Question

Two metal plates each of area form a parallel plate capacitor with air in between the  plates. The distance between the plates is . A metal plate of thickness and of same area is inserted between the plates to form two capacitors of capacitances and as shown in the figure. The effective capacitance of the two capacitors is C' and the capacitance of the capacitor initially is C, then is :

475402
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A

B

C

D

Hard

Solution

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Correct option is B)

Let the gap for capacitor 1 be x and that for capacitor 2 be y. Then,
and

Since the two are in series, 



Hence ,

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