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Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ______ V.

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answer is 6.

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Detailed Solution

Initial charge on C = 18 CV

Initial charge on 3C = 54 CV

Let final common potential difference = V'

$\begin{array}{l} 9 {CV}^{'} + 3 {CV}^{'} = 18 CV + 54 CV \\ \Rightarrow 12 {CV}^{'} = 72 CV \Rightarrow V^{'} = 6 V \end{array}$

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