A parallel plate capacitor has plate area \(40 \mathrm{~cm}^2\) and plate separation 2 mm . The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 5 . The capacitance of the system is ( \(\varepsilon_0=\) permittivity of vacuum)

As the two capacitors are in series combination,
\(\frac{1}{\mathrm{C}_{\text {eq }}}=\frac{1}{\mathrm{C}_1}+\frac{1}{\mathrm{C}_2}=\frac{1}{\frac{\mathrm{~A} \varepsilon_0 k}{t}}+\frac{1}{\frac{A \varepsilon_0}{d-t}}=\frac{t}{\mathrm{~A} \varepsilon_0 \mathrm{k}}\) \(+~\frac{d-t}{\mathrm{~A} \varepsilon_0} \)
\( =\frac{1 \times 10^{-3}}{40 \times 10^{-4} \times 5 \varepsilon_0}+\frac{\left(2 \times 10^{-3}-1 \times 10^{-3}\right)}{40 \varepsilon_0 \times 10^{-4}} \)
\( \therefore \quad \frac{1}{\mathrm{C}_{\mathrm{eq}}}=\frac{1}{20 \varepsilon_0}+\frac{1}{4 \varepsilon_0} \)
\( \therefore \quad \mathrm{C}_{\mathrm{eq}}=\frac{10}{3} \varepsilon_0 \quad \mathrm{~F}\)