State two uses of capacitors in electrical circuits.
Three uncharged capacitors of capacitance $C_1$, $C_2$ and $C_3$ are connected in series, as shown in Fig. 4.1. A charge of $+Q$ is placed on plate A of the capacitor of capacitance $C_1$. State and explain the charges that will appear on the remaining plates of the capacitors. You may annotate Fig. 4.1 if you want.
Use your result from (i) to obtain an expression for the equivalent capacitance of the capacitors.
A capacitor of capacitance $12\,\mu\text{F}$ is charged using a battery of e.m.f. $9.0\,\text{V}$, as shown in Fig. 4.2. Switch $S_1$ is closed and switch $S_2$ is open. The capacitor is then disconnected from the battery by opening $S_1$. Calculate the energy stored in the capacitor.
The $12\,\mu\text{F}$ capacitor is now joined to an uncharged capacitor of capacitance $20\,\mu\text{F}$ by closing $S_2$. Switch $S_1$ stays open. The total energy now stored in the two capacitors is $1.82 \times 10^{-4}\,\text{J}$. Suggest why this value differs from your answer in (i).