Answer:
Option A
Explanation:
initial effective capacity of the series combination is
$\frac{1}{C_{1}}=\frac{1}{C_{}}+\frac{1}{C_{}}=\frac{2}{C_{}}$
$\Rightarrow$ $C_{1}=\frac{C}{2}$
Effective capacity of the series combination with dielectric material is
$\frac{1}{C_{1}}=\frac{1}{C}+\frac{1}{KC}$
$\frac{1}{C_{2}}=\frac{1}{C_{}}\left[1+\frac{1}{K}\right]$
$\therefore$ $C_{2}=\frac{C}{\left(1+\frac{1}{K}\right)}=\frac{CK}{(K+1)}$
The change in the effective capacitance is $\triangle C= C_{2}-C_{1}$
$=\frac{CK}{\left(1+K\right)}-\frac{C}{2}=C\left[\frac{K}{K+1}-\frac{1}{2}\right]$
$=C\left[\frac{2K-K-1}{( 2(K+1)}\right]=\frac{C}{2}\left[\frac{K-1}{K+1}\right]$
