Physics 9702 · AS & A Level · Discharging a capacitor
Discharging a capacitor — practice question
Fig. 7.1 shows a circuit that contains a capacitor with capacitance $C$ and a resistor with resistance $R$. At the start, the switch is open and the potential difference (p.d.) across the capacitor is $12\,\text{V}$. At $t = 0$ the switch is closed, so the capacitor discharges through the resistor. Fig. 7.2 shows how the charge $Q$ on the capacitor varies with the p.d. $V_C$ across it as the capacitor discharges. Fig. 7.3 shows how the current $I$ in the resistor varies with the p.d. $V_R$ across the resistor as the capacitor discharges.
(a)[1]
State how $V_C$ and $V_R$ are related.
(b(i))[2]
Determine the capacitance $C$, in $\mu\text{F}$.
(b(ii))[2]
Determine the resistance $R$, in $\text{k}\Omega$.
(b(iii))[2]
Determine the time constant $\tau$ of the circuit.
(c)[3]
Use Fig. 7.2, Fig. 7.3 and your answer in (a) to explain why the way $Q$ varies with $t$ is exponential.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$V_C = V_R$” …