Question

by inserting a plate of dielectric material between the plates of a parallel plate capacitor the energy is increased 5 times the dielectric constant of the material is

Answer 1

Dear Student,
$$\begin{gathered} Letdielectriccons\tan tofthematerialisK \\ then \\ C=C_{0}K \\ hereassumingbatteryisconnectedfromthecapacitor \\ sovoltagewillbecons\tan tatcapacitor \\ {U}_i=\frac{C_0{V}^2}{2} \\ {U}_f=\frac{K{C}_0{V}^2}{2} \\ \frac{U_i}{U_f}=\frac{\frac{C_0{V}^2}{2}}{\frac{K{C}_0{V}^2}{2}} \\ \frac{1}{5}=\frac{1}{K} \\ K=5 \end{gathered}$$
Regards