PHY 242 Laboratory for 10/15/98

The A.C. LRC Circuit

In this exercise you will measure the reactance of a capacitor (also called a condenser) and an inductor (also called a transformer, coil or rf choke) to a 60 Hz AC voltage source and confirm the relationship among impedance, rms current and rms voltage. The rms voltage across each element individually, as well as for any combination of elements, is related to the rms current by Vrms = IrmsZ, where Z is the impedance for that element or combination of elements. The general expression for the impedance is:

where w is the angular frequency of the source. Note that although the elements are in series, the total impedance is not just the sum of the individual impedances.

1. Capacitive Reactance

Measure the resistance of the resistor provided using the digital multimeter. Place the resistor and capacitor in series with the variable AC voltage source (called an autotransformer or variac) using alligator clips. Adjust the variac to approximately 20 volts rms.

Using the multimeter, measure the rms voltage at the variac (V13) and across each element (V12 and V23). Determine the rms current using the value of the resistor and the rms voltage across it. Find the reactance of the capacitor using the rms voltage across the capacitor and the rms current. Using the fact that the AC frequency from the variac is 60 Hz (angular frequency w = 120p r/s), find the capacitance. Check to see if the rms voltage applied by the variac divided by the total impedance of the circuit is consistent with the value of the rms current initially determined from the resistor. Note that with no inductor in the circuit, cL will be zero.

2. Inductive Reactance

Repeat the above procedure for the inductor in series with the resistor. It will be necessary to measure the internal resistance (r) of the coil with the multimeter. This resistance can be considered to be in series with the inductor. The rms voltage you measure across the inductor will actually be the voltage across the inductor and the internal resistance r. You must include the internal resistance in the expression for the impedance of the inductor. Find the value of the reactance and inductance of the inductor.

Note that with no capacitor in the circuit, cC will be zero.

3. Capacitive and Inductive Reactance

Place all three elements in series and measure the rms voltage across all possible combinations of one, two, and three elements. It will be necessary to change the position of two elements to obtain all possibilities. Compare the voltages you measured with those you expected based upon theory and using the values of cC and cL calculated in parts 1 and 2. For those combinations involving the inductor, do not forget the internal resistance r.
Why is the rms voltage across the combinations not equal to the sum of the individual voltages? Under what special conditions would they be equal?