Question

Two parallel plate capacitors of capacitances $C$ and $2C$ are connected in parallel and charged to a potential difference $V$. The battery is then disconnected, and the region between the plates of $C$ is filled completely with a material of dielectric constant $K$. The common potential difference across the combination becomes :

• A. $\frac{2V}{K+2}$
• B. $\frac{V}{K+1}$
• C. $\frac{3V}{K+3}$
• D. $\frac{3V}{K+2}$

Answer 1

The correct option is D $\frac{3V}{K+2}$

Initially both capacitors are at potential $V$.
Charge on both plates are $CV$ and $2CV$.
When we put dielectric between the plates of $C$,
$C^{\prime }=KC$
Common potential, $V_C=\frac{Q_1+Q_2}{C_1+C_2}=\frac{CV+2CV}{KC+2C}=\frac{3V}{K+2}$