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 capacitor C is completely filled with a material of
dielectric constant K. The potential difference across the
capacitors now becomes....

Answer 1

Total charge will remain unchanged.
Hence, $Q=Q^{\prime }$
or $3CV=(KC+2C)V^{\prime }$
$\therefore$ $V^{\prime }=\left(\frac{3}{K+2}\right)V$