10

Charging and discharging capacitors

A capacitor is made part of two (connected) circuits that allow it to be charged and discharged (Figure 1, left). There is a resistive element in each of the two branches of the circuit. The charging circuit (the branch on the left in the circuit diagram) contains a power supply or a battery. If a previously uncharged capacitor is charged, its voltage behaves as in the diagram on the right of Figure 1. During discharging, the voltage drops as seen in the diagram at the center of Figure 1. Note that the speed of charging and discharging is different.

Movie 1 shows a variation on this theme. Two communicating capacitors are in a circuit containing an additional resistor through which both discharge.

Interpretation

The behavior of the capacitor in the circuits shown here is analogous to that of a fluid tank that is charged or discharged through a pipe. In fact, the charging and discharging circuits are equivalent to what we would build in a hydraulic system (the power supply corresponds to a pump, the resistive elements replace the pipes).

We can interpret a capacitor as a storage element for electric charge. The larger the amount of charge stored, the higher the voltage. With standard capacitors and ohmic resistors, we get good models of the behavior of the circuits if we assume the relation between charge and voltage of a capacitor to be linear—as in the case of a straight walled tank filled with oil.

[Note: A capacitor consists of two elements one of which is positively charged while the other carries the equivalent negative charge—so the total charge of a capacitor is zero. Note the use of capacitors in circuits: There are two wires connected to the device, one for inflow and one for outflow of charge during operation. If we want a hydraulic analogue of the charging of a capacitor, we could imagine two tanks both filled to the same level. We define this as the zero level. Charging means filling one of the tanks at the expense of the other. Even though the quantity of liquid has not changed, there now is a pressure difference.]