Four identical thin, square metal sheets, $S_1, S_2, S_3$, and $S_4$, each of side $a$ are kept parallel to each other with equal distance $d( < < a)$ between them, as shown in the figure. Let $C_0=\varepsilon_0 a^2 / d$, where $\varepsilon_0$ is the permittivity of free space.
Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.
| $List-I$ | $List-II$ |
| ($P$) The capacitance between $S_1$ and $S_4$, with $S_2$ and $S_3$ not connected, is | ($1$) $3 C_0$ |
| ($Q$) The capacitance between $S_1$ and $S_4$, with $S_2$ shorted to $S_3$, is | ($2$) $C_0 / 2$ |
| ($R$) The capacitance between $S_1$ and $S_3$, with $S_2$ shorted to $S_4$, is | ($3$) $C_0 / 3$ |
| ($S$) The capacitance between $S_1$ and $S_2$, with $S_3$ shorted to $S_1$, and $S_2$ shorted to $S_4$, is | ($4$) $2 C_0 / 3$ |
| ($5$) $2 C_0$ |
IIT 2024, Advanced
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