The capacitor: Q = CV on DC and on AC
A capacitor is two metal plates with an insulator between them. When a voltage V is across it, it stores a charge Q = CV, where C is its capacitance in farad (F); in practice we use µF, 1 µF = 10⁻⁶ F. On a DC source the current flows only for a short time while the capacitor charges, until its voltage equals the source voltage; then the current is zero, because the insulator does not let charge cross. On an AC source the voltage keeps reversing, so the capacitor charges and discharges in every quarter of the cycle. Charge moves to and fro in the wires, and no charge crosses the insulator, yet an AC current is present in the circuit. The current is largest when the voltage is changing fastest, which is when the voltage passes through zero, and it is zero when the voltage is at its peak and not changing for a moment. So the current leads the voltage by 90° (the voltage lags the current by 90°). That is the opposite of the pure coil. Never take a capacitor apart or join its two ends with a wire: it can hold charge.
| Quarter of the cycle | Source voltage | Capacitor | Current (positive = onto the upper plate) |
|---|---|---|---|
| 1 | rises from 0 to +max | charges | positive, falls from maximum to 0 |
| 2 | falls from +max to 0 | discharges | negative, grows from 0 to maximum |
| 3 | goes from 0 to −max | charges the other way | negative, falls from maximum to 0 |
| 4 | rises from −max to 0 | discharges | positive, grows from 0 to maximum |
Paper only. Copy the table of the four quarters and add a row for the moment “voltage at its peak” and a row for “voltage passing through zero”. In each row write the current: zero, or the largest. Then compare with the pure coil of Week 12, where the voltage led the current, and write one sentence on the difference.