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Question

# Two parallel plate capacitors with capacitances C and 2C are joined in parallel and the combination is connected to a battery of potential difference V. If the battery is now removed and a material of dielectric constant K is filled between the plates of capacitor C completely, then what will be the potential difference across the two capacitors?

A
VK+2
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B
2VK+2
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C
3VK+2
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D
3VK2
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Solution

## The correct option is C 3VK+2 Let the initial potential difference be V So, the initial charge on first capacitor, q1=CV Initial charge on second capacitor, q2=2CV As the battery is disconnected and a dielectric is introduced, the charge will redistribute on the capacitors. However, as this is an isolated system, charge will remain conserved. Let, the new potential difference be V′ which will be the same for both capacitors as they are connected in parallel. If q′1 and q′2 are the final charges on the capacitors, then from the conservation of charge q1+q2=q′1+q′2 ⇒CV+2CV=KCV′+2CV′ ⇒V′=3VK+2 Hence, option (c) is the correct answer.

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