Discharging a capacitor

Figure 5.1 shows how the charge Q on one plate of a capacitor varies with potential difference V. In Fig. 5.2, the capacitor is connected to an 8.0\,\text{V} power supply together with two resistors R and S. R has resistance 25\,\text{k}\Omega and S has resistance 220\,\text{k}\Omega. The switch may be set to either position X or position Y.

Feb/March 2022

Three capacitors are arranged as in Fig. 4.1. Find the total capacitance, in $\mu\text{F}$, of the three-capacitor network.

Feb/March 2024

A capacitor with capacitance $C_1$ is placed in series with another capacitor of capacitance $C_2$. Show that the combined capacitance $C$ of the two capacitors is given by $\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2}$.

Feb/March 2025

Fig. 6.1 depicts a capacitor with capacitance $C$ in series with a resistor of resistance $R$. At the start, the switch is open and the capacitor has a p.d. of $12\,\text{V}$ across it. When $t = 0$, the switch is closed, so a current $I$ flows through the resistor. Fig. 6.2 gives the way $I$ changes with $t$.

May/June 2024

Fig. 6.1 illustrates a capacitor with capacitance $C$ in series with a resistor of resistance $R$. At the start, the switch is open and the capacitor has a p.d. of $12\ \text{V}$ across it. When $t = 0$, the switch is closed, producing a current $I$ in the resistor. Fig. 6.2 plots how $I$ changes with $t$.

May/June 2024

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.

May/June 2025

Fig. 8.1 shows an unfinished circuit diagram of a bridge rectifier.

May/June 2025

A capacitor with capacitance $470\,\mu\text{F}$ is joined to a battery with electromotive force (e.m.f.) $24\,\text{V}$ in the circuit shown in Fig. 5.1. The two-way switch $S$ is first in position $X$. Wires $P$ and $Q$ are the same long straight wires, each having a resistance of $5.6\,\text{k}\Omega$. They are set close to one another and run parallel. Wire $Q$ is attached to a voltmeter. At $t = 0$, switch $S$ is changed to position $Y$ so that the capacitor discharges through wire $P$.

Oct/Nov 2022

A capacitor with capacitance $C$ and a resistor with resistance $R$ are arranged as shown in Fig. 6.1. At the beginning, the capacitor is charged and the switch is open. The switch is then closed at time $t = 0$. Fig. 6.2 and Fig. 6.3 show, respectively, how the charge $Q$ on the capacitor and the potential difference (p.d.) $V$ across the resistor vary with $t$.

Oct/Nov 2022

A capacitor with capacitance $470\,\mu\text{F}$ is joined to a battery with electromotive force (e.m.f.) $24\,\text{V}$ in the circuit shown in Fig. 5.1. The two-way switch $S$ starts at position $X$. $P$ and $Q$ are identical long straight wires, each having a resistance of $5.6\,\text{k}\Omega$. The wires are positioned close to one another and run parallel. Wire $Q$ is attached to a voltmeter. At time $t = 0$, switch $S$ is changed to position $Y$, causing the capacitor to discharge through wire $P$.

Oct/Nov 2022

A capacitor $C$ has been charged until the potential difference (p.d.) $V$ across its terminals is $8.0\,\text{V}$. It is then connected into the circuit of Fig. 6.1. Initially, the switch is open. The switch is closed at time $t = 0$.

Oct/Nov 2023