Capacitance

1. Charging a Capacitor

1. Obtain a commercial capacitor with capacitance C = 470 µF (or some similar value), a programmable voltage source, and an amp-meter (or multi-meter that can measure current).
2. With the voltage source set to 0 V, connect the "+" terminal of the voltage source to one terminal of the capacitor, with the amp-meter in between, and connect the "−" terminal of the voltage source to the other terminal, as in Figure 1. The connection can be made with cables with clamps or banana plugs into receiving ports on the capacitor and instruments.
3. Switch the voltage source from 0 V to 1 V (in about 1 s), and observe the transient current reading on the amp-meter. Do the same for 2 V, 5 V, and 10 V (for each target voltage; this means first go back to 0 V, then switch to the target voltage in about 1 s). Note that the transient current is larger for a larger target voltage, as expected from Equation 2.
4. Program the voltage source to generate a voltage ramp from 0 V to 10 V in 5 s, and record the "steady state" reading of the amp-meter during the middle of the ramp. Repeat for a ramp time of 10 s, 20 s, and 30 s. Plot the observed current versus the voltage ramp rate (in V/s).

2. Tuning the Capacitance

1. Turn off the voltage source and replace it with a 300 V battery, and replace the amp-meter by a 1 MΩ resistor (the purpose of this resistor is to provide extra protection to limit the current in the circuit); also replace the commercial capacitor with a parallel plate capacitor with an adjustable separation between the plates.
2. Obtain a high-impedance voltmeter (or "electrometer") and connect it to measure the voltage difference V between the two plates (the high impedance impedes the discharge of the capacitor during the experiment when the electrometer is connected). See Figure 5.
3. Connect the 300 V battery to the parallel plate capacitor, wait until the electrometer reaches the steady state of 300 V (now the capacitor is fully charged by the 300 V source), and then quickly disconnect the voltage source from the plates. See Figure 6. The electrometer should still read 300 V.
4. Now increase the distance d between the plates to larger values such as 15 mm, 10 mm, and 5 mm, and observe and record the corresponding voltage reading on the electrometer (V); plot V versus d.
5. Increase d back to ~ 20 mm, insert a plastic slab between the two plates and observe what happens to V read by the electrometer. The reduction of V between the plates (with charge Q fixed in this case) results from the larger dielectric constant ε of the plastic (compared to air) as the medium of the capacitor (refer to Equations 1 and 3).

3. Parallel and Series Capacitances

1. Obtain a capacitance meter (a "LCR meter" or a multi-meter with a capacitance measurement mode); obtain a breadboard to facilitate the electrical connections in this part of the experiment.
2. Obtain two commercial "ceramic" capacitors with a capacitance of 1 µF, and use the capacitance meter to verify their capacitance, as in Figure 2.
3. Connect the two capacitors in parallel, and use the capacitance meter to measure the total capacitance (between points A and B, see Figure 3).
4. Connect the two capacitors in series, and use the capacitance meter to measure the total capacitance (between points A and B, see Figure 4).

Figure 3: Diagram showing two capacitors connected in parallel.

Figure 4: Diagram showing two capacitors connected in series.

Figure 5: Diagram showing the charging up of a capacitor using a voltage source, while reading the voltage with an electrometer.

Figure 6: After quickly disconnecting the voltage source in Figure 5, the voltage and charge on the capacitor should remain.