Two parallel plate capacitors of capacity C and 3 ,C are connecte… - Vidyadip

Question

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

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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