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Question

A capacitor stores 60 μC charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of 120 μC flows through the battery. The dielectric constant of the material inserted is :

A
1
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B
2
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C
3
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D
none
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Solution

The correct option is C 3
The capacitance before filled with dielectric is C=Aϵ0d
The capacitance after filled with dielectric is C=Akϵ0d=kC
Initial charge, Q=60μC and total charge after filled with dielectric Q=120+60=180μC
Here, Q=CV and Q=CV=kCV
QQ=kCVCV
k=QQ=18060=3

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