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

Inductor:

- When you are not taking data, please disconnect the battery; this
will increase its lifespan.

- 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.

- 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.

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

- Close the switch and start the stopwatch. When the multimeter reads
1.00 volts, stop the watch and
(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).*record the charging time, t*_{c}in a table like the one below.

- 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.

- 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.)

- 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, t*_{d}.

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

- 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.*

- 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.*

- 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 t _{c}t _{d}1 2 Avg 1 2 Avg 1 2 Avg 1 2 Avg

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

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

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

- 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 t _{c}t _{d}1 2 Avg

*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.*

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

- 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 t _{c}t _{d}1 2 Avg

*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.

- Sketch sine, square, and triangle waves labeling and explaining amplitude, period, and frequency.
- 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.

Back to the Electricity and Magnetism Manual