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 the capacitor C is completely filled with a material of dielectric constant k. What is the potential difference across the capacitors now?

Explanation

If charges `Q_1" and "Q_2` be given to the capacitors, then
`Q_1 =CV, Q_2 = 2CV`
Total charge `= Q_1+Q_2= CV+2CV= 3CV`
If the region between the plates of capacitor C is filled with a meterial of dielectric constant `k`, its capacitance will be `kC`.
Total capacitance `= kC+2C= (k+2)C`
Ptential difference across the capacitors `= (3CV)/((k+2)C)= (3V)/(k+2)`.