Question

A slab of material of dielectric constant K has the same area as the plates of a parallel plate capacitor but has a thickness $\left(3/4\right)d$, where $d$ is the separation of the plates. The ratio of the capacitance $C$ (In the presence of the dielectric) to the capacitance $C_0$ (in the absence of the dielectric) is :

Answer 1

$C=\frac{E_{0}A}{\frac{\left(3/4d\right)}{k}+\frac{\left(1/4d\right)}{1}}$
$C_0=\frac{E_{0}A}{d}$
$=\frac{E_{0}A}{d(\frac{3}{4k}+\frac{1}{4})}$
$C=\frac{4C_0}{(3+k)}$
$\frac{C}{C_0}=\frac{4}{3+k}$