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. The potential differences across the capacitors now becomes...........

Options

A. `(2V)/(K+2)`
B. `(V)/(K+2)`
C. `(3V)/(K+3)`
D. `(3V)/(K+2)`

Answer

D

Explanation

`V_(c)=(Q_(1)+Q_(2))/(C_(1)+C_(2))=(CV+2CV)/(KC+2C)=(3V)/(K+1)`.