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In the figure shown the effective capacity across P and Q is (the area of each plate is ‘a’)

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$\frac{a \in_{0}}{d} [\frac{K_{1}}{2} + \frac{K_{1} + K_{2}}{K_{2} K_{3}}]$

$\frac{a \in_{0}}{d} [\frac{K_{1}}{2} + \frac{K_{2} K_{3}}{K_{2} + K_{3}}]$

$\frac{a \in_{0}}{2 d} [\frac{K_{2}}{2} + \frac{K_{1} K_{3}}{K_{1} + K_{3}}]$

$\frac{a \in_{0}}{3 d} [\frac{K_{3}}{2} + \frac{K_{1} K_{2}}{K_{1} + K_{2}}]$

answer is A.

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Detailed Solution

$\begin{array}{l} C_{1} = \frac{K_{1} \in_{0} (\frac{A}{2})}{d}; C_{2} = \frac{K_{2} \in_{0} A}{d}; C_{3} = \frac{K_{3} \in_{0} A}{d} \\ ∴ C = \frac{C_{2} C_{3}}{C_{2} + C_{3}} + C_{1} \end{array}$

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