RC Circuits Theory

1. Use a DVM (Digital Volt Meter) to measure the output voltage (Vo) of the "voltage divider" to which the battery is connected. Adjust the voltage divider so that Vo does not exceed 1 V. Open LoggerPro. Set each of the two Instrumentation Amplifiers (IA) to the +/-1 V scale. Calibrate the IA by connecting the red and black leads first to each other (V = 0) and then to the voltage divider output (V = Vo). In the circuit below one IA will be used to measure Vc in CH1; the other, Vr in CH2.

2. In the circuit below use R = 100 kohm and C = 4.7 µF (so RC is of the order 0.5 s). Be sure to measure their actual values (R_{actual} and C_{actual}).

a. Charging Procedure: Start LoggerPro. Be sure to select an appropriate data acquisition rate. Throw the switch to charge C. Use the fitting routine in LoggerPro to obtain the RC time constant from both the Vr and Vc measurements. Compare it with the expected value.

NOTE!! You may not want to use the entire data set for your fit. Do your results depend on the time interval over which you have performed the fit?

b. Start LoggerPro. Throw the switch to discharge C. Repeat the analysis you performed in part a.

c. Repeat a. and b. for R = 100 kohm and C = 2.2 µF.

c. Repeat a. and b. for R = 47 kohm and C = 2.2 µF.

3. Set up the circuit below with C about 0.47 µF and R about 4.7 kohm. Be sure to measure their exact values. Set the oscillator at about 50 Hz with a sine wave output.

Use the two channels of the oscilloscope to view Vr and Vc. Note the phase difference between them. Use the Keithley to measure V_{R}, V_{C} and V_{T}, the voltage output of the oscillator. Repeat for 100Hz and 200 Hz.

Compare V_{TOTAL}^{2} and V_{R}^{2} + V_{C}^{2 } and V_{R}/V_{C} with 2πfRC

4. Measure the capacitance of each of three capacitors in the 0.1 µF to 0.5 µF range. Measure their capacitance when the three are connected in series and also when they are connected in parallel. Compare with the expected values.