Question

A combination of parallel plate capacitors is maintained at a certain potential difference. When a $3mm$ thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by $2.4mm$. Find the dielectric constant of the slab.

• A. $4$
• B. $5$
• C. $3$
• D. $6$

Answer 1

The correct option is B $5$

Capacitance in parallel plate capacitor is given by

$C=\frac{{ϵ}_{0}A}{d}$

Now introducing a slab of thickness $t$, the capacitance $C^{\prime }$ is

$C^{\prime }=\frac{{ϵ}_{0}A}{d^{\prime }-t(1-1/K)}$

Now $q=CV$ as it remains same so,

$C=C^{\prime }$

$\frac{{ϵ}_{0}A}{d}=\frac{{ϵ}_{0}A}{d^{\prime }-t(1-1/K)}$

$d=d^{\prime }-t(1-1/K)$

$d=d+2.4\times {10}^{-3}-3\times {10}^{-3}(1-1/K)$

On solving we get

$K=5$

Hence correct answer is B.