What does the capacitance of a parallel plate capacitor mean?
Two capacitors with capacitances $C_1$ and $C_2$ are joined in parallel to a power supply with electromotive force (e.m.f.) $E$, as shown in Fig. 5.1. Show that the total capacitance $C_T$ of the pair is $C_T = C_1 + C_2$. Give your working. You may annotate Fig. 5.1 if you want.
A pair of capacitors with capacitances $22\,\mu\text{F}$ and $47\,\mu\text{F}$, together with a resistor of resistance $2.7\,\text{M}\Omega$, are arranged in the circuit of Fig. 5.2. The battery provides an e.m.f. of $12\,\text{V}$. Show that the two capacitors together have capacitance $15\,\mu\text{F}$.
The two-way switch $S$ starts at position $X$, so the capacitors are fully charged. Using the data from (c)(i), calculate the total energy stored in the two capacitors.
The two-way switch is then shifted to position $Y$. Find the time taken for the potential difference (p.d.) across the $22\,\mu\text{F}$ capacitor to fall to $6.0\,\text{V}$.