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Question

A capacitor is made of two plates. The first plate is flat plate of area A and second plate having a stair like structure as shown. The area of each stair is A3 and height is a. Find the capacitance of the assembly if C=ε0Aa.


A
1118C
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B
1718C
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C
1311C
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D
1113C
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Solution

The correct option is A 1118C

From the given figure it is clear that, the given arrangement behaves as parallel combination of three individual capacitors.

Since area A, and seperation between the plates are given. So, we can get individual capacitances of all three plates as follows,

C1=ε0×A3a=ε0A3a ; C2=ε0×A32a=ε0A6a ; C3=ε0×A33a=ε0A9a

Therefore, the equivalent capacitance or net capacitance,

Ceq=C1+C2+C3

Ceq=ε0Aa (13+16+19)

Ceq=1118C [C=ε0Aa]

Hence, option (a) is the correct answer.

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