Define capacitance.
Three capacitors with capacitances $C_1$, $C_2$ and $C_3$ begin uncharged. They are then linked in series to a battery, as shown in Fig. 7.1. The battery provides a potential difference $V$ across the three capacitors. Show that the equivalent capacitance $C$ of the capacitors is given by $\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}$.
A battery with e.m.f. $12\,\text{V}$ and negligible internal resistance is joined to a circuit containing two capacitors and a resistor, as shown in Fig. 7.2. The capacitors have capacitances of $200\,\mu\text{F}$ and $600\,\mu\text{F}$. The switch can be set to positions A and B. (i) Move the switch to position A. Calculate: 1. the total capacitance of the two capacitors, 2. the charge on the $600\,\mu\text{F}$ capacitor, 3. the potential difference across the $600\,\mu\text{F}$ capacitor. (ii) Now move the switch from position A to position B. Calculate the potential difference across the $600\,\mu\text{F}$ capacitor after it has lost $50\%$ of its initial energy.