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# Rectangular Alternating Voltage for a Capacitor

To investigate the behaviour of a capacitor in an AC circuit, let us first work through a theoretical scenario. As shown in the left-hand part of the diagram below, a capacitor is connectable via a switch S and a resistor *R* to one of two direct voltage sources (e.g. batteries) of different polarities. Varying the switch position then supplies the RC network with a periodically changing rectangular alternating voltage. As a result, alternating current flows "through" the capacitor (right-hand side of diagram). The capacitor is first charged, during which process the charging current falls and the potential across the capacitor rises. On reversal of the voltage polarity, a charging current starts to flow in the opposite direction; the capacitor discharges, its potential drops to zero and then rises again in the opposite direction. The dashed curve shows how the capacitor potential (voltage) characteristic would have continued had the switch stayed in position. When it switches, however, the capacitor charges up again and so on. In other words, the capacitor appears to "conduct" alternating current by way of repeated re-charging. Its AC resistance is finite in contrast to its "infinite" DC resistance.

The following animation illustrates these relationships.

The diagram shows that current flows through the capacitor while the voltage is still building up across the plates and is at its highest before the voltage has risen very much. Similarly, discharge current flows strongly before the capacitor voltage has dropped perceptibly. One speaks here of a *phase shift* between the current and voltage. In capacitors, the current leads the voltage, in contrast to resistive loads, for instance, where the current and voltage are in phase.

The curve also reveals that the current is at its highest at the beginning, after which it drops sharply. The higher the switching frequency, the higher the average current, since the charge/discharge current characteristic is within a range where the current is high for a greater proportion of the time. As a result, the effective resistance of a capacitor can be expected to drop as the frequency of the alternating current increases. Also to be expected is a rise in the alternating current as the capacitance increases since the charging phase then takes longer and the current remains high for a greater proportion of the time. In other words, AC resistance can be expected to be smaller as the capacitance increases.