nearly resistanceless wires Otherwise the wires are the only resistor in the circuit and become very hot e If the motor stops spinning IMMEDIATELY shut off the voltage supply or your motor will begin to turn into a gaseous state 1 Begin with your card Write your name on the card by the box containing the word magnet Main framework 193 2 Cut along the solid lines and fold along the dotted lines Taking your time to make things nice in the motor construction will ensure your motor runs well and is easily fixed if it breaks down 194 3 Carefully use a sharp poker to poke out the marked black dots Wiggle the two axial dots so that the motor axis will turn easily with low friction Never poke through the paper with your finger on the other side Always lay the paper flat over the magnet and use the magnet s hole to poke holes in your paper
90. eparation across a large conductor in the presence of an electric field Determine the acceleration on a charged particle by the electric field produced by charged cathode ray plates Determine the hidden arrangement of conducting plates in a cathode ray tube Determine the resistivity of Nichrome wire Determine if a grain of wheat bulb is Ohmic Determine the behaviors of multiple capacitors Build and measure a capacitor Measure the properties of a motor Maximize mutual inductance Discover the anti resonance of a parallel RLC circuit Broadcast sound waves through the air to a receiver 297 Other 298
91. er nearer to the center of the system 12 Also just as with magnetic field lines electric field lines cannot intersect If they did it would be ambiguous in which direction a test charge would feel a force if it were at that point But the force direction caused by an electric field is always unique so such crossings cannot happen If you draw electric field lines crossing it makes it easy for your TA to mark your answer wrong By point of intersection can t happen 1 1 In the following picture depicting equipotential lines dashed lines of constant voltage sketch the corresponding electric field lines draw the electric field lines with solid lines Be sure to label the direction of the electric field lines using arrows using the assumption that Vour lt Vin Note that Vout gives the value of the voltage for the entire dotted line it touches similarly for Vin Think topographical maps Draw on the picture below an example field line is shown on the picture Note the perpendicular symbol is used to emphasize the electric field line intersecting the equipotential line perpendicularly You do not have to draw the perpendicular symbols 73 1 2 In the following picture assume Voyr lt Vm Describe how each of the two test charges shown would move if placed where shown using arrows to show the direction of each charge s acceleration vector Draw on the picture below and write an explanation below the picture
92. esent real valued quantities that oscillate in time like voltages in an AC circuit Since a complex number has a real and imaginary part z x iy a complex number can also be thought of as a vector in the complex plane imaginary axis real a axis X 0 A complex number can also be expressed in polar form z re where r is the radial distance from the origin r x y and 0 is the phase angle from the real axis tan y x Euler s formula relates the complex polar form to the geometry of the phasor re rcos irsin 6 When applied to a phasor Euler s formula shows that if we use the complex number system to describe a real system we can recover the real values by keeping the real term and ignoring the imaginary term Real fre l rcos The concept of phasors can be applied to voltages in a sinusoidally driven RLC circuit VAO V e where if you need the actual value of the voltage at any time you must use the real part Real V t V cos a Phasors are not stationary when describing time dependent quantities Because phasors are functions of time they rotate around in the complex plan 279 Imaginary Im V t V t V e rotates around the complex plane in time Note that the real value of the voltage is the projection of the phasor onto the real axis using the cosine of the angle and this real voltage changes in time as the phasor rotates That is good since we want the real pa
93. etermine the current of the circuit and use the oscilloscope to measure the resistor s voltage amplitude how could you then turn this value into the current amplitude Hint ohmic Observe the voltage across the capacitor and the total circuit voltage simultaneously using a bottom ground configuration You should see the shark fin pattern that is modulated by the alternating square wave source voltage turning on then off amp 3 9 Use a double cursor measurement to find the time it takes for your charged capacitor to decrease by half in SI units so use scientific notation 3 10 When a physical quantity decays exponentially the time it takes for it to decay to 2 its original value is called the half life t Imagine that you need to find the capacitance and are able to measure this half life time t Make a formula that gives the capacitance C in terms of t by solving the half life 1 equation for C X V e Show your work 165 3 11 Combine the results of the previous questions and calculate the experimentally determined capacitance C of your capacitor using your half life measurement in 3 9 This is a way to determine your capacitance with a single measurement of the half life 3 12 Now use the double cursor method to find the time it takes for your capacitor to discharge from 17 of its initial value to of its initial value The decaying exponential function has the unique property that e
94. f the report Open Ended Discussion 10 points 1 2 paragraphs 1 page double spaced Choose one of the open ended experiments from the two weekly activities to write about Describe your experimental goal and the question you were trying to answer Explain the ideas you came up with and what you tried If your attempts were successful explain your results If your attempts resulted in failure explain what went wrong and what you would do differently in the future You must write using sentences amp paragraphs bulleted lists are unacceptable Graphs 5 points attach to your typed report Graphs must be neatly hand drawn during lab on graph paper Your graphs must fill the entire page requires planning ahead include a descriptive title labeled axes numeric tic marks on the axes and unit labels on the axes If instructed to calculate the slope of the line of best fit write it directly on the graph Week 7 1 4 1 6 3 14 Week 8 2 4 Take Home Quizzes 2x5 points 10 points attach after your Graphs Selected Worksheet Pages 5 points attach after your Take Home Quizzes Your TA will choose which pages you need to hand in 153 This page intentionally left blank 154 Week 7 Pre Lab RC Circuits DC Source Examine charging up the capacitor in an RC circuit In this circuit the capacitor begins without any charge on it and is wired in series with a resistor and a constant voltage source The voltage source
95. fact to search the range of driving frequencies for the resonant driving frequency using the technique described in section 4 of this lab Compare this observed value to your predicted value 250 Gq 4 12 Collect data of Zap na VS farive and record below Then graph the data on separate graph paper A slightly incorrect example on purpose so you can t just copy with a larger resistance is shown to help guide you Lesistor amplitude fa rive freso nance 251 This page intentionally left blank 252 Section 5 authentic assessment One solenoid and each of the four capacitors on the capacitor board allows you to construct four unique RLC circuits not counting the resistance possibilities You need to find the four resonant frequencies of each of these RLC circuits using the method described in section 4 on the phase relationship between the resistor and source voltages Use the same solenoid as a different group so that you can compare answers The inductor and capacitor voltage amplitudes can be larger than the source voltage amplitude Voltages over 20 V can cause nasty shocks and very large currents can be generated near resonance in circuits with a large quality factor Q You should approach any circuit with care not touching the components while the circuit is powered In designing a circuit one must either use a large resistance to limit the dangerous currents near resonance or have a firm theoretical under
96. find how macroscopic charge separation works on a large conductor Design an experiment to find how a cathode ray conductor produces an electric field that may accelerate charged particles Design an experiment to probe the hidden structure of a cathode ray tube Design an experiment to analyze the microscopic electrical properties of an unknown material Design an experiment to analyze the microscopic electronic properties of an unknown device Design an experiment to analyze the behavior of compound capacitors Design an experiment to build and measure a homemade capacitor Build a working motor and design an experiment to analyze its behavior Design an experiment to maximize mutual inductance Design an experiment to determine the anti resonant behavior of an multiple component circuit Transmit and detect sound ways through the air using radio waves Also to detect ambient electromagnetic radiation and determine its frequency e Be familiar with basic laboratory equipment and should be able to design and carry out experiments to answer questions or to demonstrate principles O O Skills developed throughout lab especially the open ended component Use of DMM electroscope Faraday ice pale wires with various types of leads resistors capacitors inductors solenoids modern digital oscilloscopes function generators RF modulators antennae motors and magnets compasses e Be able to communicate their results through writte
97. g another student check your work please ask your TA 4 1 Show a student in a different group that you can successfully measure the capacitance of a capacitor with only one measurement Once you are successful have them sign below Note if someone is stuck please give them advice Yes I have seen this student successfully find a capacitor s capacitance using the measurement of the half life They are able to use this property of exponential decay Student Signature 168 Section 5 open ended When capacitors are added in series they have a combined capacitance determined by one of the two following equations l C C J C or effective 1 1 effective as an C Q Design an experiment to determine which mathematical relationship is correct and which is incorrect You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of
98. ge requires planning ahead include a descriptive title labeled axes numeric tic marks on the axes and unit labels on the axes If instructed to calculate the slope of the line of best fit write it directly on the graph Week 9 none Week 10 5 4 Take Home Quizzes 2x5 points 10 points attach after your Graphs Selected Worksheet Pages 5 points attach after your Take Home Quizzes Your TA will choose which pages you need to hand in 189 This page intentionally left blank 190 Week 9 Pre Lab Motors A magnet has a strong magnetic field near its surface but this field becomes very weak away from the magnet surface When a current carrying wire of length L passes through a magnetic field the magnetic field provides a force on the wire given by Fem Biag L I xB The force on the wire above is out of the page as determined by the right hand rule Bpa is weak L ls B Boise IS strong Note that I is written as a vector to describe the direction of the current and the cross product indicates that the right hand rule must be used to find the direction of the force You can use this simple concept to make the real motor The motor is made of current carrying wire loops that can rotate about an axis shown as a dashed line in the picture below The part of the wire loop that passes through the magnetic field experiences a magnetic force upon it This magnetic force causes a net torque on the wire loop yielding ang
99. get that the solenoids must remain immediately adjacent to each other Now examine the equipment with the continuously variable capacitance The variable capacitor is made of two sets of overlapping plates One set can be rotated so that it overlaps more or less with the other set of plates When they maximally overlap the capacitor has the highest capacitance it can provide When the plates don t overlap at all the capacitance is Zero In addition to the capacitor plates there is a diode and speaker connector in parallel to the capacitor Remember that the diode eliminates half the oscillating voltage sent to the speaker 264 Now let s be sure you can make the sound Clean your ear speaker with alcohol and connect it to the earplug on the capacitor assembly Set your function generator to 3 600 Hz Connect your function generator to the A and B connections on the variable capacitor assembly as shown below Slowly increase the output voltage of the function generator until you can hear the signal Ask for help if you have any doubts about the proper operation of these devices PRIMARY SECONDARY SOLENOID SOLENOID amp 1 3 Give yourself a hearing test Find the upper end of the frequency range of your hearing or another student if you do not want to test your own hearing It may be significantly less than your classmates if you are older or have suffered hearing loss due to loud noises Also note any intermediate
100. gn of the voltage across the solenoid caused by the back EMF 3 1 Move the north pole slowly toward one side of your solenoid Write what you see on your oscilloscope positive or negative induced voltage You should see some induced voltage or you are moving too slowly Try using 500 ms div 1 2 second division and 50 mV div to clearly see the response Your observations amp 3 2 Move the north pole quickly toward same side of your solenoid as in 3 1 Write what you see on your oscilloscope and compare the amplitude of the induced voltage with 3 1 Your observation and comparison 221 3 3 Use the equation for Faraday s Law lt to explain why the amplitude 3 2 was larger than 3 1 3 4 Now move the south pole quickly toward the same side of your solenoid as in 3 1 and 3 2 Write what you see on your oscilloscope and compare your result with that of 3 3 Your observation and comparison 3 5 Use Lenz s Law to explain the difference between your observations in 3 3 and 3 4 Your explanation 222 Section 4 finding the mutual inductance If you take a solenoid and drive it with an alternating current it will produce an alternating magnetic field inside its coils If you then take another solenoid that is unpowered and place it nearby so that the changing magnetic field of the first solenoid reaches inside the coils of the second solenoid then a voltage will be induced in the second solenoid desp
101. half the time Do not forget the resistor as it protects the diode from being destroyed by a large current Then set up your oscilloscope in the bottom ground set up to measure the voltage across the resistor on the y axis and the applied voltage on the x axis red1 Vamp 3 V CV ground Since the voltage source is oscillating some of the time it is in the correct direction to turn on the diode so that current can flow and some of the time is in the opposite direction so that no current flows 3 1 When current is not flowing through the circuit which component has zero voltage drop across it and why 145 3 2 When current flows through the circuit what is the approximate voltage drop across the light emitting diode Hint use the band gap energy Experimentally determine if the diode is Ohmic by constructing its current versus applied voltage graph should look something like example figure below You may want to increase the source frequency so that the oscilloscope trace makes a solid line Note that you cannot directly measure the current through the LED with the oscilloscope Therefore answer the following questions first in order to learn how to construct the Itep vs V appliea graph llep responding to different V a possible non Ohmic graph AV applied many various applied V s 3 3 In this circuit how is the current through the LED related to the current through the resistor a
102. hasors to devise a method to find V t and ideal inductor Vaca t the two ideal components for the very real solenoid resistor You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the next page 289 5 1 hypothesizing planning 5 2 observations data 5 3 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 290 This page intentionally left blank 291 Appendix 292 This page intentionally left blank 293 Assessment Learning Outcomes Introductory electricity amp magnetism laboratory students should be prepared for leadership roles in an increasingly diverse technological and highly
103. hat are sinusoidal in time A B or Both 187 THQ 2 2 points Vsou rce t C For the above sinusoidally driven circuit C 7x10 F and R 7 000 Q At what driving frequency fp would you find the resistor and capacitor voltage amplitudes to be equal 188 Unit 5 Lab Report Instructions Unit Lab Report 40 points Use the following section titles in your report Images text or equations plagiarized from the internet are not allowed Remember to write your report alone as collaborating with a lab partner will make you both guilty of plagiarism Please label your lab report sections Title 0 points A catchy title worth zero points so make it unique and fun Mini Report 10 points 4 5 paragraphs 2 double spaced pages Choose one of the following sections about which to write your mini report Week 9 Section 2 or Week 10 Section 3 Write a mini report for one particular section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable Please label your mini report sections o Abstract Write 2 3 sentences about the goals of this section Describe the concepts you were investigating and how the experimentation you performed allowed you to investigate these concepts Write 2 3 sentences summarizing the pr
104. he driving frequency Xo ET Note that the capacitor s D resistance decreases with higher driving frequencies 173 Z is the impedance of the whole circuit Z acts like the total resistance of the circuit measured in Q Z R Xz At very high driving frequency Xc becomes very small so that Z R Notice that the source voltage is now written with a source phase shift Osni the capacitor voltage has a phase shift of n 2 and the resistor voltage has no phase shift This can be seen in the following graph V t What this means in practice is that we use the resistor voltage as a reference for all other components in the circuit i e we will measure the phases of each component in relation to what is happening inside the resistor This is because the resistor is ohmic and can always provide the time dependent current via Ohm s law simply by dividing the resistor voltage by resistance Vp t L sc t R 4 In the previous graph the source voltage can be seen as the negative sum of the components voltages V V t V t This is due to the conservation of energy The source voltage is phase shifted from the resistor voltage by an amount arctan a The v is also included as an additional phase shift but it is equivalent to multiplying by 1 sin t 7z sin t which emphasizes that electric potential in the circuit is conserved V t V t V t X Examine the amplitude
105. her receiving solenoid We will use a capacitor in the second receiving circuit to make an RLC receiving circuit By changing the capacitor of the receiving circuit we can adjust its resonant frequency Therefore we will be able to tune our receiver to a particular radio frequency Now you would like to listen to your transmitted wave But there is a huge problem Whenever the wave is positive it causes an upward force on the speaker and whenever it is negative it causes a downward force on the speaker The modulated wave is oscillating up and down with the rapid radio frequency much too fast for the speaker to respond to It just sits there quivering The trick is to add a diode to the output Remember that a diode is a quantum mechanical component that only allows current to flow in one direction once a turn on voltage has been reached determined by the semiconductor band gap energy This will allow only positive voltage to reach the speaker _Modulate Wave Transmitted by Diode to Speaker Quantum mechanical turn on voltage of diode Pulses let through by the diode move speaker with frequency of desired audio wave d The speaker now gets pushed out a maximum distance at the maximum amplitude of the pulse and relaxes at the minimum Zii Would you be able to hear the speaker if the direction of the diode in the circuit was reversed Explain your answer 261 Never insert the speaker directl
106. hould give your resistance as the slope and thereby check its experimentally measured resistance see how close you got with your DMM redo if bad write data here and plot graph on separate graph paper 1 3 Experimentally verify that the 100 Q resistor and the 200 Q resistor in series produce an equivalent resistance of 300 Q by taking voltage current data and making the appropriate graph Your voltage data should be gathered from across both resistors simultaneously since you want to treat them as a single resistor and find their equivalent resistance Remember that the current is the same through both resistors Do not apply such a large voltage that the resistor becomes very hot dangerous and non ohmic write data here and plot graph on separate graph paper 116 Section 2 compound circuits 100 Q 2002 lt 100 Q 10 Q 2 1 The circuit shown above has 3 resistors in parallel which together are in series with another resistor Extend your equation for the parallel resistance of two resistors to find the equivalent resistance of three resistors in parallel SI units Also provide a small sketch of the simplified circuit G 2 2 Now use the formula for the equivalent resistance of resistors in series to predict the total resistance of this circuit SI units 117 2 3 Now set up the circuit and test your prediction by simply using the DMM as an Ohmmeter Redo 2 1 and 2 2 until you are sure you are ca
107. ilable D cell AA cell AAA cell C cell 9 volt 6 volt Measure the voltage of two 1 5 volt batteries in series Measure the voltage of two 1 5 volt batteries in parallel Make a short table of your results below G 2 2 If you measure the voltage of a battery to be 1 5 V then switching the DMM leads will cause you to measure 1 5 V Explain why this happens using the concept that a voltmeter is a voltage subtraction machine Too much electrical potential energy in the charge carriers can melt the tungsten filament of a bulb 25 Measure current by using one DMM lead and placing the DMM in series next to the component you are measuring see following figure When you are not sure how large the current may be always use the DMM on the large current setting large fuse then switch to the small current setting if appropriate small fuse 2 3 Measure the current through a single small incandescent light bulb powered by a 1 5 V battery Check your result with another group s to be sure that your DMM measures current correctly Write your measured current in SI units Note that many times in lab you may only need to describe the magnitude of a current while on a lecture exam you usually need to describe its direction as well d 2 4 Measure the resistance of a single cold unpowered light bulb This is not a useful observation since a light bulb is non ohmic it s resistance changes when used in a circ
108. in the circuit I mplitude I mplitude Large R Small R fy rive fy rive huama koura The sharpness of the resonance peak is measure by the quality factor Q The larger the quality factor the sharper the peak Q is found to be given as o L Q resonance R 3 1 What are the units of Q 3 2 Say you were building a circuit that needed to operate at many possible driving frequencies and you wanted to avoid shorting out the components with a large current Should you use a larger or smaller resistance 3 3 Say you were building a circuit that needed to operate at one specific frequency near resonance and you wanted to maximize the current through the circuit to do some work Should you use a larger or smaller resistance 245 In today s lab you usually want to use as small of a resistance as possible while still being safe in order to obtain a nice sharp peak in the current amplitude This will make it easier to find the resonance frequency However it is not always desirable to have a large quality factor In some mechanical systems bridges buildings etc a pronounced response to a driving frequency can cause destruction The most accurate way to find fresonance 1s to utilize the fact that at resonance Vgr t and Vource t are exactly in phase with each other with equal amplitudes You should place each of these voltages on your oscilloscope channels and examine an XY formatted display The resonance frequen
109. inverted Experimentally observe the 90 phase shift that shows the oscillating inductor voltage leads the oscillating resistor voltage by 7 2 90 Make a quick sketch of your observations below and check with students in other groups to see that you are getting things correct Warning at very low frequencies you will not see a phase shift between V and Vp explained in the next passage At very low frequencies the self induced back EMF goes to zero because dB dt is nearly zero You would then think that V 0 V However many inductors are made of such long amounts of wire that they have a sizeable resistance that makes the inductor act in part as a resistor Two resistors in series will be in phase so that you will not measure any phase shift in this case when the frequency it too low 1 8 Check for yourself that the solenoid acts as a pure resistor at very low frequencies Below what frequency is it obvious that the phase shift between V and Vx is no longer 1 2 217 Section 2 Lenz s law Restating previous ideas Faraday s Law states that a changing magnetic field will induce a dbs d lt Technically this equation shows that the induced voltage is proportional to voltage the rate of change of the magnetic flux but the magnetic flux is just the magnetic field integrated over the surface area of the circuit In simple situations where the area is constant this just do _U A B _ dt dt adding
110. ion 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Magnetism and Electrostatics magnetism electrostatics basics electroscopes charging by induction faraday ice pail electrified sphere and grounded sphere authentic assessment open ended Week 2 Take Home Quiz Unit 2 Lab Report Instructions Week 3 Pre Lab Electric Field Mapping Week 3 Lab Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Electric Field Mapping sketching electric fields 2 D electric fields on conductive paper connecting the concepts of voltage and electric field exploring electric fields authentic assessment open ended Week 3 Take Home Quiz Week 4 Pre Lab Cathode Ray Tube Week 4 Lab Section 1 Section 2 Section 3 Cathode Ray Tube cathode ray tube derivations testing the cathode ray tube equations authentic assessment Section 4 open ended Week 4 Take Home Quiz Unit 3 Lab Report Instructions Week 5 Pre Lab Vulture Iguana Rabbit Week 5 Lab Vulture Iguana Rabbit Section 1 experimentally determining resistance Section 2 compound circuits Section 3 the internal resistance of a DMM Section 4 authentic assessment Section 5 open ended Week 5 Take Home Quiz Week 6 Pre Lab Oscilloscope Week 6 Lab Oscilloscope Section 1 semiconductors and quantum mechanics Section 2 time dependent voltage on the oscilloscope Section 3 non ohmic diodes Section 4 authentic assessment Sec
111. irst setting the wave to oscillate between 1 5 V and 1 5 V and then using the DC offset to shift your signal to have Vmm 0 volts The voltage across the capacitor should look like shark fins on your oscilloscope as the capacitor exponentially charges and then exponentially discharges Do this now and check discuss with students in other groups to make sure you are getting it correct and understanding fully Use the same bottom ground setup as shown below red1 163 amp 3 4 Based on the bottom ground setup shown previously which oscilloscope channel gives the voltage of the function generator source and which the voltage across the capacitor 3 5 In this setup is there any special feature of the oscilloscope that will allow you to view the voltage on resistor The answer is yes but explain amp 3 6 During the time interval that the square wave source voltage is at 3 V is the capacitor being charged or discharged Which circuit below describes the situation R C Veoured 3 7 During the time interval that the square wave source voltage is at 0 V is the capacitor being charged or discharged R C Vsou rce i a 164 3 8 The following is an important reminder that you won t need in today s lab but is important to remember Many times you may need to find the current in a circuit The component you must measure is the resistor because it is the only ohmic device if you want to d
112. it etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of the concepts and equations of this unit It is all right to sound repetitive with other parts of the report Open Ended Discussion 10 points 7 2 paragraphs 1 page double spaced Choose one of the open ended experiments from the two weekly activities to write about Describe your experimental goal and the question you were trying to answer Explain the ideas you came up with and what you tried If your attempts were successful explain your results If your attempts resulted in failure explain what went wrong and what you would do differently in the future You must write using sentences amp paragraphs bulleted lists are unacceptable Graphs 5 points attach to your typed report Graphs must be neatly hand drawn during lab on graph paper Your graphs must fill the entire page requires planning ahead include a descriptive title labeled axes numeric tic marks on the axes and unit labels on the axes If instructed to calculate the slope of the line of best fit write it directly on the graph Week 1 none Week 2 none so 5 points for free this unit Take Home Quizzes 2x5 points 10 points attach after your Graphs Selected Worksheet Pages 5 points attach after your Take Home Quizzes Your TA will choose which pages you need to hand in
113. ite the fact that the wires of each solenoid in no way touch each other This is the process of mutual inductance and is the basis of transformers in transmission lines Transmitter Receiver Oscillating transmitting Transmitting magnetic fields magnetic fields anns Oscillating transmitting voltage ATA voltage received is measurable The definition of the mutual inductance is M Ereceiv er amplitude transmitter dI to receiver transmitter dt amplitude The mutual inductance parameter M can be used to encapsulate all the geometric information of the combined solenoids It is used in engineering so that you can calculate the transmitted voltage from an applied current without having to calculate the magnetic field and geometric y E a M dI transmitter S factors with a rearranged version receiver transmitter measured in henries to receiver dt or H 4 1 If you have two solenoids close together with M 0 2 H and you drive one circuit with a current t 6sin 666 A find the amplitude of the induced voltage in the second solenoid 223 The derivative of the sinusoidal current is dI transmitter i Op d zm R resistor transmitter t amplitude amplitude Thus M i E receiver R transmitter to receiver Op resistor transmitter amplitude This result can be used to experimentally determine the mutual inductance of combined solenoids Now you will experimentally study the process of
114. itors Be careful to only apply voltage correctly to the electrolytic capacitor or you will damage it the negative terminal is clearly marked on the capacitor You will discharge your capacitor in an RC circuit with approximately 10 kQ Remember the time dependent equation for the voltage across a discharging capacitor V t Vie ke 1 1 What time constant t RC should you expect with R 10 kQ and C 1000 uF 1 2 Since approximately four time constants 4t allows the circuit to discharge to about 2 of its initial value because 5555 0 012 or more accurately e 0 018 how long should you measure the decay of the capacitor s charge in order to make an accurate graph that doesn t take all day to collect data 157 1 3 Charge an electrolytic capacitor without resistance in the correct direction using the 9 Volt battery this happens quickly since there is very little resistance Next wire the capacitor to discharge through a 10 kQ resistor if the resistance is too small the capacitor will discharge too rapidly to measure Collect voltage time data by having the DMM measure voltage across the capacitor while it discharges through the resistor using a stopwatch You should collect more data at the beginning when there is rapid voltage change Record your data here 1 4 Make a raw graph of your data by plotting V eap t vs t On separate graph paper Next you will linearize your da
115. ke in the entire area surrounding the bar magnets Some of the field lines will disappear out of the drawing area only to reenter in another location of the drawing area Discuss your predictions with other lab groups 1 3 Use your compass to test your prediction for each of the arrangements in the previous figure Discuss how this checking is done and explain any inconsistencies between your measurements and predictions 47 Section 2 electrostatics basics If you rub a glass or plastic rod with some fabric or synthetic fur electrons will be transferred between the rod and the fabric leaving a charged rod with which to experiment If the charged rod is brought into the presence of insulating material containing polar molecules the charged rod may attract the dielectric material even though the insulating material is actually neutral by causing the rotation of the polar molecules When the polar molecules rotate the opposite charge will be closer to the rod so that there is a net attractive force between the dielectric insulating material and the rod But if the charged rod transfers some of its charge to the insulator then both the rod and the insulator would have the same charge and thus would repel each other 2 1 Use a charged rod to pick up little pieces of dielectric insulating material packing peanuts or little pieces of paper Observe the behavior of the Explain whether there is polar molecule rotation in the insulato
116. lab report you will need to Write a Mini Report Do not write an Open Ended Attach the graphs you create for the makeup lab There is no Take Home Quiz for the makeup lab Attach the all the Worksheet Pages you completed for the makeup lab 277 Makeup Lab Report Instructions Unit Lab Report 10 points toward the unit during which you were absent Use the following section titles in your report Images text or equations plagiarized from the internet are not allowed Remember to write your report alone as collaborating with a lab partner will make you both guilty of plagiarism Please label your makeup lab report sections Title 0 points A catchy title worth zero points so make it unique and fun Mini Report 3 points 4 5 paragraphs 2 double spaced pages Choose one of the following sections about which to write your mini report Makeup Lab Section 3 Write a mini report for one particular section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable Please label your mini report sections o Abstract Write 2 3 sentences about the goals of this section Describe the concepts you were investigating and how the experimentation you performed allowed you to investigate these concepts Write 2 3 sentences sum
117. late the electric field in a 10 cm strip of conductive paper with 10 volt across it They understand how important it is to think about a physical situation before manipulating it Student Signature 87 Section 6 open ended Use the cathode ray tube conductive paper shown below to find out what would happen to a positive test charge of 3 0 nC placed initially at rest at three unique locations on the conductive paper points A B and C shown in the picture below You must use the equation F gE and Newton s second law of motion to calculate the magnitude of the acceleration of the test charge if its mass was 10 ug Cathode Ray Tube Conducting Paper C 10 Volts Q 3 A 0 Volts You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on
118. lb as 0 75 V iz If a 6 V battery had been used instead of a 1 5 V battery what would the voltage drop across a single light bulb be 23 Now imagine adding the extra identical light bulb in parallel with the first shown in the following figure Charge flowing through this circuit will lose all of its electrical potential energy if it follows the path to the left or all of its electrical potential energy if it follows the path to the right The moving charge cannot flow through both bulbs simultaneously so half the current must go one way and half the other b R d Bulb Which one may think of using the following picture voltage height 1 5 V AXaLLYg o V d f The current leaves the battery with 1 5 V and takes one of two paths through a light bulb in which the voltage drops to 0 V A DMM would measure the voltage of either light bulb as 1 5 V 613 If a 6 V battery had been used instead of a 1 5 V battery what would the voltage drop across a single light bulb be 24 Section 2 circuit basics Remember that you measure voltage by using two DMM leads and placing the DMM in parallel with the component you are measuring Be sure your DMM is set to measure DC voltage so that the internal circuit of the DMM provides an enormous resistance Otherwise you may blow a DMM fuse or worse 2 1 Use your DMM to quickly measure the voltages of the following batteries if ava
119. lculating your prediction correctly and or making the measurement correctly 400 Q 2009 lt 7100 Q 10 Q d 2 4 Power the circuit from the previous problem Be careful not to use too large of a voltage or the resistors will become very hot Measure the voltage drop across each of the resistors in parallel What do you find and why 118 2 5 Measure the voltage across the 10 Q resistor Does this value make sense i e does it equal the total applied voltage minus the voltage across the parallel components 2 6 Measure the total circuit current How must the currents in each of the resistors above compare to this Measure each of the currents in the resistors and check that this is so Don t cut corners here or you will not do well on the lab practical 119 As more components are added to the circuit the problem solving becomes more complex Here you must solve for the total current Ipattery the total resistance Rota as well as the voltages across and currents through each of the components R34 Q R 2Q Ven First find the total equivalent resistance This must be done in steps 4Q 9V 19 is 40 9V Ra Ni Ra 9 V 120 2 e First collapse the first two parallel components R ar Tie 3 Q Then collapse R R 14 ar the two series components R R R aoe Q Since this is actually the total resistance of the circuit assuming an ideal battery which has zero internal resistance
120. ld make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the following page 232 8 1 hypothesizing planning 8 2 observations data 8 3 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 233 This page intentionally left blank 234 Week 10 Take Home Quiz Score ___ 5 THQ 1 1 point Which law of physics indicates that a changing magnetic field may induce a voltage in a circuit THQ 2 1 point What mathematical operation allows one to decompose a wave into its frequency components THQ 3 1 point What fundamental physics principle justifies Lenz s Law 235 THQ 4 2 points A single circular loop of wire of radius a 0 2 m encloses a sinusoidally oscillating spatially uniform magnetic field B 3cos 500r T Use d Faraday s law E t oe to calculate the induced voltage across the wire loop as a function of time t 236 Unit 6 Lab Report Instructions Unit Lab Report 40 points Use the following section titles in your report Images text or equations plagiarized from the internet are not allowed Remember to writ
121. line In today s lab we don t have any circuit components that cause phase shifts in their voltages i e capacitors or inductors These will be used in later labs Since both resistor voltages are oscillating in phase they will both reach zero simultaneously Thus they will trace a diagonal line that some experimentalists simply consider an ellipse viewed on edge 2 11 How does the height and width of the ellipse in your x y measurement relate to the voltage amplitudes across each resistor 144 Section 3 non ohmic diodes A diode is a one way circuit component If a potential difference is applied the wrong way across a diode it will act as an infinite resistance and not conduct electricity If a voltage is applied correctly across a diode and above a minimum value the diode will act with almost zero resistance and allow the current to flow through it This strange behavior is entirely quantum mechanical and non Ohmic This turn on effect is related to the band gap energy of the semiconducting materials the diode is made of Note that vacuum tubes perform a similar function to diodes and are not quantum mechanical in nature Create the powered diode circuit with a light emitting diode LED in series with a resistor On many diode boards the diode is already soldered in series with a 330 Q resistor Start using a very low source frequency so that you can see the LED blinking as current passes through the LED
122. lly a voltage that oscillates sinusoidally can be written as a time dependent function with time measured in seconds s V t 6sin 27 60 t volts where f 60 Hz 277 60 1 s and Vamplituae 6 volts If you are given the oscillating function V t 8 21sin 2250 r volts you should be able to find the various components V amplitude 8 21 volts 2250 1 s f 358 Hz and mT T 1 f 0 0028 s Imagine you have a 1 5 V battery and you put its voltage on the oscilloscope screen You will see a constant 1 5 V on the oscilloscope screen Y axis Voltage 0 5 volts per division X axis Time 1 second per division A division is one small square on the oscilloscope screen 133 Given the sinusoidally oscillating voltage V t 8 21sin 225 t this will appear on the oscilloscope screen as Y axis Voltage 2 volts per division PTT Tr Tr rN X axis Time 1 7 millisecond per division Note that the amplitude is 8 21 V so that the voltage on the oscilloscope screen is seen to reach slightly higher and lower than 4 divisions in the y direction This is because the oscilloscope is set to 2 volts per division Note that the period is 0 0028 s or equivalently 2 8 ms Thus on the screen you see one full wave appearing about every 3 divisions in the x direction This is because the oscilloscope is set to 1 millisecond per division 134 Week 6 Lab Oscilloscope Students Absolutely Mu
123. lopes of lines of best fit etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of the concepts and equations of this unit It is all right to sound repetitive with other parts of the report Open Ended Discussion 10 points 1 2 paragraphs 1 page double spaced Choose one of the open ended experiments from the two weekly activities to write about Describe your experimental goal and the question you were trying to answer Explain the ideas you came up with and what you tried If your attempts were successful explain your results If your attempts resulted in failure explain what went wrong and what you would do differently in the future You must write using sentences amp paragraphs bulleted lists are unacceptable Graphs 5 points attach to your typed report Graphs must be neatly hand drawn during lab on graph paper Your graphs must fill the entire page requires planning ahead include a descriptive title labeled axes numeric tic marks on the axes and unit labels on the axes If instructed to calculate the slope of the line of best fit write it directly on the graph Week 11 none Week 12 4 12 Take Home Quizzes 2x5 points 10 points attach after your Graphs Selected Worksheet Pages 5 points attach after your Take Home Quizzes Your TA will choose which pages you need to hand in 237 This
124. m This voltage that is created by the changing magnetic field is call the back EMF or the self induced EMF EMF stands for electromotive force which seems a very bad convention since it is really a voltage and not a force blame history The crucial point is that it is the rate of change of the magnetic flux that determines the amount of the voltage across the inductor solenoid Faraday s law does not specify whether the magnetic field flux producing the voltage is from an external source or from the magnetic field that the solenoid itself has created voltage e t where is the magnetic flux which has units of magnetic field times External Inductance Self Inductance R R soi Bincident VYQIO L An oscillating external B causes an Oscillating voltage source causes oscillating induced voltage induceg across the B inside inductor which induces a voltage inductor Einduced across the inductor If the magnetic field is from an external source like a radio wave that happens to travel through the solenoid then the induced voltage created across the solenoid could be used to detect the presence of the magnetic field The induced voltage will act like a voltage source and cause a current that can be measured If the magnetic field is created by the solenoid itself then the induced voltage created across the solenoid will oppose the voltage source of the circuit and the inductor will
125. m to zero so that conservation of energy is assured Check You should find that V O cure 6 V 7 8 V V 0 esis 6 V i 0 V V O capacitor OLV i 20 V VQ inductor OLV 412 V Added together gives VO ta O V i 0 V 281 This page intentionally left blank 282 Makeup Lab RLC Circuit using Phasors Students Absolutely Must Learn e Understand complex numbers written in polar form versus Cartesian form e Understand how the real component of a complex number can describe real voltages e How to use phasors for Vr Vc and Vu to predict the magnitude and phase shift of the source voltage e Advanced oscilloscope techniques Section 1 review sinusoidally driven RLC circuits In a circuit where an inductor resistor and capacitor RLC are connected in series and driven by a sinusoidal AC source the voltage across each of the components varies with time reaching a maximum and a minimum at regular intervals The properties of the RC circuit and RL circuit studied previously combine in a straightforward manner Combining the results obtained in previous labs we can measure the voltage across each component with respect to time as done below V Ct resistor R mplitude COS Dyiivel VD soure Voire COS Mprivel T Proure z amplitude a a V t capacitor Xc i T irpitade cos Darivel 2 V inductor XL 7 Te hitide cos Varivel 2 AR amplitude 2 2 1 where L mplitude a Z JR
126. marizing the procedure Write 2 3 sentences summarizing the results and what the results mean with regard to the concepts you were investigating It is best to write the abstract last o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Provide a description of the data you obtained such as data tables Restate any measured values calculated slopes of lines of best fit etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of the concepts and equations of this unit It is all right to sound repetitive with other parts of the report Do not write an open ended discussion Graphs 1 point attach to your typed report Graphs must be neatly hand drawn during lab on graph paper Your graphs must fill the entire page requires planning ahead include a descriptive title labeled axes numeric tic marks on the axes and unit labels on the axes If instructed to calculate the slope of the line of best fit write it directly on the graph Makeup lab 2 3 There is no take home quiz Selected Worksheet Pages 1 point attach after your graph Hand in all your makeup lab worksheet pages 278 Makeup Pre Lab RLC Circuit using Phasors Phasors are vectors in the complex plane used to repr
127. mp 3 4 Which component of your circuit is known to be ohmic 146 3 5 While the circuit is in operation if you know the voltage across the resistor and its resistance what can you find Your answers to the previous questions should help you understand that you need to measure the voltage across the resistor in order to find the current through the resistor Therefore you need to create the Vr VS Vapplied graph and turn it into the Iren vs Vappliea graph simply by dividing the y values by the resistors resistance AVR llep a non Ohmic graph R AV AV onii applied applied many various many various applied V s applied V s VeurN ON 3 6 Make measurements to obtain the first graph and use it to calculate and create the second graph Finally your measurements allow you to experimentally obtain the quantum mechanical property of the material the turn on voltage so record this value below Note that due to the direction the diode is soldered into the circuit some students may have inverted readings on the oscilloscope You may simply uninvert this on your graph paper Note Techincally the voltage drop across the LED increases as it grows brighter This is why the slope isn t exactly a constant 1 R 147 Section 4 authentic assessment 4 1 Quickly set up a working circuit of a resistor powered by a sinusoidal voltage at 100 Hz and measure the current amplitude through the resist
128. mutual inductance Use a function generator to drive a solenoid in series with a 10 ohm resistor Use a sinusoidally oscillating source voltage of 5 volts amplitude This solenoid is the transmitter As the current oscillates in the solenoid s wire an oscillating magnetic field is created inside the solenoid due to Ampere s law Hook up the other undriven solenoid directly to the oscilloscope This solenoid is essentially the receiver It will detect the presence of changing magnetic fields just as you saw in section 3 Place the solenoids together as close as possible so that you can measure the maximum induced voltage amplitude in the receiver Placing soft iron inside the coils can increase the magnetic field inside the solenoids so that transmission is increased this is done in most transformers including the giant transformers in power lines 4 1 Make the single measurement to experimentally determine the mutual inductance M of your two combined solenoids Record data and make calculations below 224 Section 5 finding the self inductance Self Inductance The logical flow of ideas is e The oscillating voltage source causes an oscillating current in the circuit and solenoid e The oscillating current inside the solenoid wire causes an oscillating magnetic field inside the solenoid coils e The oscillating magnetic fields cause a changing back EMF across the solenoid This is shown graphically for an oscilla
129. n LED each have energy roughly equal to the band gap energy of the semiconductor Laser diodes are conceptually similar to LEDs and have led directly to the digitized age of music More and more electrical engineering programs requiring their majors to gain a firm understanding of quantum mechanics Not a question 136 Section 2 time dependent voltage on the oscilloscope The following picture shows the digital oscilloscope and labels its most common features screen menu calcs amp info menu buttons shows 0 volts for each channel cursor control measure cursor triggering contro usual channel controls You now need to practice using the digital oscilloscope so that you are prepared to make measurements with it Keep in mind that the oscilloscope is simply a tool that allows you to analyze the details of a rapidly changing voltage With that in mind you will now practice the more common measurements that are made as well as their uses Your TA will most likely have demonstrated how to use it at the beginning of lab but each student will forget different features at the beginning stages so work together and ask lots of questions 137 2 1 Hook the two output leads of your function generator to the two leads of channel 1 of your oscilloscope Use the oscilloscope to examine the voltage vs time graphs of many different sine waves square waves and saw tooth waves created by the function generator o
130. n reports O Throughout the semester students write six biweekly unit themed lab reports using general and specific writing guidelines Though a revision editing process is untenable students will be given their first graded report in advance of the due date of their second report so they can learn from mistakes discuss alternate writing strategies with the TA etc 295 Graduates of the introductory electricity amp magnetism laboratory should e Have a broad education that will allow them to succeed in diverse fields such as business law medicine science writing etc O Writing skills critical thinking skills creative problem solving skills communicating ideas amp information teamwork skills leadership skills working with time constraints e Have mastered the introductory theoretical techniques and electricity and magnetism experimental techniques that are commonly expected for students at this level Across the world all introductory electricity and magnetism students must be able to O O Apply Gauss s Law to find the electric field Wire circuit components in series and parallel Use a DMM to measure current voltage amp resistance Reason about global circuit properties based upon the arrangement of the components Understand polarization use the process of induction use an electrometer and Faraday ice pail and calculate the attractive electrostatic force caused by polarization Understand how an e
131. n the vertical direction D k 7 a what you would see on the CRT screen if the accelerating voltage was increased Explain why this would happen using a physical argument i e not using math Your answer and explanation 101 Section 2 testing the cathode ray tube equations V 5x V adjusting Vax and observing Dx If all goes well you will be able to find an experimental value for the x geometrical constant without breaking the CRT open to measure it by hand 2 1 Use tape on screen to mark position of electron beam when there is NO DEFLECTION Vax set to zero to find the origin of the CRT Be sure to record V and keep this value constant for the rest of this section V is the sum of Vg and Vc on the CRT power module and should be set as high as possible while the scintillation dot is still in focus Record your constant accelerating voltage V You will now experimentally test the horizontal CRT deflection equation D k by G 2 2 Adjust Vax on the horizontal plates and mark D on the tape for several values of Vax make a data table with at least 5 data points Record your data table of Vax and D 2 3 Create graph of D vs Vax by hand Graph D vs Vax on graph paper Your data should give you a straight line d 2 4 Measure the slope of the line of best fit Since D k ns a the slope will equal k a so multiply by V to obtain k Record your result for k here in SI
132. nce 1 4 Place a solenoid in series with a 100 Q resistor and drive this simple RL circuit with a sinusoidal source voltage with 10 Hz very slow and 5 volts source amplitude Set your oscilloscope to measure the voltage across the resistor Find how much current is flowing through the resistor and therefore the solenoid the current amplitude 215 1 5 Qualitatively examine what happens to the current in the solenoid by examining resistor voltage as you increase the driving frequency from 100 Hz to higher frequencies Your observations The impedance y of an inductor is found to be vy where L is the self inductance parameter of the solenoid and Qgrive is the angular driving frequency The total circuit impedance without a capacitor is given by Z 4 R y The total circuit impedance Z has units of ohms for a reason it acts as the total resistance of the circuit and thus can be combined with the V source amplitud source voltage to determine the circuit s current I jimae eme amplitude Z i 1 6 V source amplitude Z angular driving frequency griye Was increased This is another way to think about question 1 5 Since anpiitude explain how the current would change if the 216 1 7 Now using the same circuit as the previous questions set up your oscilloscope to measure the voltage of both the resistor and inductor using a middle ground configuration with one channel
133. nd Eq causes a deflection in the horizontal direction In the CRT figure below draw arrows correctly depicting the direction and magnitudes of these fields Do you best to draw E in the three dimensional picture 1 7 Now examine a pair of charged deflection plates see figure The voltage difference between the plates is Vay Assume the plates are separated by a distance d Assume Va is positive 0 Volts 96 1 8 Find the magnitude and direction of the electric field between the plates E in terms of d and Vay ignore any edge effects Your answer 1 9 Determine the acceleration a felt by an electron inside the space between the plates using e m and E Your answer 1 10 Now examine what happens when an electron enters the space between the vertical deflection plates see figure coordinates y X If the electron enters with a velocity in the z direction of v and travels the length of the plates w how long does it take for the electron to reach the other side At Write your answer for At using w and v Your work and answer 97 1 11 Explain why this time At is not affected by the acceleration in the y direction caused by the deflection plates Your explanation 1 12 As the electron traverses the space between the deflection plates it is accelerated in the y direction y Using the kinematics equation Ay 1 2 a At to find vertical displacement Ay of the
134. nergy landscape produces forces or equivalently how an electric potential landscape produces electric fields and use voltage measurements to calculate an electric field Calculate how voltages accelerate charged particles and carry out a long and complex mathematical derivation Understand how to analyze a circuit built from Ohmic components and build Ohmic circuits and measure their properties Use an oscilloscope to measure rapidly changing voltages build circuits and measure their properties Use a digital oscilloscope to investigate RC circuits driven with square waves and sinusoidal waves Use a digital oscilloscope to investigate RL circuits driven with sinusoidal waves Use a digital oscilloscope to investigate RLC circuits and radio transmission principles Design simple radios e Be familiar with the principles and practice of engineering and should be able to apply their knowledge to solve state of the art problems both individually and as part of a team O O Individuals must be able to Makea light bulb work Use a compass to label the poles of a magnet Measure voltage to find an electric field Predict the behavior of moving charges in a magnetic field Build and test simple circuits Build a working motor Build a resonating circuit to detect ambient radio waves Teams must devise an experiment to Measure the equivalent resistance of parallel components 296 Measure the macroscopic charge s
135. ng it 2 8 A student is asked to change the amplitude of a voltage source and begins to push buttons on the oscilloscope Why is the student s TA disappointed amp 29 A student is analyzing a working circuit and is asked after to measure some other feature of the circuit The student starts turning knobs on the function generator Explain why the student s TA is yelling in a panicky voice Hint the phrase ruined the previous measurements should appear in your answer 162 Section 3 examining fast RC circuits with an oscilloscope Most digital electronics make extensive use of capacitors However the decay rates are typically much too rapid to measure with a DMM In this part of the lab you will create an RC circuit using a 0 1 uF capacitor and a 1 KQ resistor and you will rapidly charge and discharge the capacitor with an oscillating square wave 3 1 Calculate the time constant t that an RC circuit using a 0 1 uF capacitor and a 1 kQ resistor produce 3 2 You should choose a period of 207 or rather a frequency of 1 20t Hz so that there is plenty of time for the capacitor to discharge fully Calculate this frequency 3 3 Set up the RC circuit shown below powered by a 0 V to 3 V square wave at the frequency you calculated in the previous question with R 1 kQ and C 0 1 uF Use your function generator to create a square wave with a voltage alternating between Vym 0 V and Vmax 3 V by f
136. ngle charge to understand why a charge attracts a polarizable molecule 10cm Calculate the attractive net force in newtons between the upper charge and the dipole beneath two rigidly connected opposite charges It is 10 cm to the midpoint of the dipole so add or subtract 0 5 cm for distances Note that e 1 6x10 C and kg 9x10 N m C 66 Unit 2 Lab Report Instructions Unit Lab Report 40 points Use the following section titles in your report Images text or equations plagiarized from the internet are not allowed Remember to write your report alone as collaborating with a lab partner will make you both guilty of plagiarism Please label your lab report sections Title 0 points A catchy title worth zero points so make it unique and fun Mini Report 10 points 4 6 paragraphs 2 double spaced pages Choose one of the following sections about which to write your mini report Week 3 Section 2 or Week 4 Section 2 Write a mini report for one particular section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable Please label your mini report sections o Abstract Write 2 3 sentences about the goals of this section Describe the concepts you were investigating and how the experimenta
137. ns can be given enough energy to escape the valence band and move into the conduction band And so you may now guess at how semiconductors provide us a way to create digital electronics that is electronics that is either on or off 1 or 0 With semiconductors we either 135 provide enough voltage to allow them to conduct electricity on or 1 or we don t apply a voltage and the semiconductor cannot conduct electricity off or 0 The most important property of a semiconductor is the minimum distance between the valence and the conduction band because this represents the amount of energy needed to turn on the semiconductor and enable to conduct electricity This is called the band gap energy 1 1 If the temperature is low so that each electron in the valence band of the semiconductor has an average kinetic energy much less than the band gap energy explain whether the semiconductor acts as a conductor or insulator Gq 1 2 Imagine that an external voltage source is applied across the semiconductor so that each valence electron has more kinetic energy Approximately what must the applied external voltage be in order for the semiconductor to transition from an insulator to a conductor Hint energy equals charge times electric potential Diodes are layered semiconductors and in a simple circuit act as one way components Light emitting diodes LEDs have a myriad of practical uses The photons emitted by a
138. ns conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 208 Week 9 Take Home Quiz Score 5 THQ 1 5 points Make your motor work for a non physics person parent friend English major etc and have them sign the below affidavit confirming that they saw your motor working However you do not need to have the affidavit notarized Show a non physics person that you can successfully build a working motor Note if someone is stuck please get advice from another student Yes I have seen this student build a motor that successfully runs on electrical input power I am considering getting one myself Non physics person signature 209 This page intentionally left blank 210 Week 10 Pre Lab Solenoids A current carrying wire creates a magnetic field around the wire This magnetic field may be u I dsxr zn r If there is a high degree of symmetry you may choose to find the magnetic field produced by the current carrying wire using Ampere s Law fB eds u1 whole o Ampere s Law simplifies finding a magnetic field in the same manner that Gauss s Law simplifies finding an electric field Examine the ideal solenoid also called inductor where a very long coil of wire carries a current I is found to have a nearly uniform magnetic field inside the coils and a nearly zero magnetic field outsi
139. object 8 d object mgd f onenviron mert travels But mgh is the familiar formula for gravitational potential energy so we know we are doing things correctly 202 Of course I through Or Vos may not be constant as the motor operates but we can treat these motor motor as average values for now Also the motor will not always be able to make contact through the wire brushes so that current does not flow to the motor at all times If the motor is only in contact with the source for 30 of the time then Poo 0 3 Daal input hrough across power motor motor The oscilloscope in the lab is very useful in determining what percentage of the time current is flowing through the motor 2 1 A motor is on 50 of the time at 4 V and 0 03 A It lifts a 0 02 kg of paper clips upward 0 8 m in 6 s Calculate the electrical power going into the motor the power output by the motor as work and the power lost as friction In order to measure the current through the motor a rather imprecise value is obtained from the power supply readout A much better value for the current may be obtained by placing the motor in series with a 1 Q resistor and using the oscilloscope to find the current through the resistor and therefore the motor Remember to get the current in the resistor by measuring voltage and dividing by R The efficiency of the motor is given by lt If the motor is made to lift objects fficiency input
140. ocedure Write 2 3 sentences summarizing the results and what the results mean with regard to the concepts you were investigating It is best to write the abstract last o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Provide a description of the data you obtained such as data tables Restate any measured values calculated slopes of lines of best fit etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of the concepts and equations of this unit It is all right to sound repetitive with other parts of the report Open Ended Discussion 10 points 1 2 paragraphs 1 page double spaced Choose one of the open ended experiments from the two weekly activities to write about Describe your experimental goal and the question you were trying to answer Explain the ideas you came up with and what you tried If your attempts were successful explain your results If your attempts resulted in failure explain what went wrong and what you would do differently in the future You must write using sentences amp paragraphs bulleted lists are unacceptable Graphs 5 points attach to your typed report Graphs must be neatly hand drawn during lab on graph paper Your graphs must fill the entire pa
141. on of the defined current Your answer to the previous questions should show the electrons moving in the opposite direction from the electric field The defined current would be in the same direction as the electric field 36 Section 6 authentic assessment A popular video shown to education majors has an interviewer approaching students during graduation at Harvard and MIT The interviewer provides a light bulb a single wire and a battery Very many of the graduates could not make the bulb light They were most likely not engineering majors This video is supposed to teach teachers that simple concepts can be misunderstood despite expensive training Not on our watch You never know where these video makers might come next so we must be prepared Use a single wire a 1 5 V battery and a small bulb and make the bulb light up If you are uncomfortable having another student check your work please ask your TA 6 1 Show a student in a different group that you can successfully light a bulb with a wire and a battery Once you are successful and have them sign below Note if someone is stuck please give them advice Yes I have seen this student light a bulb They are well prepared for surprise interviews Student Signature 37 Section 7 open ended Listed below are several formulae for finding a total resistance for two resistors combined in parallel Most of these formulae are wrong You need to find the correct formul
142. oncept of steepness of the voltage landscape to explain the difference of these electric field strengths 77 In the laboratory we find is easiest to use a voltmeter to make measurements of the electric potential using a DMM However this gives us values and not formulas for V so that we are not able to find E by taking partial derivatives of V We must have a way of estimating E in the lab from voltage measurements This technique will be illustrated using the following problem The following picture shows that a student has used a DMM to construct two equipotential voltage lines and wishes to find the electric field at some point between them V volts XN gt V 5 volts n Ri a S 1 First we draw an estimate of the best electric field line component that lies between the two equipotential lines and measure its distance d V volts N V 5 volts N TE St E 7 x s s d 2cm Next we approximate the magnitude of E using differences in place of derivatives _ 2 V lz x av 100 This gives the magnitude the size of the hypotenuse and now Ad 0 02 m we must break it up into components to get the electric field as a vector 78 must be estimated or y measured with a protractor 750 to calculate the legs x and Y components of E 60 45 100 Vim 57 Vim 30 J 9 39 82 Vim 15 10 Now notice that for this
143. onest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc 5 1 hypothesizing planning 5 2 observations data 5 3 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 149 This page intentionally left blank 150 Week 6 Take Home Quiz Score 5 THQ 1 3 points Which would be the best choice for time steps At when graphing V t 8sin 5 000 t volts with time measured in s in order to observe 3 10 oscillations on the graph below V t 5 151 THQ 2 2 points red 1 red 1 red 2 middle inverted ground 200 Q 200 Q Which method is better for measuring the separate voltages of two components simultaneously middle ground or bottom ground 152 Unit 4 Lab Report Instructions Unit Lab Report 40 points Use the following section titles in your report Images text or equations plagiarized from the internet are not allowed Remember to write your report alone as collaborating with a lab partner will make you both guilty of plagiarism Please label your lab report sections Title 0 points A catchy title worth zero points so make it unique and fun Mini Report 10 points 4 6 paragraphs 2 double spaced pages Choo
144. or Actually you can only measure voltage with an oscilloscope so you must do this by measuring the voltage drop amplitude across the resistor and applying a V amplitude special amplitude version of Ohm s law 7 Do Actually Ohm s law amplitude is valid for any point in time so it must hold at the instant when the current and voltage reach their maximums amplitudes Show your results to a student in a different group If you are uncomfortable having another student check your work please ask your TA Yes I have seen this student use the voltage measurements of an oscilloscope to obtain the amplitude of the current through a resistor In other words they know how to find the voltage amplitude and divide by the resistance Student Signature 148 Section 5 open ended Prove that a grain of wheat light bulb is non ohmic because of heating affects by examining the correct graph on the oscilloscope You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on h
145. or and capacitor in parallel and drive them sinusoidally see above figure What electrical possibilities might this new compound device hold for the future of mankind Well use your anachronistic oscilloscope to find out Try to deduce why this circuit may be said to have an antiresonant frequency a different kind of effect on the circuit current You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the next page 254 6 1 hypothesizing planning 6 2 observations data 6 3 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 255 This page intentionally left blank 256 Week 11 Take Home Quiz Score 5
146. ork please ask your TA 6 4 1 Record the kinds of stations you find Yes I have seen this student use an RLC circuit to find invisible sound carrying light waves We then rocked out to some jamming tunes Student Signature 273 Section 5 open ended Imagine that you are about to finish a very long semester of electricity and magnetism labs and that all you have left to do is a single open ended creative design question Using two of the large 1 H solenoids stored in the corner of the room create your own radio station Specifically find a way to transmit unmodulated sound waves from one solenoid through the air and listen to the sound using a second solenoid not connected in any way to the transmitting solenoid Decide on what pitch to broadcast using theoretical predictions based on the numerical values of the components you have on hand Points are awarded for loudness not really At the following prompts design an experiment to loudly broadcast unmodulated sound waves using two large solenoids among other electronics components Then implement your experiment and record your observations You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using thes
147. ou are prepared to make measurements with it Keep in mind that the oscilloscope is simply a tool that allows you to analyze the details of a rapidly changing voltage With that in mind you will now practice the more common measurements that are made as well as their uses 160 2 1 Hook the output of the function generator directly to one of your oscilloscope channels and be sure the other channel is shut off Create a sinusoidal wave with your function generator with a very small voltage i e use a special feature of the function generator and a frequency in the 1 100 kHz range Use the autoset button to quickly get your signal on the screen so you can adjust your function generator DC offset correctly Be sure that your channel is on 1x probe and that your trigger is set to the correct source Do this now and check you work by interacting with students in other groups No response necessary 2 2 Use the oscilloscopes measure feature to determine the average voltage of your sine wave Be sure to have about 7 10 full oscillations appear on the oscilloscope screen as the oscilloscope measure feature actually uses the screen for its data and too few oscillations will create error in the averaging Record your measurement here 2 3 Get the digital oscilloscope to tell you on its screen the wave s period and frequency using the oscilloscope s features Record your measurements here d 2 4 Get the digital oscilloscope
148. ou must write using sentences amp paragraphs bulleted lists are unacceptable Graphs 5 points attach to your typed report Graphs must be neatly hand drawn during lab on graph paper Your graphs must fill the entire page requires planning ahead include a descriptive title labeled axes numeric tic marks on the axes and unit labels on the axes If instructed to calculate the slope of the line of best fit write it directly on the graph Week 5 1 2 1 3 Week 6 3 5 two graphs Take Home Quizzes 2x5 points 10 points attach after your Graphs Selected Worksheet Pages 5 points attach after your Take Home Quizzes Your TA will choose which pages you need to hand in 111 This page intentionally left blank 112 Week 5 Pre Lab Vulture Iguana Rabbit The resistance of a circuit component is the voltage drop across the component divided by the V SORE current flowing through the component R T If a circuit component has a high resistance it will require a larger applied voltage to obtain a desired current through the component Note that even though a 12 V car battery can deliver a great deal of power it will not light a household light bulb which has a high resistance designed for the much higher 120 V household voltages Imagine you are in the desert and there is a vulture flying in the sky and a rabbit and an iguana walking on the ground The rabbit sees the vulture flying over the iguana This i
149. p Lab near the end of the semester Therefore you may only makeup lab at most If you are writing your biweekly lab report and you have been absent 1 week then you may only earn 75 of the possible lab report points 30 out of the total possible 40 If you have a valid and documented excused absence completing the makeup lab and writing the report for it will allow you to earn the remaining 10 points for the unit during which you were absent as earn the 5 points for the beginning of lab quiz that you were absent for When you are writing your biweekly lab report and you have been absent 1 week then e Write the Mini Report using the section for which you were present e Write the Open Ended Discussion using the open ended activity for which you were present e Attach the graphs you created for the week you were present e Attach the Post Lab Quiz for the week you were present e Attach the Selected Worksheet Pages you completed for the week you were present For the makeup lab report you will need to Write a Mini Report Do not write an Open Ended Attach the graphs you create for the makeup lab Attach the Take Home Quiz for the makeup lab Attach all the Worksheet Pages you completed for the makeup lab 15 Unit 1 Lab Report Instructions Unit Lab Report 40 points Use the following section titles in your report Images text or equations plagiarized from the internet are not allowed Remember to write your report alone as
150. particular coordinate system the x component points in the negative direction along the x axis and the y component points in the negative y direction so that the final yi m electric field vector is given by E 822 579 1 5 In the following picture depicting labeled equipotential lines calculate the electric field at the marked point Be sure to find Ey and Ey and write your final answer in vector notation Show your calculations in the space next to the picture a protractor is provided above ee Pa rs V 6 volts ka TI _ S F p V 4 volts s P oy r Ma gaT aiii Sy H f 2 7 r ig M I 1 1 wi ge a N N N E 4 Cyn SS va I A ry sy 1 to i 2 vfs 1 1 4 I I 1 l L1 r 3 1 I 11 Pa sa SN W 0 volts Pi Pus oN Y S m ca Si as s 2 1 4 Sa sa a NM 2 volts 242l 222 ee aa pa 7 x upia 7 ee TYm ia ee em a o m Cai ee oo W pE 79 Section 2 2 D electric fields on conductive paper Do not write on the conductive paper especially with pencil because the graphite conducts as well as the paper and thus ruins it Erase any pencil markings you see The above picture shows two point charges with 10 volts of electric potential difference between them The dotted lines represent lines of constant voltage For instance all points on the dotted line to the
151. power vertically then the output power can be found via the force of gravity AE out ut E awu MgA so that P aou mg output ooy z At At 2 2 Calculate the efficiency of the motor from the previous question 203 Speed of Rotation The rotational speed of a motor is typically measured in revolutions per minute RPM You will need to use the oscilloscope to find the time of one full oscillation the period turn this into frequency and finally into RPMs Use simple factor labeling to do this 1 1 i il cycles feo SS 60 2 or 60f ead or 60f RPMs seconds 1 minute minute minute 2 3 A motor turns once in 0 02 s how many RPMs is it rotating at Observing the Motor Parameters The easiest way to observe the behavior of the motor is with a middle ground measurement between a 1 Q resistor and the motor in series This will provide the following graph on the oscilloscope screen though it may take some effort to find the correct time scale The percent of time that the motor is on is simply t t2 T Using the run stop button to collect data from the oscilloscope is useful for this because the triggering will be very sensitive and the will continuously lose the signal Vinge on on on on off off off off off t Vmotor on Le yp t tz V riiit th V resistor on 204 2 4 In the previous picture why is the voltage across the motor equal to the source voltage when the motor is off Yo
152. r charge transfer between the rod and insulator or both 48 G 2 2 Draw a series of pictures cartoon with explanatory text explaining why the insulating material sticks to the rod Use the concept of microscopic charge separation dipoles Show plus minus signs to signify where excess charges have accumulated or dipoles to signify how charges have microscopically separated If you do not know whether the excess charge on the rod is positive or negative then assume it is negative Cartoon Frames Subsection B A silver coated pith ball i e a conductor has virtually no mass so we can easily see how it reacts to charge Note that it is basically a piece of round cork covered in silver to become a conductor pith ball conductor When a charged object approached the pith ball conductor the pith ball is at first attracted to the charged object 49 Gy Initial attraction However when the pith ball touches the charged object it immediately becomes repelled by the charged object Gy repulsion after touching 2 3 Take the charged glass rod and slowly bring it near the pith ball Make observations of the behavior of the pith ball If you do not observe the repulsive feature of the pith ball activity then your pith ball may not have enough silver paint on it and is therefore not a good conductor In this case find another lab group that has a nicely conducting silver painted pith ball Write your obser
153. r sheet of regular graph paper use differences to approximate and graph Ex x 0 vs x Use your previous voltage graph along the line of symmetry y 0 This requires calculating the electric field in the x direction only for points along the line of symmetry but this is alright since E 0 along this line due to the symmetry of the system Make a copy for both lab partners An example is shown below answer on separate graph paper V x 0 x cm iel ZAV 0 10 _ 3 _ 159 V m y vields Ax 05 03 02 E x 0 150 o amp 75 0 x cm 84 Section 3 connecting the concepts of voltage and electric field 3 1 Find and draw the equipotential lines for the parallel plate conductive paper two long bars of silver paint and sketch them on graph paper using dashed lines Find at least five equipotential lines between the plates Be sure to find the potential in each region outside the parallel plates This should take only a few minutes Make a copy for both lab partners answer on separate graph paper 3 2 Fill in V and x in the below table using the data you just obtained Compute AV and Ax and use these to find the electric field which may be in the positive or negative x direction depending on which plate was grounded AB C DE point V AV X Ax E gt migoulin w 3 3 What do you notice about the strength of the electric field e
154. r the plate set to 0 V Four equipotential lines are shown between the plates as dotted lines Note that they are parallel and equally spaced The electric field points down the voltage hill from left to right Several arrows have been drawn to show the electric field Note that they are all the same size and direction indicating that the electric field is constant and uniform between the conducting plates 10 V 8 V 6 V 4 V 2 V OV t x cm 0 2 4 6 8 10 The electric field between the plates can be calculated using any two data points Points at A and B have been chosen at random The electric field calculated using these two points is using meters for distance E x x 100 Ad 0 06 0 04 0 02 gt ZA aa 4 6 2 N m 76 Now examine what happens when the distance between the plates is reduced by half 10 8642 OM The equipotentials are still parallel and equally spaced The electric field is still constant and uniform between the plates but the arrows are drawn twice as long to indicate that now the electric field is twice as large as before Let s check this using the points A and B that have been shifted from their previous positions et Ms ie ae 200 Ad 0 03 0 02 0 01 g m lest D gt 1 4 In each example the plates are electrified with the same electric potential difference of 10 V and yet their electric field strengths are very different Use the c
155. rce voltage at any instant in time if the voltage amplitude of one increases then the other must decrease Therefore there must be some specific driving frequency when the amplitude of the resistor voltage matches the capacitor voltage Visor Veapacitor fOr a specific angular driving frequency amplitude amplitude D match ea R Xe Realizing that Kiir F V sire and V apieitor Vane gt setting these two voltages equal amplitude Z amplitude amplitude amplitude R ho X when at the matching angular driving frequency p match you get E V pure Veoune Which Z amplitude Z amplitude simplifies to Xo R In other words the voltage across the capacitor equals the voltage across the resistor if their resistances are equal which kind of makes sense If not talk it out with other students or the TA The single measurement method for finding the capacitance of an unknown capacitor makes use of the previous equation Xo R All you need to do is adjust the driving frequency of your circuit until the capacitor voltage amplitude and the resistor voltage amplitude are equal Then te 1 she use Xo R substituting X for the specific p match to find the capacitance D match 179 2 2 Substitute X into X R and then solve for C Be sure to realize Mp match that this equation is only true when the circuit is being driven at the specific frequency p quar that makes the resistor and
156. rcuit resistance and total circuit current Then calculate the current through the 3 ohm resistor 3V 124 2 10 Calculate the total circuit resistance and total circuit current Then calculate the current through the 3 ohm resistor 3V 1Q 2 3Q 1Q 22 2 11 Calculate the total circuit resistance and total circuit current Then calculate the current through the 3 ohm resistor 3V 1Q 2Q 2 12 Would you have predicted that the total current for the last two circuits would be so different Explain why the addition of the single 1 Q resistor in the fourth circuit increases the total current by almost 300 Your answer and explanation 125 Section 3 the internal resistance of a DMM Your DMM has a very large internal resistance Sometimes it is important to know this value because if you try to measure circuits with comparably large resistances the DMM begins to carry an appreciable part of the circuit current throwing off measurements For example in the following picture a DMM is used to measure the voltage across a resistor Consider what happens if the internal resistance of the DMM is near to that of R It behaves like any resistor by letting current flow through it which we don t want because the DMM is then part of the circuit Since DMM actually measures voltage by determining the current flowing through it a false reading is obtained We can find the internal resistance of the DMM by deriving
157. reat each parallel set of resistors as a single equivalent resistor R 2 Q L V3 Riotal 5 ohms otal liie 2 amps V V 8 volts I 1 1 amp 10V R 8Q V V 2 volts Ipattery L V I I amp 122 Here is an example where you must solve for total current Ipattery total resistance Reguivalent as well as the voltages and currents in each of the components R 4 Q Requivatent First find the total equivalent resistance This must be done in steps First collapse the first two parallel components R o Then collapse this with R3 R TE fa R R fig te Finally collapse these with the remaining R4 R move Ry Ri Ta With the total resistance you may use Ohm s law to find the total current V aiie 99 sae 99 Battery Amps This is also the same current as in R4 J Amps You can now Resective 50 find the voltage across R4 V R 1 Volts Now note that R R and R are in parallel so that V V2 V3 conservation of energy in loops Subtract V4 from the total voltage to find the voltage across each parallel component Vi V V Seen a Volts 25 25 2 2 Now you can easily find the current in each component J lt lt Amp 5 el ii S 1 2 and ale AR Ry 75 3 123 2 8 Calculate the total circuit resistance and total circuit current Then calculate the current through the 3 ohm resistor 3V amp 29 Calculate the total ci
158. rges repel and unlike charges attract How the process of charging by induction works How to design and conduct an experiment to address an open ended question Check that your compass is aligned correctly with the Earth s magnetic field If it is not remagnetize it with a block of powerful magnets or get your TA to help Use your compass to check the labeling of any magnets provided to you Students in previous labs often remagnetize soft iron magnets If your magnet s is magnetized incorrectly get your TA to help you fix it by tapping it while in a strong magnetic field or while a strong DC current moves through it there may be a remagnetizing device in the lab Section 1 magnetism LS Unmagnetized iron filings before being placed in magnetic field 4 lt l 45 1 1 Sketch the magnetic field produced by a bar magnet by placing it underneath this worksheet and sprinkling some iron filings onto the top of your page The flakes will show you the field lines but you will need to sketch the direction of the field lines by identifying the magnetic poles using your compass Don t let the magnet under the paper touch the filings or things will get messy The magnetic field lines for opposing magnetic poles demonstrate the repulsive force between them 46 1 2 For the following double bar magnet arrangements in the following figure predict the magnetic field lines by sketching what you think they will look li
159. rt Graphs must be neatly hand drawn during lab on graph paper Your graphs must fill the entire page requires planning ahead include a descriptive title labeled axes numeric tic marks on the axes and unit labels on the axes If instructed to calculate the slope of the line of best fit write it directly on the graph Week 3 2 1 to 2 5 one graph 3 1 4 1 to 4 2 one graph Week 4 2 3 2 7 2 11 Take Home Quizzes 2x5 points 10 points attach after your Graphs Selected Worksheet Pages 5 points attach after your Take Home Quizzes Your TA will choose which pages you need to hand in 67 This page intentionally left blank 68 Week 3 Pre Lab Electric Field Mapping Read the following short pre lab upon which you will take a quiz at the beginning of lab A graph of the potential energy for an object shows the forces it experiences since the object will seek to roll downhill to the position of lowest potential energy The steeper the slope the stronger the force pushing the object downhill U x y potential energy dotted lines show constant energy U x potential energy D Fer to right A stable equilibrium A B C unstable Equilibrium Fyer to right and forward B Fyer to left one dimensional two dimensional A charge creates an electric field around it This electric field can be described by drawing vector arrows around the charge with the
160. rt of the phasor to describe a sinusoidally oscillating voltage Real WV t Vz cos t Each of the component voltages in a sinusoidally driven RLC circuit may be described with phasors V t el Parivel Brite i V t Voua amplitude V a Marivel ji resistor resistor msistor m Parive ty l V t V lowers V t capacitor capacitor inductor _ V inductor e amplitude amplitude Imaginary Note that adding the complex phasors is equivalent to adding all the voltages of the circuit The sum must equal zero snitt is negative in the above example 280 Pre Lab Practice Questions R ohm V source C fa rad L henry A sinusoidally driven RLC circuit has a frequency of f 1 100 Hz or s and a source voltage amplitude of V o 10 V The SJ o 27f 6912 components are chosen so that at this frequency R 3 Q 7 10 Q v7 6 Q and thus Z R y 7 5 9 ies R This gives Vp V e 6 V Ve V n 20 V and Z amplitude i Z anplitude V o V oue 12 V LO aE z source Z amplitude It also indicates that g arctan Z7 e 0 93 radians 53 1 Thus V t oue 10e 6217 023 7 i V VO 6e 1ni V V 20 em V 20 9125 t capacitor e V t inductor e V Decompose each of the four circuit voltages into real and imaginary components for t 0 s Then check that the sum of the real parts equals zero and separately the sum of the imaginary parts su
161. s electrical friction When someone knows the proportionalities of a variable they can write an equation for that variable with an unknown constant R pa Here the resistivity p is a constant of proportionality relating the total resistance of a wire to its length and area Find the resistivity of Nichrome wire Vv Across SECTION L You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the next page 129 5 1 hypothesizing planning 5 2 observations data 5 3 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 130 Week 5 Take Home Quiz Score 5 THQ 1 5 points 10 6V 1Q 1Q a What i
162. s a pneumonic Vulture Iguana Of course the ee f V device to remember the definition of resistance R T gt Rabbit sees vulture sees the iguana on the ground with the rabbit V IR and the iguana sees the vulture l V flying over the rabbit J rs Please never get these equations wrong on a test AV a For an ohmic resistor the equation R implies the resistance is the same value no constant for ohmic do ee matter what voltage is applied and the current changes with voltage to keep the ratio constant It should be noted that resistance of a material often depends on its temperature Since a light bulb gets hotter as more voltage is applied across it the light bulb s resistance grows with its brightness So a light bulb definitely is non ohmic Ohmic resistors have a constant ratio of current to voltage so data collected at different applied voltages or different applied currents depending on how you run your experiment will provide lines with constant slope I V Real batteries have internal resistances that affect their performance by decreasing their effective voltage For example if you take a 1 5 V battery and attach a 0 000001 ohm resistor like a wire you will NOT obtain a 1 500 000 amp current As the battery tries to supply a large current it will heat up and its internal resistance will grow thereby lowering the voltage supplied to the resistor until only a small voltage
163. s kinetic energy to the accelerating voltage V of the apparatus use V q and AK Be sure to check your answer with other students or your TA Your formula 1 3 Write a formula that describes the final velocity of the electron if it starts from rest and you know the work done on the electron use vt me Va and q Be sure to check your answer with other students or your TA Your formula 1 4 Explain what the sign of the accelerating voltage difference V must be in order for your formula in 1 A 2 to make sense Reconcile this with your knowledge of how negatively charged particles respond to an electric field Your explanation 94 1 5 Now try out your formula using some numerical values If the electron starts at the position x 0 on the following graph find out the speed of the electron once it has reached the area of constant electric potential Remember that electrons flow upward in the voltage landscape You should use the electron charge q 1 60x10 C and the electron mass m 9 11x10 kg Your calculations and answer in SI units Va x 95 Now you know how to find speed of the electrons after they are initially accelerated you will study how the electrons are deflected by the charged deflecting plates 1 6 There are three electric fields affecting the trajectory of the electron E accelerates the electron initially to a high speed E4 causes a deflection in the vertical direction a
164. s sphere creates a large electric field around it that will affect any nearby spheres including those of your neighbors With a second grounded sphere nearby initially uncharged you will use the metallic paddle and Faraday ice pail to investigate the net charge on the grounded sphere caused by the electric field of the electrified sphere An illustrative picture is provided that may or may not correctly show the charge distribution on the grounded sphere constant voltage 30V Ground e 1000 V e 2000 V 3000 V ground ground 6 1 Experimentally determine if the grounded sphere has a net charge or if it is simply neutral with macroscopic charge separation 6 2 If the grounded sphere has a net charge explain where this excess charge came from i 6 3 Experimentally determine if the grounded sphere has a similar charge distribution to that shown in the figure or if the figure is wrong 60 Section 7 authentic assessment Magnets surround you in your everyday life How upsetting it is to think that most people are incapable of determining a simple north or south pole on an unlabeled magnet If you are uncomfortable having another student check your work please ask your TA 7 1 Find an unlabeled magnet in the lab and use a compass to determine the north pole of the unlabeled magnet First be sure your compass agrees with the Earth s magnetic field Explain your work to a student in a different lab
165. s the total equivalent resistance of this circuit b What is the total current supplied by the battery c What is the voltage drop across any single resistor d What is the current passing through any single resistor e By only removing one single wire how could this circuit be made to have a total equivalent resistance of 2 Q Draw your answer on the circuit diagram by placing an X on the wire to be removed 131 This page intentionally left blank 132 Week 6 Pre Lab Oscilloscope Before actually using the oscilloscope you need to be able to understand and predict what will appear on the oscilloscope screen An oscilloscope is a device that measures voltage differences over time It can be used to study rapidly oscillating voltages For example the voltage supplied by a wall outlet oscillates at the incredibly slow rate of 60 Hz Hertz Hz is the SI unit for linear frequency representing the number of oscillations per second However the oscilloscope can easily measure an oscillation of 1 MHz or more Most DMMs indicate that they can measure an oscillating voltage However a DMM can only make average measurements of sinusoidal 60 Hz voltages In other words a DMM is only useful for alternating current measurements AC on household circuits not radios or other electronics Remember T 1 f with SI units s and 2 7 with SI units 1 s An oscilloscope is needed to examine voltages that change in time Mathematica
166. scillating voltage supply Be sure to experiment with all sorts of frequencies voltage amplitudes and DC offsets Practice making the voltage functions fit nicely on the oscilloscope screen Take the time to twiddle every knob and switch Once you feel comfortable with your understanding of each operational control of the oscilloscope and function generator write a short statement explaining what each control does But don t write a user s manual 138 The purpose of this next material is to show you that you should never measure the function generator amplitude until after you wire it to your circuit Use the function generator to create a 5 volt sine wave with 1 000 Hz frequency Use the oscilloscope as shown in the picture below to set the function generator amplitude correctly at 5 0 volts Veource t Vuaxsin at 9 where Vmax 5 Volts w 2x 1 000 Hz Use this sinusoidal voltage to power a 100 Q resistor Use the oscilloscope to measure the voltage drop across the resistor set up as shown in the picture below Vsource t VuaxSin wt o A where Vmax 5 Volts w 2x 1 000 Hz G 2 2 What should the voltage drop across the resistor be according to conservation of energy Be sure your measurement with the oscilloscope indicates this 139 Now switch to a 10 Q resistor and examine the voltage drop across it Theoretically this smaller resistor should still have the same 5 Volt difference amplit
167. scope may also be charged by touching it with a charged object The gold leaf will still rise but this time through a process related to the repulsion of excess charge if you touch the scope with a highly charged object the leaf will be ripped from the scope due to intense electrostatic pressure It won t be really fun to watch either 52 3 1 DO NOT TOUCH THE SCOPE FOR THIS QUESTION Be sure your electroscope is discharged by grounding it Usually your body can remove any excess charge on the electroscope so simply touch it Now bring a positively charged glass rod near to but not touching the electroscope and examine the rising of the gold leaf Use the picture template below to show how the charges on the metallic bar gold leaf are arranged that cause the gold leaf to rise Do this by drawing plus and minus signs Remember that the metallic bar gold leaf conductor is still neutral 53 3 2 TOUCH THE SCOPE WITH THE ROD FOR THIS QUESTION With an initially neutral electroscope touch the end of the electroscope with a positively charged glass rod and transfer positive charge to the metallic bar gold leaf conductor by touching the electroscope Use the picture template provided below to show how the charges on the metallic bar gold leaf are arranged that cause the gold leaf to rise with plus and minus signs 54 3 3 TOUCH THE SCOPE ONLY WITH YOUR HAND With an initially neutral electroscope bring the positively
168. se one of the following sections about which to write your mini report Week 7 Section 3 or Week 8 Section 3 Write a mini report for one particular section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable Please label your mini repot sections o Abstract Write 2 3 sentences about the goals of this section Describe the concepts you were investigating and how the experimentation you performed allowed you to investigate these concepts Write 2 3 sentences summarizing the procedure Write 2 3 sentences summarizing the results and what the results mean with regard to the concepts you were investigating It is best to write the abstract last o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Provide a description of the data you obtained such as data tables Restate any measured values calculated slopes of lines of best fit etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of the concepts and equations of this unit It is all right to sound repetitive with other parts o
169. sive 62 1 s E 0 16 a drive X Onel 9 62 Q e Z JR X Xc 0 68 Q source Ponce tar Xe 0 74 radians Voue Veoune SiN Oj sf Prin 7 38in 62t 0 74 z V amplitude gt V C Sasi Voe sin y 2 2 sin 62r V amplitude X m T V t aair V sin t 0 71 sin 62t JVeipaiot Z Ne drive z z V X m mT e V t inductor a Vaido sim Darivel re 2 7 s n 62t aa V Z amplitude 2 2 Vois 5 oe amplitude 4 4 A amplitude Z Notice that at this driving frequency of the three circuit components the inductor has the largest voltage amplitude and would appear the largest on the oscilloscope screen 240 Week 11 Lab RLC Circuit AC Source Students Absolutely Must Learn e How to use the sinusoidal solutions of the RLC circuit components and what they mean including phase shifts e How to relate the RLC circuit current to other circuit parameters especially the circuit impedance e How conservation of energy and calculus explain the 7 2 phase shifts e How to determine the resonance features of the RLC circuit and how the various parameters affect resonance e Advanced oscilloscope techniques Section 1 measuring with two oscilloscope channels In electronics you may use the oscilloscope to simultaneously measure the voltage of two adjacent components Connecting your inductor capacitor and resistor in series should
170. st Learn e How to relate the mathematics of the sine function to the appearance on the oscilloscope screen of a sinusoidally oscillating voltage e The basic concept of how a semiconducting component works especially relating to its band gap energy or turn on voltage e How to use an oscilloscope to measure voltage e How to set up middle ground and bottom ground simultaneous voltage measurements Section 1 semiconductors and quantum mechanics Generic Plot of Energy Bands for Semiconductor Energy eV conduction band empty AE is called Band Gap Energy valence band filled with electrons Momentum The above graph shows the energy bands for a generic semiconductor which must be calculated using quantum mechanics This graph shows a plot of possible energy states for electrons inside semiconducting material such as one would find in a computer chip Though an in depth discussion of this advanced topic cannot be given here the most essential points can be provided The lower energy band of a semiconductor is completely full of electrons It is out of room so to speak Electrons in this low energy band cannot accept extra energy unless it is sufficiently large enough to move the electron into the next energy band called a conduction band Thus a very cold semiconductor cannot conduct electricity because the electrons are stuck in the valence band But if enough voltage is applied to a semiconductor the electro
171. standing of the maximum currents that the circuit can produce while still proceeding with caution If you are uncomfortable having another student check your work please ask your TA 5 1 Show a student in a different group that you can successfully measure the resonance frequency of an RLC circuit four circuits compare your data with theirs Once you are successful have them sign below Note if someone is stuck please give them advice Yes I have seen this student successfully find the resonance frequencies of four RLC circuits Their results match mine Either they are doing it right or we are both wrong in the same way Student Signature 253 Section 6 open ended Pretend that you are an old timey inventor You have already discovered the coiled wire device now called inductor and the metallic parallel plates device now called capacitor Resistors were discovered by a competitor of yours It is still a sore subject around the workshop You have begun to combine these new components together in order to observe their compound behavior You already found that when the inductor and capacitor are combined in series and driven sinusoidally the circuit produces a special resonant frequency where the current in the circuit is a maximum This means that civilization can now make electronics that select specific driving frequencies and suppress frequencies far from resonance Now you try combining the induct
172. stant of the cardboard You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the following page 184 4 1 hypothesizing planning G 4 2 observations data amp 43 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 185 This page intentionally left blank 186 Week 8 Take Home Quiz Score 5 THQ 1 3 points A B V source t a Which capacitor circuit s has time dependent resistor and capacitor voltages A B or Both b Which capacitor circuit s has resistor and capacitor voltages that are exponential in time A B or Both c Which capacitor circuit s has resistor and capacitor voltages t
173. stor and explain why this makes sense 142 Now use the oscilloscope to measure the voltage across each resistor simultaneously on both channels by setting up a middle ground set up as shown in the figure below Note that the middle ground measurement requires that the function generator NOT be grounded use a 3 to 2 prong plug adapter on the function generator The voltage between red 1 and ground will tell you the potential difference across the 100 Q resistor while the voltage between red 2 and ground will tell you the inverted voltage across the 200 resistor The voltage reading is inverted because the order of the positive and negative leads of the second channel are reversed the same thing would happen with a simple DMM when you switch the leads red 1 red 2 channel black inverted middle ground 200 Q 2 8 What must you do mathematically to find the total voltage drop across both resistors amp 29 Are the two oscillating voltages across the resistors in phase with each other 143 2 10 Determine the amplitudes of the voltage differences across each resistor and explain why this makes sense Using the same middle ground set up as in the last problem measure the changing voltage across both resistors in X Y mode so that one of the resistor voltages is plotted on the x axis and the voltage of the other resistor is plotted on the y axis You should see an ellipse edge on i e a diagonal
174. stract Write 2 3 sentences about the goals of this section Describe the concepts you were investigating and how the experimentation you performed allowed you to investigate these concepts Write 2 3 sentences summarizing the procedure Write 2 3 sentences summarizing the results and what the results mean with regard to the concepts you were investigating It is best to write the abstract last o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Provide a description of the data you obtained such as data tables Restate any measured values calculated slopes of lines of best fit etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of the concepts and equations of this unit It is all right to sound repetitive with other parts of the report Open Ended Discussion 10 points 1 2 paragraphs 1 page double spaced Choose one of the open ended experiments from the two weekly activities to write about Describe your experimental goal and the question you were trying to answer Explain the ideas you came up with and what you tried If your attempts were successful explain your results If your attempts resulted in failure explain what went wrong and what you would do differently in the future Y
175. ta by taking the natural logarithm of your voltages Since Veal Vie Rc taking the natural logarithm of the function cancels the exponential In Ve In V In e so hji In V RC The function y t gt t In V is the equation of a line with a slope of 1 RC and y intercept of In V Thus if you make the graph of In Voup paper you will obtain a line with a slope equal to 1 RC if your data is exponentially related vs t on regular Cartesian graph 158 1 5 Linearize your data by taking the natural logarithm of your measured voltages In V Record your data here or in your table from 1 3 1 6 Graph your linearized data by taking the natural logarithm of your measured voltages In V and plot these vs t on regular graph paper This should give you a line with slope equal to 1 RC On separate graph paper then calculate slope and record here 1 7 Find your experimentally measured value of capacitance C from the slope of your linearized data graph and the value of the resistor s resistance R 159 Section 2 more oscilloscope practice The following picture shows the digital oscilloscope and labels its most common features screen menu calcs amp info menu buttons shows 0 volts for each channel ar om a a autoset cursor L gt a control cursor triggering control usual channel controls You now need to practice using the digital oscilloscope so that y
176. tes will cause electrons to be transferred from one material to another Pull one insulator out of the pail at a time to determine the sign of the net charge on the paddle remaining in the pail Even if charge is transferred between them together they should be net neutral If you don t observe this then you should 1 use alcohol and hairdryers to remove any initial excess charge on the paddles don t forget the handles and 2 make any highly charged lab partners stand some distance away If your lab is in a region with high humidity it is difficult to keep significant excess charge on objects If the air is dry excess charge can end up everywhere Record your results 5 3 Now prove to yourself that a charged conductor will transfer charge to an uncharged conductor when they touch Induce excess charge into a conductor as done earlier in the lab and record the sign of the excess charge Take another conductor with a handle often a paddle with a metallic face that is initially neutral and use the Faraday ice pail to prove that it is neutral Transfer some of the excess charge from the first conductor to the second conductor by touching them together Prove that charge was successfully transferred from the one conductor to the other Record your results 59 Section 6 electrified sphere and grounded sphere Two conducting spheres are provided Connect one sphere to a voltage generator to be electrified with a large positive voltage Thi
177. the circuit s wires are labeled 3 0 V Reulb gt 15M w gt m A lt Se w gt 4 m a 0 V a 43 If the negative lead of your DMM was placed at location d predict what the voltage readings would be on the DMM screen if the positive lead was placed at each other location in turn Be sure to include the sign of the electric potential voltage difference Your predictions in SI units a 4 4 If the negative lead common ground of your DMM was placed at location a predict what the voltage readings would be on the DMM screen if the positive lead was placed at each other locations in turn Be sure to include the sign of the electric potential voltage difference Your predictions in SI units amp 45 Now set this circuit up and test your predictions Record each of your results and if some of your predictions were wrong explain the mental misconceptions you held Your observations in SI units and any explanations of misconceptions 32 Now imagine the circuit from the previous subsection with a section of wire removed 3 0 V 4 iM C4 rs Ww gt i m A lt a Ww gt 4 4 m A lt 0 V da 4 6 If the grounding lead of your DMM was placed at location d predict what the voltage readings would be on the DMM screen if the positive lead was placed at each other location in turn Be sure to include the sign of the electric potential voltage difference
178. the concepts and equations of this unit It is all right to sound repetitive with other parts of the report e Open Ended Discussion 10 points 1 2 paragraphs 1 page double spaced Choose one of the open ended experiments from the two weekly activities to write about Describe your experimental goal and the question you were trying to answer Explain the ideas you came up with and what you tried If your attempts were successful explain your results If your attempts resulted in failure explain what went wrong and what you would do differently in the future You must write using sentences amp paragraphs bulleted lists are unacceptable e Graphs 5 points attach to your typed report Graphs must be neatly hand drawn during lab on graph paper Your graphs must fill the entire page requires planning ahead include a descriptive title labeled axes numeric tic marks on the axes and unit labels on the axes If instructed to calculate the slope of the line of best fit write it directly on the graph e Take Home Quizzes 2x5 points 10 points attach after your Graphs e Selected Worksheet Pages 5 points attach after your Take Home Quizzes 14 Rules for Excused Absences You should always email your TA as soon as you know that you will be missing a lab You are not permitted to attend a different lab than the one for which you are registered If you have a valid excuse with documentation then you may complete the Makeu
179. the electron can travel through the CRT unhindered by collisions with air molecules upward and outward describe which way the electron is deflected An electron moves from low to high voltage An electron accelerated from 50 V to 200 V will experience a AV of 150 V V x 200 150 100 50 Oo gt 50 Volts 200 Volts E gt 91 The work done on a charged particle when moving between voltages is given by the formula W done on object qAV An electron has a charge of q 1 9x10 coul so that if an electron moves between two plates with AV 150 V the electric field will do W 2 85x10 J of work on the electron The work energy theorem states that Wione on AK object 7 so this work done on the electron changes it s kinetic energy by K 2 85x10 J If we assume the electron started at rest and since an electron has a mass of 9 1x10 kg AK n 07 2 85x10 J Thus one may solve for the final velocity of the electron v ZAK 8x10 m s m which is 3 the speed of light roughly 15 million miles per hour 92 Week 4 Lab Cathode Ray Tube Students Absolutely Must Learn How charged particles behave in a scalar electric potential field How charged particles behave in an electric vector field How to relate kinematics mechanics concepts to electricity concepts How a CRT works how parallel plates of different voltages affe
180. ting circuit with a resistor and inductor in series voltage The current in the solenoid creates a magnetic field inside the solenoid due to Ampere s Law The changing magnetic field inside the solenoid causes a back EMF voltage due to Faraday s Law Notice that dI dt causes a phase shift The above figure demonstrates the cause and effect relationships responsible for creating the voltage drop across a solenoid even though it is just one long conducting wire 225 If you are examining an RL circuit driven by a sinusoidal voltage source then you will obtain the following equations describing the voltages of the components Notice the similarity to Va V sire sin pt F p amplitude R V t ae Vogts sin f Z amplitude source X A VA WV sin mE EE Z amplitude 2 Compare to the RC circuit that is sinusoidally driven V t e ears sn o z Z amplitude 2 Notice that like the capacitor voltage the inductor voltage is phase shifted from the resistor voltage by 7 2 X is the inductive reactance of the solenoid and is given by X L Compare this to the L g y L drive p The inductive reactance of an RL circuit capacitive reactance of the RC circuit Xo Dative is directly proportional to the driving frequency It is recommended that you use a 1 000 Q resistor 5 1 If you increase the driving frequency in a sinusoidally driven RL circuit does the voltage you measure across th
181. tion 5 open ended Week 6 Take Home Quiz Unit 4 Lab Report Instructions Week 7 Pre Lab RC Circuits DC Source Week 7 Lab RC Circuits DC Source Section 1 examining slow RC circuits with a stopwatch Section 2 more oscilloscope practice Section 3 examining fast RC circuits with an oscilloscope Section 4 authentic assessment Section 5 open ended Week 7 Take Home Quiz Week 8 Pre Lab RC Circuit AC Source Week 8 Lab RC Circuit AC Source Section 1 examining the components Section 2 experimentally finding the capacitance Section 3 authentic assessment Section 4 open ended Week 8 Take Home Quiz Unit 5 Lab Report Instructions Week 9 Pre Lab Motors Week 9 Lab Motors Section 1 constructing the motor Section 2 making measurements Section 3 authentic assessment Section 4 open ended Week 9 Take Home Quiz Week 10 Pre Lab Solenoids Week 10 Lab Solenoids Section 1 creating magnetic fields inside the solenoid 106 109 111 113 115 115 117 126 128 129 131 133 135 135 137 145 148 149 151 153 155 157 157 160 163 168 169 171 173 175 175 179 183 184 187 189 191 193 193 202 206 207 209 211 213 213 Section 2 Lenz s law Section 3 induced solenoid voltage by external magnetic fields Section 4 finding the mutual inductance Section 5 finding the self inductance Section 6 fast Fourier transform FFT detection of frequencies Section 7 authentic assessment Section 8 open ended Week 10 Take
182. tion you performed allowed you to investigate these concepts Write 2 3 sentences summarizing the procedure Write 2 3 sentences summarizing the results and what the results mean with regard to the concepts you were investigating It is best to write the abstract last o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Provide a description of the data you obtained such as data tables Restate any measured values calculated slopes of lines of best fit etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of the concepts and equations of this unit It is all right to sound repetitive with other parts of the report Open Ended Discussion 10 points 1 2 paragraphs 1 page double spaced Choose one of the open ended experiments from the two weekly activities to write about Describe your experimental goal and the question you were trying to answer Explain the ideas you came up with and what you tried If your attempts were successful explain your results If your attempts resulted in failure explain what went wrong and what you would do differently in the future You must write using sentences amp paragraphs bulleted lists are unacceptable Graphs 5 points attach to your typed repo
183. u may want to explain with circuit diagrams Later in the lab you will need to measure these two components motor and resistor simultaneously in order to calculate the RPMs and the power Since Pana Laa V cok fraction of time motor is on I ornk Vooo fraction of time motor is on Vilao V fraction of time motoris on R motor on you can obtain the power used by the motor friction using only the pictured measurements 205 Section 3 authentic assessment Always start with low voltage less than 2 V when connecting your motor to the DC power supply Then start the motor by spinning it with your fingers You should be able to feel with your fingers which way the motor is being pushed to rotate This will tell you which way to spin it You may have to keep increasing the supply voltage to keep your motor spinning Never let your motor stay connected to the source with current running through it when it is not spinning because the insulation will rapidly melt away 3 1 Show your TA that you can successfully build a working motor Note if someone is stuck please give them advice Yes I have seen this student build a motor that successfully runs on electrical input power This will be an indispensible skill should they find themselves lost at sea TA signature 206 Section 4 open ended Imagine you wish to sell your motor on Ebay You will need to describe as many of your motor s f
184. ude as the 100 Q resistor However you should notice the voltage amplitude decrease This is a result of the function generator output changing The smaller resistor will allow a greater current to flow through the circuit but the function generator has a maximum current that it is able to produce Therefore once the resistance becomes too low the function generator cannot output the full 5 volts That is why you must measure your output voltage after you wire your function generator to your circuit Just like a battery a function generator has an internal resistance 50 Q 2 3 Imagine that you are about to use the function generator to power a circuit Explain why you should measure the amplitude of the source voltage coming from the function generator after you have hooked up the function generator to your circuit Many students get bad data because they forget about this subtle issue d 2 4 Ven Use the equation 7 E in with the 10 Q resistor to find the amp maximum current amplitude Jamplitude max that the function generator is able to produce 140 You may use the oscilloscope to measure the voltages of two circuit components separately using the oscilloscopes two separate channels The two oscilloscope channels each have a ground black lead and both grounds are actually connected inside the oscilloscope so that only one ground needs to be connected to the circuit A common mistake is for students to try and san
185. uency 30 000 Hz t This isn t the frequency you want to hear you are not able to but it does oscillate so quickly as to create a large induced voltage in the receiving solenoid I e it oscillates quickly enough to be transmitted into the receiving circuit through the mutual inductance of the transformer overlapping solenoids So what to do There is a low frequency wave that carries the information we wish to transmit but can t and there is a high frequency wave that we don t care about that is easily transmitted The solution is to combine the two waves together by multiplying them This modulated wave has the properties of both waves it carries information about the audio frequency component and it oscillates quickly enough to generate a highly induced voltage in the receiver circuit The following picture shows what a modulated wave looks like Modulated Sub Radio 30 000 Hz with Audio 1500 Hz V t The envelope wave is the low frequency oscillation while the high frequency oscillation is called the carrier wave Together they are the modulated wave 260 Week 12 Lab RLC Radios Students Absolutely Must Learn e How the RLC circuit s resonance may be used in technology e How to modulate a carrier wave and envelope e Advanced oscilloscope techniques Section 1 introducing the equipment In today s lab we would like to transmit a modulated sound wave transmitted by one solenoid into anot
186. uit its resistance grows with increasing temperature Write your measured resistance in SI units 2 5 Measure the resistance of your finger from tip to base and write the result in SI units Compare your measurements to those of other students Explain what might account for such a wide range of varying finger resistances 26 One way of thinking about a circuit with constant current is to use a sort of voltage height diagram The y axis represents voltage potential energy per unit positive charge voltage height 1 5 V o V d 2 6 Experimentally verify that the voltage supplied by the battery is equal and opposite to the voltage drop across the light bulb What fundamental physical law assures that this happens Hint what is a fundamental conserved quantity in physics Using the previous figure Now examine two light bulbs in series voltage height 1 50 V 0 75 V 0 V 2 7 Experimentally verify that the AV supplied by the battery is equal to the sum of the AV s across each light bulb Then experimentally verify that the current leaving the battery is the same as the current in the first bulb is the same as the current in the second bulb Finally measure the resistance of two separate single cold bulbs and then measure their total resistance when placed in series Record your results and check with neighbors Using the previous figure 27 Section 3 circuit behavior
187. ular acceleration The wire loop will therefore rotate faster and faster until the torque from the magnetic force equals any frictional torque in the motor At this time the loop will reach a constant angular speed o 191 The only difficulty in making a motor is to ensure that the current always travels in the same direction as it passes through the magnetic field no matter how the loop itself is oriented Examine the following picture to better understand what this difficulty is if the current supplied to the wire loop is always the same for each lead of the wire loop rotate In this before and after picture you can see that when the wire loop rotates 180 the force will now push the loop in the opposite direction because the direction of the current through the magnetic field will be reversed Unless you want to make a fancy electronic rocking chair this is not good motor design Instead you will need to design your motor so that the current always flows in the same direction for the part of the wire loop inside the magnetic field as is shown in the next picture brushes allow good contact as loop rotates In this motor set up when the wire loop rotates 180 the manner in which current is supplied to the loop is changed in order to get the current to flow in the same direction for the part of the loop experiencing the magnetic force 192 Week 9 Lab Motors Students Absolutely Must Learn e How motors work o Lor
188. vations 50 d 2 4 Draw a series of pictures cartoon with explanatory text describing why the pith ball is first attracted to the charged object and then repelled Use the concept of macroscopic charge separation on a conductor Show plus minus signs to signify where excess charges have accumulated signify how charges have macroscopically separated If you do not know whether the excess charge on the rod is positive or negative then assume it is positive Cartoon Frames 51 Section 3 electroscopes A gold leaf electroscope is a device used to detect charged objects It is made by fastening a thin strip of pure gold to a metallic bar encased in a conducting housing Note that the solid metallic bar and the gold strip act as a single conductor since they are connected The strip of gold has been processed to be extremely thin a few hundred atoms so that it is actually only worth a few dollars but a real pain to install so please don t touch it as it will disintegrate upon contact with your finger solid metallic bar with round end very thin strip of pure gold metallic enclosure An electroscope detects excess charge by the rising of its gold leaf The electroscope may detect the presence of a charged object that is brought near to but not touching the top of the scope through a process involving macroscopic charge separation In this case there is no excess charge on the metallic bar gold leaf conductor The electro
189. verywhere between the plates as well as outside the plates 85 Section 4 exploring electric fields 4 1 Find a novel conducting paper of silver paint that looks interesting to you Find and sketch its equipotential lines on graph paper using dashed lines This should take only a few minutes hurry up Make a copy for both lab partners answer on separate graph paper 4 2 Sketch the electric field lines on your previous equipotential graph using solid lines This should take only a few minutes hurry up answer on separate graph paper 86 Section 5 authentic assessment Students must be supplied with a strip of conductive paper 1 cm by 10 cm with alligator clips attached at either end Find the average electric field strength and direction between two points of conductive paper 10 cm apart electrified by a 10 volt electric potential difference Hint You may solve this problem experimentally by making measurements or theoretically by making a calculation One method is much easier If you are uncomfortable having another student check your work please ask your TA 5 1 Show a student in a different group that you can successfully calculate the average electric field magnitude and direction between 10 cm of conducting paper electrified by 10 volt Once you are successful have them sign below Note if someone is stuck please give them advice Yes I have seen this student theoretically calcu
190. vious work However do not use previous results to answer the question but instead think of an easier way to determine which geometric constant is larger Here is a hint given a certain deflection voltage which direction seems to use that deflection voltage more You should need to collect very little data to answer which geometric constant is larger upward and outward describe which way the electron is deflected You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the next page 106 4 1 hypothesizing planning amp 4 2 observations data a 43 calculations conclusion I the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature
191. y into your ear without first verifying that the sound level is safe Now you will experimentally use a sound wave to modulate a radio frequency wave First examine the equipment with two solenoids PRIMARY SECONDARY SOLENOID SOLENOID This device allows you to see how two solenoids interact via Faraday s law There is a small visible gap that separates the two different coils of wire If you look carefully you can see that GND connects to the left side of the primary solenoid and ANT connects to the right side of the primary You can also see that A connects to the left of the secondary and B to the right In addition to these connections there are some junctions sticking out of the top of the solenoids These allow you to use smaller portions of each solenoid if you want less inductance L We will always want to use the connections at ANT and A This forces the current to travel in the parts of the primary and secondary that are adjacent to one another 262 secondary circuit L sec PRIMARY SECONDARY SOLENOID SOLENOID For example if you wanted to half the inductance of the secondary circuit shown above you would simply reconnect the B terminal to the midpoint of the secondary solenoid so that only half of that solenoid is used shown below secondary circuit Lsec 2 PRIMARY SECONDARY SOLENOID SOLENOID 263 Gq 1 2 How many possible primary solenoid inductances are possible How many secondary Don t for

Introductory Electricity & Magnetism Lab Manual, 2 nd Ed.

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Introductory Electricity &amp; Magnetism Lab Manual, 2 nd Ed.

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Introductory Electricity & Magnetism Lab Manual, 2 nd Ed.