Question

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 $d(\ll a)$ between them, as shown in the figure. Let $C_{0}=\varepsilon_{0} \mathrm{a}^{2} / \mathrm{d}$, 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 | |
|--------|--------|
| (P) | The capacitance between $S_{1}$ and $S_{4}$, with $S_{2}$ and $S_{3}$ not connected, is |
| (Q) | The capacitance between $S_{1}$ and $S_{4}$, with $S_{2}$ shorted to $S_{3}$, is |
| (R) | The capacitance between $S_{1}$ and $S_{3}$, with $S_{2}$ shorted to $S_{4}$, is |
| (S) | The capacitance between $S_{1}$ and $S_{2}$, with $S_{3}$ shorted to $S_{1}$, and $S_{2}$ shorted to $S_{4}$, is |

| List-II | |
|---------|--------|
| (1) | $C_{0}$ |
| (2) | $C_{0}/2$ |
| (3) | $C_{0}/3$ |
| (4) | $3C_{0}/2$ |
| (5) | $2C_{0}$ |

Accepted Answer

(C) $\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 1$

Answer

(A) $\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 5$

Answer

(B) $\mathrm{P} \rightarrow 2 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 1$

Answer

(D) $\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 5$

JEE Advanced · 2024 · 26 May 2024 · Paper 1 · Capacitance

Solution

More JEE Advanced questions on Capacitance

List-I
(P)	The capacitance between $S_{1}$ and $S_{4}$ , with $S_{2}$ and $S_{3}$ not connected, is
(Q)	The capacitance between $S_{1}$ and $S_{4}$ , with $S_{2}$ shorted to $S_{3}$ , is
(R)	The capacitance between $S_{1}$ and $S_{3}$ , with $S_{2}$ shorted to $S_{4}$ , is
(S)	The capacitance between $S_{1}$ and $S_{2}$ , with $S_{3}$ shorted to $S_{1}$ , and $S_{2}$ shorted to $S_{4}$ , is

List-II
(1)	$C_{0}$
(2)	$C_{0} /2$
(3)	$C_{0} /3$
(4)	$3 C_{0} /2$
(5)	$2 C_{0}$