Question

You are given two parallel plate capacitors $C_1$ and $C_2$. The space between the plates of $C_2$ is now filled with dielectrics $K_1$ and $K_2$ as shown. Find the capacitor $C_2$ in terms of $C_1$ and the dielectric constants $K_1$ and $K_2$.

Answer 1

$C_1=\frac{{ϵ}_{o}A}{d}$

$C_2=\frac{2{ϵ}_{o}A}{d}\left[\frac{K_1{K}_2}{K_1+K_2}\right]$

$C_2=2C_1\left[\frac{K_1{K}_2}{K_1+K_2}\right]$