Question

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 capacitors 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 :-

• A. $\frac{V}{K+n}$
• B. $V$
• C. $\frac{(n+1)V}{(K+n)}$
• D. $\frac{nV}{K+n}$

Answer 1

Answer: (C)

After fully charging, battery is disconnected

Total charge of the system $=CV+nCV$
$=(n+1)CV$
After the insertion of dielectric of constant $K$

New potential (common)
$V_C=\frac{\text{ total charge }}{\text{ total capacitance }}$
$=\frac{(n+1)CV}{KC+nC}=\frac{(n+1)V}{K+n}$.