PHYSC 3322
Experiment 1.2
6 February, 2016
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 (   2f ,
where f is the frequency). The current I t  is given by
It  I 0 cost   ,
(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
Z
V
,
I
(3)
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
6 February, 2016
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 3. Series
(capacitor voltage).
Figure 2.
(current).
Series
resonant
circuit
resonant
circuit
resonant
circuit
Figure 4. Series
(inductor voltage).
Figure 5. Series resonant
(combined voltage).
circuit
Figure 6. Parallel resonant circuit
(current).
2
PHYSC 3322
Experiment 1.2
6 February, 2016
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