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Question

Two parallel plate capacitors have their plate areas 100 cm2 and 500 cm2 respectively. If they have the same charge and potential difference, and the distance between the plates of first capacitor is 0.5 mm, then the distance between the plates of second capacitor is

A
0.10 cm
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B
0.15 cm
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C
0.20 cm
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D
0.25 cm
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Solution

The correct option is D 0.25 cm
Since the potential difference and charge on capacitor is same for both capacitors.

From the relation of capacitance,

Q=CVQV=C=Constant

C1=C2

Using the formula of capacitance of parallel plate capacitor, we get

A1ϵ0d1=A2ϵ0d2 .........(1)


Here A1=100 cm2; A2=500 cm2; d1=0.5 mm; d2=d

Substituting in eq. (1)

100ϵ00.5=500ϵ0d

d=2.5 mm=0.25 cm

Hence, option (d) is correct.

Why this question?Concept : The capacitance of a parallel plate capacitor is the ratio of charge on capacitor to the potential difference between its plates.

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