Question:
Four identical rectangular plates with length, $l=2 \mathrm{~cm}$ and breadth, $\mathrm{b}=\frac{3}{2} \mathrm{~cm}$ are arranged as shown in figure. The equivalent capacitance between $\mathrm{A}$ and $\mathrm{C}$ is $\frac{\mathrm{x} \varepsilon_{0}}{\mathrm{~d}}$. The value of $\mathrm{x}$ is (Round off to the Nearest Integer)
Solution:
$\mathrm{C}_{\mathrm{eq}}=\frac{2 \mathrm{C}_{0}}{3}=\frac{2}{3} \frac{\mathrm{E}_{0} \mathrm{~A}}{\mathrm{~d}}$
$\mathrm{C}_{\mathrm{eq}}=\frac{2 \epsilon_{0}}{3 \mathrm{~d}} \times\left(2 \times \frac{3}{2}\right)=2\left(\because \mathrm{A}=1 \mathrm{~b}=2 \times \frac{3}{2}\right)$