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 $\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2}$.
Three identical capacitors, each with capacitance $C$, are arranged in the network shown in Fig. 5.1. The graph in Fig. 5.2 shows how the charge $Q$ varies with the potential difference (p.d.) $V$ between terminals X and Y. Show that $C$ is equal to $44\,\mu\text{F}$.
The capacitor network in Fig. 5.1 is first charged and then connected to a resistor of resistance $54\,\text{k}\Omega$. The capacitor network discharges through the resistor. Determine the time constant $\tau$ of the circuit. Give a unit with your answer.
Determine how long it takes for the discharge current to fall to $15\%$ of its initial value.