State two separate functions that capacitors perform in electrical circuits.
Three uncharged capacitors with capacitances $C_1$, $C_2$ and $C_3$ are connected in series to a battery of electromotive force (e.m.f.) $E$ and a switch, as shown in Fig. 6.1. Once the switch is closed, plate P of the capacitor with capacitance $C_1$ carries charge $+q$. Show that the equivalent capacitance $C$ of the three capacitors is given by the expression $\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dfrac{1}{C_3}$.
A student has four capacitors, each having capacitance $20\,\mu\text{F}$. Draw circuit diagrams to show how some or all of the capacitors may be connected to give a combined capacitance of $60\,\mu\text{F}$.
A student has four capacitors, each having capacitance $20\,\mu\text{F}$. Draw circuit diagrams to show how some or all of the capacitors may be connected to give a combined capacitance of $15\,\mu\text{F}$.