A level Physics · Edexcel 9PH0 · Topic 7B

Capacitors

Key points

A capacitor stores charge on two plates separated by an insulator. Capacitance $C = \frac{Q}{V}$ , measured in farads (F).
Energy stored = area under a $Q$ – $V$ graph: $W = \frac{1}{2}QV = \frac{1}{2}CV^2 = \frac{Q^2}{2C}$ .
Discharging through a resistor, charge, current and p.d. fall exponentially: $Q = Q_0e^{-t/RC}$ , and similarly for $I$ and $V$ .
The time constant $\tau = RC$ is the time for $Q$ to fall to $\frac{1}{e}$ (about 37%) of its starting value. After $5RC$ the capacitor is effectively discharged.
Taking logs gives a straight line: $\ln Q = \ln Q_0 - \frac{t}{RC}$ , so the gradient of $\ln V$ against $t$ is $-\frac{1}{RC}$ .
While charging, current falls exponentially and $Q$ rises as $Q = Q_0(1 - e^{-t/RC})$ .
Core practical: use a data logger or voltmeter and stopwatch to record p.d. during discharge and find $RC$ .

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A capacitor stores charge, and therefore energy, on two conducting plates separated by an insulator. These notes cover capacitance, stored energy, exponential charging and discharging, and core practical 11.

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