Question

In a parallel plate capacitor, the separation between the plates is $3\, mm$ with air between them. Now a $1\, mm$ 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

$C_{0} =\frac{\epsilon_{0} A}{d} $
$C_{m} =\frac{\epsilon_{0} A}{\left[d^{\prime}-t+t / k\right]} $
By question
$C_{m} =C_{0} $
$\frac{\epsilon_{0} A}{d} =\frac{\epsilon_{0} A}{\left[d'-t+t / k\right]} $
$d'-1+\frac{1}{2}=3$
$d'=4-\frac{1}{2}=\frac{7}{2}=3.5\, mm$