Physics - Capacitor Question with Solution | TestHub

Capacitance of a paralle plate capacitor $\mathrm{C}=\frac{\epsilon \mathrm{A}}{\mathrm{d}}$ here $\epsilon$ is the permitivity of the medium For air medium $\epsilon ={\epsilon }_0=8.85\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}\therefore {\mathrm{C}}^{\prime }=\frac{{\epsilon }_0\mathrm{A}}{\mathrm{d}}\dots .1$ whearas for dielectric medium capacitance $\mathrm{C}=\frac{\epsilon \mathrm{A}}{\mathrm{d}}\dots 2$ From 1 and 2 $$\begin{array}{l}\frac{\mathrm{C}}{{\mathrm{C}}^{\prime }}=\frac{\epsilon }{{\epsilon }_0}\\ \therefore \epsilon =\frac{15}{3}\times 8.85\times 10^{-12}=\left(44.25\times 10^{-12}\right)=0.44\times 10^{-10}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^2\end{array}$$ Hence the permitivity of the medium $\epsilon =0.44\times 10^{-10}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^2$