Question

Four metal plates are arranged as shown. Capacitance between $X$ and $Y$ is ($A\to$ Area of each plate, $d\to$ distance between the plates)

• A. $\frac{3}{2}\frac{{ϵ}_{0}A}{d}$
• B. $\frac{2{ϵ}_{0}A}{d}$
• C. $\frac{2}{3}\frac{{ϵ}_{0}A}{d}$
• D. $\frac{3{ϵ}_{0}A}{d}$

Answer 1

The correct option is C $\frac{2}{3}\frac{{ϵ}_{0}A}{d}$

Equivalent circuit is shown in the above figure.

Capacitance of each capacitor, $C=\frac{A{ϵ}_o}{d}$ ......(1)

Equivalent capacitance of capacitors connected in parallel $C^{\prime }=C+C=2C$

Equivalent capacitance between X and Y, $C_{eq}=\frac{C\times 2C}{C+2C}=\frac{2}{3}C$

$⟹$ $C_{eq}=\frac{2}{3}\frac{A{ϵ}_o}{d}$