Four identical thin, square metal sheets, $S_1, S_2, S_3$ and $S_4$ , each of...

2 months ago 1

Four identical thin, square metal sheets,

S_{1}, S_{2}, S_{3}

$S_1, S_2, S_3$ and

S_{4}

$S_4$ , each of side

a

$a$ are kept parallel to each other with equal distance

d (≪ a)

$d(\ll a)$ between them, as shown in the figure. Let

C_{0} = ε_{0} a^{2} / d

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

ε_{0}

$\varepsilon_0$ is the permittivity of free space.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

P \to 3; Q \to 2; R \to 4; S \to 5

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

P \to 2; Q \to 3; R \to 2; S \to 1

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

P \to 3; Q \to 2; R \to 4; S \to 1

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

P \to 3

$\mathrm{P} \rightarrow 3$ ;

Q \to 2; R \to 2; S \to 5

$\mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 5$

Solution:

For P

All are in series

\begin{matrix} C_{e q} = \frac{C_{0}}{3} \\ P \to (3) \end{matrix}

$\begin{gathered} C_{e q}=\frac{C_0}{3} \\ P \rightarrow(3) \end{gathered}$
For Q

\begin{matrix} C_{e q} = \frac{C_{0}}{2} \\ Q \to (2) \end{matrix}

$\begin{gathered} C_{e q}=\frac{C_0}{2} \\ Q \rightarrow(2) \end{gathered}$
For R

\begin{matrix} C_{e q} = \frac{2 C}{3} \\ R \to (4) \end{matrix}

$\begin{gathered} C_{e q}=\frac{2 C}{3} \\ R \rightarrow(4) \end{gathered}$
For S

\begin{aligned} \Rightarrow C_{e q} = 3 C_{0} \\ S \to (1) \end{aligned}

$\begin{aligned} & \Rightarrow C_{e q}=3 C_0 \\ & S \rightarrow(1) \end{aligned}$

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Four identical thin, square metal sheets, $S_1, S_2, S_3$ and $S_4$ , each of...