In the following figure, area of each plate is A and d is separation between adjacent plates in free space. The capacitance of system between A and B is x3(∈0.Ad) if x is integer find

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In the following figure, area of each plate is A and d is separation between adjacent plates in free space. The capacitance of system between A and B is $\frac{x}{3} (\frac{\in_{0.} A}{d})$ if $x$ is integer find

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answer is 5.

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Detailed Solution

Area and distance are constant for each capacitor, so capacitance also remain constant.
Let it is C.
Question Image
The equivalent circuit can be drawn as

Hence, equivalent capacitance is $C_{A B} = \frac{(C + C) \times C}{(C + C) + C} + C = \frac{5 C}{3}$