Define capacitance of a parallel-plate capacitor.
On Fig. 7.1, sketch how the charge on capacitor X changes with p.d. as the p.d. rises from $0$ to $V$.
Determine an expression, in terms of $Q$ and $V$, for the work $W$ done on capacitor X during charging. Explain your working.
Capacitor X starts uncharged and has capacitance $C$; it is charged gradually until the p.d. across its plates is finally $V$ and the charge stored is $Q$.
A second capacitor $Y$ begins uncharged. The fully charged capacitor X in (b) is then connected to capacitor $Y$, as shown in Fig. 7.2. Capacitor $Y$ has capacitance $3C$.
Complete Table 7.1 by giving expressions, in terms of $Q$ and $V$, for the final p.d.s across the two capacitors and for the final charges on them. Use the space below for any working that you need.
State whether the total energy stored in the two capacitors is less than, the same as, or greater than the energy originally stored in capacitor X.