Two parallel plate capacitors of capacity \(C\) and \(3\,C\) are connected in parallel combination and charged to a potential difference \(18\,V\). 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 & Solution

Correct Answer

(C) \(6\)

Step-by-step Solution

Detailed explanation

Initial charge on \(C =18\,CV\)

initial charge on \(3 C =54\,CV\)

Let final common potential difference \(= V ^{\prime}\)

\(9\,CV ^{\prime}+3\,CV ^{\prime}=18\,CV +54\,CV\)

\(12\,CV ^{\prime}=72\,CV \Rightarrow V ^{\prime}=6 V\)

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