Question

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $\frac{x}{15} \frac{ε_0A}{b}$, the value of $x$ is ______?

Answer 1

The circuit is equivalent to $3$ capacitors in parallel.

$C_{eq}=\frac{ε_0A}{b}\bigg(1+\frac{1}{3}+\frac{1}{5}\bigg)=\frac{23}{15}\frac{ε_0A}{b}$

$⇒ x = 23$