Physics 9702 · AS & A Level · Capacitors and capacitance

Capacitors and capacitance — practice question

The capacitor shown in Fig. 6.1 has two parallel metal plates with air between them, separated by a variable gap $x$. The capacitance $C$ varies inversely with $x$. A supply charges the capacitor so that a potential difference (p.d.) $V$ exists across the plates.
(a)[1]

State expressions, using $C$ and $V$, for the charge $Q$ on one plate and for the energy $E$ stored in the capacitor.

(b(i))[1]

The capacitor charged in (a) is now detached from the supply. At first, the plates are separated by a distance $L$. They are then brought closer by a distance $D$, as shown in Fig. 6.2. State an expression, in terms of $C$, $V$, $L$ and $D$, for the new capacitance $C_N$.

(b(ii))[1]

State an expression, in terms of $C$, $V$, $L$ and $D$, for the new charge $Q_N$ on one plate.

(b(iii))[1]

State an expression, in terms of $C$, $V$, $L$ and $D$, for the new p.d. $V_N$ across the plates.

(c)[1]

Explain whether making the plate separation in (b) smaller causes the energy stored in the capacitor to increase or decrease.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence $Q = CV$ and $E = \tfrac{1}{2}CV^2$

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