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Q. Two capacitors of capacities $2\, C$ and $C$ are joined in parallel and charged up to potential $V$. The battery is removed and the capacitor of capacity $C$ is filled completely with a medium of dielectric constant $K$. The potential difference across the capacitors will now be:

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Solution:

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$V_{C}=\frac{2 C V+C V}{K C+2 C}$
$=\frac{3 V}{K+2}$