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PHYSC 3322 Experiment 1.2 3 November, 2012 AC Circuits Purpose The frequency response of a circuit containing reactive elements (inductors and capacitors) illustrates the importance of relative phase in the electrical behavior of multi-component circuits. The net current or voltage is the sum of the magnitudes and phases developed by the individual components. This experiment uses different combinations of the same components to illustrate the importance of relative phase in resonant AC circuits. Background The time-varying voltage V t in an AC circuit may be expressed as V t V0 cos t , (1) where V0 is the magnitude of the voltage and is the angular frequency ( 2f , where f is the frequency). The current I t is given by I t I 0 cost , (2) where I 0 is the magnitude of the current and is the relative phase between the voltage and the current. (If the circuit contains reactive components, the voltage and current are generally not in phase.) The voltage and current can also be expressed in phasor notation, in which the quantities are expressed as vectors, V and I , which rotate around the origin of the coordinate system at frequency f . The impedance of a circuit (here, circuit is defined as any combination of resistors, capacitors and inductors) can also be represented as a phasor by V Z , (3) I where the vector division is governed by the rules of complex arithmetic. Review the phasor diagrams for each type of reactive and resistive component in Chapter 36, sections 3 and 4, of Halliday and Resnick. Procedure Select a capacitor (~ 10 nF) and inductor (~ 1 mH) to form a resonant circuit. Determine the value of each component using the Elenco multimeter. To insure the greatest accuracy, plug the component leads directly into the wire clips (not the test lead jacks) on the front of the meter, rather than using test leads. Calculate the resonance frequency ( f 0 ) of series and parallel resonant circuits composed of these two components, using Halliday and Resnick as a reference. Use an oscillator (function generator) and oscilloscope to measure the current as a function of frequency for a 100 resistor over the frequency range f 0 / 2 to 2 f 0 (see Figure 1). Fix the voltage supplied by the oscillator and vary the frequency. The magnitude of the frequency is read from the frequency counter and the voltage drop across the resistor is determined from the peak-to-peak value of the waveform displayed on the oscilloscope. Use Sigma Plot to graph the peak current as a function of frequency. (This part of the procedure is intended to verify that the current, and therefore the voltage of the waveform, provided by the function generator, is independent of frequency.) 1 PHYSC 3322 Experiment 1.2 3 November, 2012 Series resonant circuit (current): Use the circuit shown in Figure 2 to determine the magnitude of the current as a function of frequency over the range f 0 / 2 to 2 f 0 . Plot the results. Figure 1. Current vs. frequency. Figure 2. Series resonant circuit (current). Figure 3. Series resonant circuit Figure 4. Series resonant circuit (capacitor voltage). (inductor voltage). Figure 5. Series resonant circuit Figure 6. Parallel resonant circuit (combined voltage). (current). 2 PHYSC 3322 Experiment 1.2 3 November, 2012 Series resonant circuit (voltage): Determine the frequency dependence of the voltage across each of the reactive elements in the circuit, as shown in Figures 3–5. Plot the results. Parallel resonant circuit (current): Determine the current as a function of frequency for the parallel resonant circuit shown in Figure 6. Plot the results. Questions Compare the results of your measurements with theoretical predictions. Discuss any discrepancies and consider possible sources of error. For the series resonant circuit, discuss how the individual voltages across the reactive components ( VC , VL ) combine to obtain the total voltage ( VT ) across the two components. Use Sigma Plot to verify your method. Plot the frequency response of the current for both the series and parallel resonant circuits on one graph. Discuss the features of the curves in the context of destructive interference. 3

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posted: | 11/3/2012 |

language: | English |

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