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Question

If the area of each plate is A (figure) and the successive separations are d,2d and 3d, the equivalent capacitance across A and B is ε0Axd. Find x :
154876_09596d1a784b4fa5bc490a08969711bc.png

Solution
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The equivalent circuit is shown in figure.
Here, C1=Aϵ0d and C2=Aϵ03d=C13
As they are in series so equivalent capacitance is CAB=C1C2C1+C2=C1(C1/3)C1+(C1/3)=C14=Aϵ04d
226670_154876_ans_643cbfaa513a4b5597c2faf81b0dc530.png

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If the area of each plate is A (figure) and the successive separations are d,2d and 3d, the equivalent capacitance across A and B is ε0Axd. Find x :
154876_09596d1a784b4fa5bc490a08969711bc.png
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