Question

A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.

Answer 1

(a) The capacitance of a cylindrical capacitor is given by

$$\begin{gathered} C=\frac{2\mathrm{\pi }{\in }_{0}l}{\ln \left({\displaystyle \frac{R_2}{R_1}}\right)} \\ \Rightarrow C=\frac{2\times 3.14\times 8.85\times {10}^{-12}\times 0.10}{\ln 2} \\ \Rightarrow C=8\mathrm{pF}\left(\because \mathrm{l}\mathrm{n}2=0.693\right) \end{gathered}$$

(b) When a capacitor of the same height with cylinders of radii 4 mm and 8 mm is taken, its capacitance comes to 8 pF, which is the same as above because the ratio of the radii is the same.