PHYSICS 220/230

Lab 7: AC Circuits

 

This lab investigates properties of various electrical circuits when an alternating potential difference is applied.

I. Addition of Voltages. Phasor Diagrams

  1. Connect the circuit shown below using a resistor R of about l000 ohms in series with a large 10 µF capacitor.

    2. Using the multimeter, measure the rms voltages across R, across C, and across the series combination of R and C. Using your known value of R, calculate the rms current in the circuit. Then determine the impedance (in this case assumed to be a perfect reactance) of the capacitor and, finally, evaluate the capacitance C.

  2. Connect the next circuit shown using a resistor R of about l000 ohms in series with an inductor.

                         

                           

The inductor coil is designated (L,r) to emphasize that it has both inductance L and resistance r. Use the multimeter to measure the rms voltages across R, across the coil, and across the series combination. Considering that R is accurately known, calculate the rms current in the circuit and then determine the impedance of the coil which contains both L and r. 

Using the following expression representing the law of cosines, evaluate the coil phase angle:

                                 

Then determine values for Vr and VL, using vector methods and evaluate r and L for the coil.

 

II. Voltage Phase Relations

Set up the following series circuit:

                             

Use the oscilloscope to explain qualitatively the phase differences between the various components.  First, look at the two voltages simultaneously using the CHOP mode of the oscilloscope for the following five connections:

Connection

Ground

X Input

Y Input

1

b

c

d

2

c

b

d

3

b

a

c

4

d

e

c

5

d

e

b


What phase difference do you see in each case, i.e., which waveform leads and by how much?  Is this what you expect?  Why?

III. Frequency Dependence of Voltage and Phase

The phase difference between two AC voltages can be studied by using a dual beam oscilloscope and comparing the time when each voltage peaks. Take the small plastic box with the knob on top and hook it up as shown below. The diagram below is drawn so that you can see what each circuit contains.

                             

A selector switch allows you to connect either R, C, L, LC series or LC parallel as the "first" element in the voltage divider, in series with the lower resistor that is always in the circuit. Once one of these has been selected and hooked into the circuit, vary the frequency of the signal generator from about 30 to 1000 Hz and observe the corresponding variations in both:

a) the magnitude of the observed CURRENT (the voltage across the lower resistor is proportional to the current), and

b) the PHASE DIFFERENCE between the total voltage supplied by the generator and the circuit current.

The Y (Ch. 2) signal on the scope is the voltage drop across the the lower resistor, which behaves like the current in the circuit.  The X (Ch. 1) signal on the scope is the source voltage, which equals the total voltage drop across the circuit.  Observe how the magnitude and phase of the current (as represented by the Y signal) change relative to the voltage (as represented by the X signal) with increasing frequency.

NOTE: You can use this AC Circuit Physlet to simulate your experiments and interpret your results.

What you should see is roughly as follows:

                           

You should qualitatively explain in your notebook why these graphs have the forms they do.  For the circuit elements we are using, the frequency scale for these graphs will run from 30 - 1000 Hz.

For the circuits that have series and parallel combinations, also find and record the RESONANT FREQUENCY evaluated from the scope.  Explain the phenomenon of resonance, and compare the resonant frequencies for the series and parallel circuits.