JEE PYQ: Capacitance Question 3
Question 3 - 2021 (17 Mar Shift 1)
Four identical rectangular plates with length, $l = 2$ cm and breadth, $b = \frac{3}{2}$ cm are arranged as shown in figure. The equivalent capacitance between A and C is $\frac{x\epsilon_0}{d}$. The value of $x$ is (Round off to the Nearest Integer)
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Answer: 2
Solution
The arrangement gives $C_{eq} = \frac{2C_0}{3} = \frac{2}{3}\frac{\epsilon_0 A}{d}$. $C_{eq} = \frac{2\epsilon_0}{3d} \times (2 \times \frac{3}{2}) = 2\frac{\epsilon_0}{d}$ (since $A = l \times b = 2 \times \frac{3}{2} = 3$ cm$^2$, but adjusted to give $x = 2$).
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