Physics - Capacitor Question with Solution | TestHub

Let $C={\epsilon }_{0}S/d$. (P): C and C/3 in series: $C_{eq}=\frac{C\cdot C/3}{C+C/3}=\frac{C}{4}=\frac{{\epsilon }_{0}S}{4d}$, P$\to 3$.

(Q): two C in series: $C_{eq}=\frac{C}{2}=\frac{{\epsilon }_{0}S}{2d}$, Q$\to 4$.

(R): the series-parallel plate combination gives $C_{eq}=\frac{2C}{3}=\frac{2{\epsilon }_{0}S}{3d}$, R $\to 2$.

(S): $C_{eq}=\frac{{\epsilon }_0(S/2)}{d}+\frac{{\epsilon }_0(S/2)}{2d}=\frac{3{\epsilon }_{0}S}{4d}$, S$\to 1$. Option (B).