Question

In a parallel plate capacitor, the separation between the plates is $3mm$ with air between them. Now a $1mm$ thick layer of a material of dielectric constant $2$ is introduced between the plates due to which the capacity increases. In order to bring its capacity of the original value, the separation (in $mm$ ) between the plates must be made-

Answer 1

Answer: 3.50

$C_0=\frac{{ϵ}_{0}A}{d}$
$C_m=\frac{{ϵ}_{0}A}{\left[d^{\prime }-t+t/k\right]}$
By question
$C_m=C_0$
$\frac{{ϵ}_{0}A}{d}=\frac{{ϵ}_{0}A}{\left[d^{\prime }-t+t/k\right]}$
$d^{\prime }-1+\frac{1}{2}=3$
$d^{\prime }=4-\frac{1}{2}=\frac{7}{2}=3.5mm$