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 $\frac{x}{15} \frac{ε_{0} A}{b}$ , The value of $x$ is _____ .

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Here the system can be considered as three capacitors in parallel. So, net capacitance is C = ε 0 A 5 b + ε 0 A 3 b + ε 0 A b C = ε 0 A b 1 5 + 1 3 + 1 1 C = 23 ε 0 A 15 b

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