# Time-Varying Circuits

## SPECIFIC OBJECTIVES

• To explore the time constant of RC (resistor-capacitor) circuits.
• To learn how capacitors combine in series and parallel configurations.

## EQUIPMENT

Circuit board, D-cell batteries (2), wires, resistors, multimeter, capacitors, stopwatch, and probe leads.

## SYMBOLS FOR CIRCUIT ELEMENTS

In this lab you will be using many electrical components, all of which will be symbolized in schematic diagrams. You will need to recognize these components in order to perform the lab effectively.

Inductor:

## PROCEDURE

The underlined passages below require an answer or a sketch in your notebook.
1. When you are not taking data, please disconnect the battery; this will increase its lifespan.

2. Connect the circuit shown below using a 100,000-ohm resistor and a 100 microfarad capacitor. Use one of the spring clips as a switch to interrupt the current flow. Start with the switch open (no current flowing). Use the multimeter in voltmeter mode to measure the voltage across the capacitor.

3. Start with no voltage across the capacitor. If the voltmeter reads non-zero, then use a small (330-ohm) resistor to short across the springs holding the capacitor. That is, touch the ends of the resistor to points B and C on the picture above to drain any charge off the capacitor plates.

4. Prepare a stopwatch. You will measure the time it takes for the capacitor voltage to build up from zero volts to 1.00 volts.

5. Close the switch and start the stopwatch. When the multimeter reads 1.00 volts, stop the watch and record the charging time, tc in a table like the one below. (You may need more rows.) Do not open the switch, but rather allow the capacitor to charge up to it maximum voltage (near 1.5 volts).

6. To speed the charging to maximum voltage, use the small resistor to short out the 100,000-ohm resistor. That is, touch the ends of the small resistor to points A and B on the picture above.

7. Prepare the stopwatch. You will now measure the time it takes for the capacitor to lose 1.00 volt from its maximum voltage. (For example, if the maximum voltage reads 1.46 V, then the final voltage at the end of the time trial will be 0.46 V.)

8. Remove the wire from the positive terminal of the battery. Touch this wire to the spring clip on the negative terminal of the battery and start the timing. When the capacitor voltage has dropped 1.00 volts, stop the watch and record the discharge time, td.

9. Repeat the charging and discharging time trial at least one more time and average the results.

10. Replace the 100-microfarad capacitor with a 330-microfarad capacitor, keep the 100,000-ohm resistor in place, and record the new charge and discharge times in the table.

11. Replace the 100,000-ohm resistor with a 220,000-ohm resistor, keep the 330-microfarad capacitor in place, and record the new charge and discharge times in the table.

12. Replace the 330-microfarad capacitor with a 100-microfarad capacitor, keep the 220,000-ohm resistor in place, and record the new charge and discharge times in the table.

 Trial Resistance Capacitance tc td 1 2 Avg 1 2 Avg 1 2 Avg 1 2 Avg

13. What is the effect on the charging and discharging times if the capacitance is roughly tripled?

14. What is the effect on the charging and discharging times if the resistance is roughly doubled?

15. How do you think the characteristic time for an RC circuit depends on R and C?

16. Return to the 100,000-ohm resistor, but now use the 100-microfarad capacitor in series with the 330-microfarad capacitor. Be sure to discharge both capacitors before connecting them in series. Record the charging and discharging times in the table below.

 Trial Resistance Two Capacitors in Series tc td 1 2 Avg

17. From the timing data, what is the effective capacitance of a 100-microfarad capacitor in series with a 330-microfarad capacitor? Do NOT use the theoretical formula for series equivalent capacitance; use the experimental timing data ONLY.

18. Is the effective capacitance less than 100 microfarad, greater than 330 microfarad, or between the 100 and 330 microfarad?

19. Keep the 100,000-ohm resistor in place, but now use the 100-microfarad capacitor in parallel with the 330-microfarad capacitor. Record the charging and discharging times in the table below.

 Trial Resistance Two Capacitors in Parallel tc td 1 2 Avg

20. From the timing data, what is the effective capacitance of a 100-microfarad capacitor in parallel with a 330-microfarad capacitor? Do NOT use the theoretical formula for parallel equivalent capacitance; use the experimental timing data ONLY. Is the effective capacitance lees than 100 microfarad, greater than 330 microfarad, or between the 100 and 330 microfarad?

Don't forget your two random and two systematic error sources.

## Explore using the function generator and oscilloscope

1. Sketch sine, square, and triangle waves labeling and explaining amplitude, period, and frequency.
2. Using the "xy" mode of the oscilloscope and two function generators, produce and sketch Lissajous figures for frequency ratios 1:1, 1:2, 1:3, 2:3, and 5:7.
Try the Java applet found by Mr. Ricciardelli

Back to the Electricity and Magnetism Manual