Question

Two parallel plate capacitors of capacity $C$ and $3C$ are connected in parallel combination and charged to a potential difference $18V$. The battery is then disconnected and the space between the plates of the capacitor of capacity $C$ is completely filled with a material of dielectric constant $9$. The final potential difference across the combination of capacitors will be______ $V$

Answer 1

Answer: 6

Initial charge on $C=18CV$
initial charge on $3C=54CV$
Let final common potential difference $=V^{\prime }$
$9C{V}^{\prime }+3C{V}^{\prime }=18CV+54CV$
$\Rightarrow 12C{V}^{\prime }=72CV\Rightarrow V^{\prime }=6V$