CAIE A-Level Physics 19.2.2 Capacitor Energy Equations

Practise calculating capacitor energy with W = ½QV = ½CV² and Q²/(2C), rearranging for Q, C or V and comparing storage when quantities change.

Exam points

calculate stored energy using W = 1/2QV = 1/2CV²
rearrange the energy formula to determine charge, capacitance or voltage
compare energy storage when capacitor quantities change

[Maximum number: 3]

A battery of e.m.f. 12 V and negligible internal resistance is connected to a network of two capacitors and a resistor, as shown in Fig. 7.2.

Fig. 7.2

The capacitors have capacitances of $200 \mu \mathrm{~F}$ and $600 \mu \mathrm{~F}$ . The switch has two positions, A and B.

The switch is now moved from position A to position B.

Calculate the potential difference across the $600 \mu \mathrm{~F}$ capacitor when it has discharged 50 % of its initial energy.
potential difference = V

energy $=1 / 2 C V^{2}$ or energy =1 / 2 Q V and C=Q / V
$\frac{1}{2} \times C \times 3^{2}=2 \times \frac{1}{2} \times C \times V^{2}$ $V=2.1 \mathrm{~V}$
A1

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19.2.2—W = 1/2 QV = 1/2 CV 2 question 1