Question

Suppose, one wishes to construct a 1⋅0 farad capacitor using circular discs. If the separation between the discs be kept at 1⋅0 mm, what would be the radius of the discs?

Answer 1

The capacitance of a parallel-plate capacitor is given by
$C=\frac{{\in }_{0}A}{d}$
Here,
A = Area of the plate
d = Distance between the parallel plates
Now,
Let the radius of the disc be r.
$$\begin{gathered} \therefore C=\frac{{\in }_{0}A}{d}=\frac{{\in }_0\left(\mathrm{\pi }{r}^2\right)}{d} \\ \Rightarrow r=\sqrt{\frac{Cd}{{\in }_0\mathrm{\pi }}} \\ \Rightarrow r=\sqrt{\frac{1\times (1\times {10}^{-3})}{8.85\times {10}^{-12}\times 3.14}}=\sqrt{35.98\times {10}^6}\mathrm{m} \\ \Rightarrow r\approx \sqrt{36\times {10}^6}\mathrm{m}=6\times {10}^3\mathrm{m}=6\mathrm{km} \end{gathered}$$

Thus, the radius of the plates of the capacitor for the given configuration is 6 km.