A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws \(25 \%\) more charge from the battery. The dielectric constant of mica is ___________ .

\(C =\frac{\epsilon_0 A}{ d }\)
\(Q _1= CV\)

\(Q _2=\left( c _{ eq }\right) v\)
\(Q _2=1.25 cv\)

\(c_{e q}=\frac{C_1 C_2}{C_1+C_2}=\frac{\frac{\in_0 A}{3} \times \frac{K \in_0 A}{2}}{\frac{\in_0 A}{3}+\frac{K \in_0 A}{2}}\)
\(c_{e q}=\frac{\left(\epsilon_0 A\right)^2\left(\frac{K}{6}\right)}{\epsilon_0 A\left(\frac{2+3 K}{6}\right)} \Rightarrow C_{e q}=\frac{K \epsilon_0 A}{2+3 K}\)
\(1.25 \times \frac{\in_0 A}{5}=\frac{K \in_0 A}{2+3 K} \Rightarrow 0.25(2+3 K)=K\)
\(2+3 K=4 K \Rightarrow K =2\)