Question 37 of 180

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 $\dfrac{x}{15}\dfrac{{\epsilon }_{0}A}{b}$, The value of $x$ is _____ .

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Answer: 23

Here the system can be considered as three capacitors in parallel.
So, net capacitance is
$C=\dfrac{{\epsilon }_{0}A}{5b}+\dfrac{{\epsilon }_{0}A}{3b}+\dfrac{{\epsilon }_{0}A}{b}$
$C=\dfrac{{\epsilon }_{0}A}{b}\left[\dfrac{1}{5}+\dfrac{1}{3}+\dfrac{1}{1}\right]$
$C=\dfrac{23{\epsilon }_{0}A}{15b}$