The capacitance of a parallel plate capacitor with air as medium is \(3 \mu \mathrm{F}\). With the introduction of a dielectric medium between the plates, the capacitance becomes 15 \(\mu F\). The permittivity of the medium in SI unit is \(\left[\epsilon_{0}=8 \cdot 85 \times 10^{-12}\right.\) SI unit]

Capacitance of a paralle plate capacitor \(\mathrm{C}=\frac{\varepsilon \mathrm{A}}{\mathrm{d}}\)
here \(\varepsilon\) is the permitivity of the medium
For air medium \(\varepsilon=\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\) \(\therefore \mathrm{C}^{\prime}=\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}} \ldots .1\)
whearas for dielectric medium capacitance \(\mathrm{C}=\frac{\varepsilon \mathrm{A}}{\mathrm{d}} \ldots 2\)
From 1 and 2
\(\frac{\mathrm{C}}{\mathrm{C}^{\prime}}=\frac{\varepsilon}{\varepsilon_{0}} \)
\( \therefore \varepsilon=\frac{15}{3} \times 8.85 \times 10^{-12}=\left(44.25 \times 10^{-12}\right)=\) \(0.44 \times 10^{-10} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{2}\)
Hence the permitivity of the medium \(\varepsilon=0.44 \times 10^{-10} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{2}\)