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 (<< 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)	\(3C_0\)
(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)	\(2C_0 /3\)
		(5)	\(2C_0\)

(A) P → 3; Q → 2; R → 4; S → 5 

(B) P → 2; Q → 3; R → 2; S → 1 

(C) P → 3; Q → 2; R → 4; S → 1 

(D) P → 3; Q → 2; R → 2; S → 5

Answer 1

Correct option is (C) P → 3; Q → 2; R → 4; S → 1 

For P

All are in series

\(C_{eq} = \frac {C_0}{3}\)

\(P \rightarrow (3)\)

For Q

\(C_{eq} = \frac {C_0}{2}\)

\(Q \rightarrow (2)\)

For R

\(C_{eq} = \frac {2C}{3}\)

\(R \rightarrow (4)\)

For S

\(\Rightarrow C_{eq} = 3C_0\)

\(S \rightarrow (1)\)