Question

By inserting a plate of dielectric material between the plates of a parallel plate capacitor at a constant potential, the energy is increased five times. The dielectric constant of the material is

Answer 1

Energy stored in the capacitor is given by,

$E_1=\frac{1}{2}C{V}^2$

After dielectric material is inserted,

$E_2=\frac{1}{2}{C}^{\prime }{V}^2$

$\frac{E_1}{E_2}=\frac{\frac{1}{2}C{V}^2}{\frac{1}{2}{C}^{\prime }{V}^2}=\frac{C}{C^{\prime }}$

$\frac{1}{5}=\frac{C}{C^{\prime }}=\frac{C}{KC}$

$K=5$