Two condensers of capacities $2C$ and $C$ are joined in parallel and charged upto potential $V$. The battery is removed and the condenser of capacity $C$ is filled completely with a medium of dielectric constant $K$. The $p.d.$ across the capacitors will now be
IIT 1988, Medium
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(a) ${q_1} = 2CV,$ ${q_2} = CV$
Now condenser of capacity $C$ is filled with dielectric $K$, therefore $C_2 = KC$
As charge is conserved
${q_1} + {q_2} = (C'_2+ 2C)V'$ $==>$ $V' = \frac{{3CV}}{{(K + 2)C}} = \frac{{3V}}{{K + 2}}$
Now condenser of capacity $C$ is filled with dielectric $K$, therefore $C_2 = KC$
As charge is conserved
${q_1} + {q_2} = (C'_2+ 2C)V'$ $==>$ $V' = \frac{{3CV}}{{(K + 2)C}} = \frac{{3V}}{{K + 2}}$
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