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Question

Two parallel plate capacitor of capacitances C and 2C are connected in parallel and charged to a potential difference V . If the batteryis disconnected and the space between the plate of the capacitor of capacince C is completely filled with a material of dielectric constant K, then the potential difference across the capacitor will be come 3V(K+2)(K+2)3V3V(K+2)3(K+2)V

A
(K+2)3V
B
3V(K+2)
C
3V(K+2)
D
3(K+2)V
Solution
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The original capacitance of the parallel combination of C and 2 C is = C +2C = 3C Total charge Q = 3CV When the capacitor C is filled with a dielectric, its capacitance becomes KC. Therefore, after the capacitor is filled with dielectric the capacitance of the combination, C' = KC + 2C = C (K + 2). However, the charge remains the same, i.e. Q = 3CV Therefore, the potential difference across the capacitors will be

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