Passage III

A capacitor is a device for storing electrical charge. Students in a science class determined the charge on a parallel-plate capacitor having a fixed capacitance (the ratio of the amount of charge on each plate to the voltage between the plates). Measurements were taken while the capacitor was being charged and while it was being discharged.

Study 1

The students constructed an electrical circuit consisting of the capacitor, which was initially uncharged, a 4-volt (4V) battery, a 10¹¹-ohm resistor, and a switch (see Figure 1).

They closed the switch and charged the capacitor. During charging, the voltage across the capacitor, ε, in V, was monitored with a voltmeter. A computer that was connected to the voltmeter plotted ε versus time, t, in seconds (sec). The results are shown in Figure 2.

Once the capacitor was fully charged, ε equaled the voltage supplied by the battery. Using the data in Figure 2, the computer calculated the charge, Q, on the capacitor at various t, in picocoulombs (pC; 1 pC = 10^-12 coulomb). The results are shown in Table 1.

Study 2

With the capacitor fully charged, the students opened the switch, removed the battery from the circuit, and substituted a picoammeter (see Figure 3) capable of measuring currents as small as 1 × 10^-12 amp= 1 picoamp (pA). Then they closed the switch, allowing the capacitor to discharge through the resistor.

While the capacitor discharged, the students measured the electrical current, I, flowing through the resistor. The computer plotted I versus t (see Figure 4) and then, using the plotted values, calculated Q for various t (see Table 2).