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The parallel combination of two air filled parallel plate capacitors of capacitance $C$ and $nC$ is connected to a battery of voltage, $V$. When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant $K$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is
$\frac{V}{{K + n}}$
$V$
$\frac{{\left( {n + 1} \right)\,V}}{{\left( {K + n} \right)}}$
$\frac{{nV}}{{K + n}}$
Solution
After fully charging, battery is disconnected.
Total chare of the system $=\mathrm{CV}+\mathrm{nCV}$
$=(n+1) C V$
After the insertion of dielectric of constant $\mathrm{K}$ New potential (common) $\mathrm{V}_{\mathrm{c}}=\frac{\text { Total charge }}{\text { Total capacitance }}$
$=\frac{(n+1) C V}{K C+n C}=\frac{(n+1) V}{K+n}$
