State two distinct functions that capacitors perform in electrical circuits.
Three uncharged capacitors with capacitances $C_1$, $C_2$ and $C_3$ are arranged in series with a battery of electromotive force (e.m.f.) $E$ and a switch, as illustrated in Fig. 6.1. Once the switch is closed, plate P on the capacitor of capacitance $C_1$ carries charge $+q$. Show that the total capacitance $C$ of the three capacitors satisfies $\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dfrac{1}{C_3}$.
A student has four capacitors available, each with capacitance $20\,\mu\text{F}$. Draw a circuit diagram to show how the student can connect some or all of the capacitors to obtain a combined capacitance of $60\,\mu\text{F}$.
A student has four capacitors available, each with capacitance $20\,\mu\text{F}$. Draw a circuit diagram to show how the student can connect some or all of the capacitors to obtain a combined capacitance of $15\,\mu\text{F}$.