JEE Advanced 2024 · Paper 1 · Physics Q15

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PhysicsList match+3 / -1Question 32 of 51

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 $C_0 = \varepsilon_0 a^2/d$ , 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.

Perspective drawing of four identical square metal sheets S₁, S₂, S₃, S₄ (left to right), each of side a, standing parallel to one another. Adjacent sheets are separated by equal gaps d (three gaps marked d, d, d along the bottom). A vertical arrow beside S₄ marks the side length a.

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
$3C_0$
2
$C_0/2$
3
$C_0/3$
4
$2C_0/3$
5
$2C_0$

P → 3; Q → 2; R → 4; S → 5

P → 2; Q → 3; R → 2; S → 1

P → 3; Q → 2; R → 4; S → 1

P → 3; Q → 2; R → 2; S → 5

Answer and worked solution

Official answer: C

Each adjacent pair of sheets forms a capacitor $C_0$ .

(P) $S_1$ - $S_4$ with $S_2$ , $S_3$ floating: three $C_0$ in series, $\frac{C_0}{3}$ . → (3)

(Q) $S_2$ shorted to $S_3$ : the middle capacitor drops out, leaving two $C_0$ in series, $\frac{C_0}{2}$ . → (2)

(R) Between $S_1$ and $S_3$ with $S_2 = S_4$ : $C_0$ ( $S_1S_2$ ) in series with [ $S_2S_3$ and $S_4S_3$ in parallel $= 2C_0$ ], giving $\frac{2C_0}{3}$ . → (4)

(S) $S_1 = S_3$ and $S_2 = S_4$ : all three capacitors join the same two nodes, in parallel, $3C_0$ . → (1)

Option (C).

Topics:Series and parallel combinations Capacitors and capacitance

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JEE Advanced 2024 · Paper 1, Physics question 15