A parallel plate capacitor has plate area \(40\,cm ^2\) and plates separation \(2\,mm\). The space between the plates is filled with a dielectric medium of a thickness \(1\,mm\) and dielectric constant \(5\) . The capacitance of the system is :

\(\frac{1}{C_{e q}}=\frac{1}{C_1}+\frac{1}{C_2}\)

\(=\frac{1}{\frac{K \in_0 A}{t}}+\frac{1}{\frac{\epsilon_0 A}{d-t}}\)

\(=\frac{ t }{ K \in_0 A }+\frac{ d - t }{\epsilon_0 A }\)

\(=\frac{1 \times 10^{-3}}{5 \epsilon_0 \times 40 \times 10^{-4}}+\frac{1 \times 10^{-3}}{\epsilon_0 40 \times 10^{-4}}\)

\(\frac{1}{ C _{ eq }}=\frac{1}{20 \epsilon_0}+\frac{1}{4 \epsilon_0}\)

\(C _{ eq }=\frac{20 \times 4 \epsilon_0}{24}=\frac{10 \epsilon_0}{3} F\)