Four identical thin, square metal sheets, $S_1, S_2, S_3$ and $S_4$, each of side $a$ are kept parallel to…

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.
  1. $\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 5$
  2. $\mathrm{P} \rightarrow 2 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 1$
  3. $\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 1$
  4. $\mathrm{P} \rightarrow 3$; $\mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 5$

Solution

For P All are in series \(\begin{gathered} C_{e q}=\frac{C_0}{3} \\ P \rightarrow(3) \end{gathered}\) For Q \(\begin{gathered} C_{e q}=\frac{C_0}{2} \\ Q \rightarrow(2) \end{gathered}\) For R \(\begin{gathered} C_{e q}=\frac{2 C}{3} \\ R \rightarrow(4) \end{gathered}\) For S \(\begin{aligned} & \Rightarrow C_{e q}=3 C_0 \\ & S \rightarrow(1) \end{aligned}\) `

Asked in: JEE Advanced 2024 (Paper 1)

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