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CU-Boulder PHYS 2020 - AC Circuits I

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Physics 2020, Spring 2006 Lab 6 page 1 of 8Lab 6. AC Circuits IINTRODUCTION: USING THE OSCILLOSCOPEIn previous labs, we studied some simple DC circuits, where the voltages andcurrents did not change with time. What happens when the voltages and currents dochange with time? It turns out that we live in a world where most circuits are in factAC (alternating current) instead of DC (direct current). In this lab, we will explore twodifferent applications of AC circuits: induced voltage in wire loops, and magnetic forceon a wire with alternating current.The goals of this lab are to learn how to use some fundamental scientific equipment(namely, the oscilloscope), to explore the mathematical expression of alternatingcurrents, voltages, and magnetic fields, and to show some real-world applications ofalternating electrical currents and magnetic fields in action.Almost every AC measurement is done using an oscilloscope, which is a very usefultool for measuring voltages that are changing in time. Think of the oscilloscope justlike the DMM we have used in previous labs – it measures voltage, but now it plots itout in time (voltage on the vertical axis and time on the horizontal axis). The grid thatyou see on the screen is used to measure the voltage and time of your signal – thinkof it like graph paper. Each little box on the grid is called a division, and you canadjust the scale of the voltage and time axes with the volts/div and the sec/divknobs, respectively. For example, if the volts/div knob is set to 5, this means thateach box on the grid is equal to 5 volts.There is small knob in the center of both the volts/div and time/div knobs, called theCAL or calibration knob. This should always be in the fully clockwise position for thevolt/div and sec/div scale settings to be correct. Under the volts/div knob is a 3-position switch which reads (AC - ground - DC). This should be in the AC position forAC measurements.Oscilloscope Front Panel Whenever you use an oscilloscope, pay close attention to the horizontal and verticalscales (SEC/DIV and VOLTS/DIV).University of Colorado at Boulder, Department of PhysicsPhysics 2020, Spring 2006 Lab 6 page 2 of 8PART I: MEASURING SOUND WAVESAt your table you should have a speaker, a signal generator, a microphone, and anoscilloscope. The speaker is driven by a signal generator which produces asinusoidal voltage of adjustable frequency and amplitude. Note that there are bothcoarse and fine adjust knobs for the frequency, as well as “decade” buttons whichcan adjust the frequency by factors of 10.When connecting the various components to each other, you will be using twodifferent types of cables: coaxial cables with BNC connectors and single cables withbanana-plug connectors. The different types of connectors are shown below:BNC cables are actually two cables in one. They are composed of an innerconductor, which is connected to the pin on the connector, and an outer conductor,which is connected to the metal housing. The outer conductor surrounds the innerconductor, so it is a coaxial cable.Connect the signal generator to the speaker, and connect the microphone to theoscilloscope. Turn the volts/div knob on the oscilloscope all the way up to maximizeits sensitivity. Place the microphone near the speaker and adjust the signalgenerator amplitude up until you can see a signal. Adjust the frequency andamplitude until you can hear a mid-range tone at a quiet but audible volume. Writedown the frequency setting of the signal generator. From the oscilloscope trace,calculate the period of the alternating voltage signal. From this, calculate thefrequency. Does your oscilloscope measurement match the setting on the signalgenerator? If not, why not?University of Colorado at Boulder, Department of PhysicsBNC cableBanana plugsBanana-to-BNC adapterPhysics 2020, Spring 2006 Lab 6 page 3 of 8Measure and record the frequency range of your hearing as follows: Adjust thefrequency up as high as possible so that you can still hear it. Calculate the frequencyfrom the oscilloscope. Then adjust the frequency as low as possible so that you canstill hear it. Calculate the frequency from the oscilloscope. You will need to adjustthe sec/div knob to make an accurate oscilloscope reading.PART II: INDUCED VOLTAGE USING TWO WIRE LOOPSRecall that magnetic fields are both created by and act on moving charges. One ofthe ways that this happens is by the process called induction. Simply put, if you puta loop of wire in a changing magnetic field (assuming the orientation is correct), avoltage is induced between the ends of the wire. For a simple loop of wire, this canbe expressed by Faraday’s law as follows:tVinducedwhere Vinduced is the voltage difference between the ends of the wire that made theloop, and  is the magnetic flux (magnetic flux is simply the area of the loop times thestrength of the field, or =A*B – again, assuming the orientation is correct). /t istherefore the rate of change of the flux. Substituting =A*B, we get:tBAVinducedImagine we were to put a sinusoidal voltage across the ends of a loop of wire. Thiswould drive an alternating current through the loop (call this I1), as plotted in the firstgraph on the next page.On the second graph, plot the B-field strength at the center of the loop (call this B1).Use the right-hand rule. Start with timepoints A, B, C, and D, then fill in the rest of theplot. Draw any diagrams that are helpful. Don’t worry about absolute magnitude, butpay attention to direction. Label your vertical axis appropriately.University of Colorado at Boulder, Department of PhysicsPhysics 2020, Spring 2006 Lab 6 page 4 of 8On the third graph, plot the local (instantaneous) slope of the B1 plot (i.e. B/t).Again, start with timepoints A, B, C, and D, then fill in the rest of the plot. Don’t worryabout absolute numbers – just get the sign and shape of the plot right.Now imagine that we put a second loop right next to the first one, so that the wire ofthe second loop surrounds the changing B-field produced by the first loop. On the fourth graph, use Faraday’s law to plot the voltage induced on the secondloop (call it V2). Draw any diagrams that are


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CU-Boulder PHYS 2020 - AC Circuits I

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