Question

Suppose one wishes to construct a $1.0farad$ capacitor using circular discs. If the separation between the discs be kept at $1.0mm$, What would be the radius of the discs?

Answer 1

Let the radius of the disc $=R$

$\therefore$ The area of the discs will be $=\pi R^2$

The distance between the two plates is $D=1mm={10}^{-3}m$

The capacitance of the capacitor is given by:

$\therefore C=\frac{{\epsilon }_{0}A}{d}$

$\Rightarrow 1=\frac{8.85\times {10}^{-12}\times \pi r^2}{{10}^{-3}}$

$\Rightarrow r^2=\frac{{10}^{-3}\times {10}^{12}}{8.85\times \pi }$

$=\frac{{10}^9}{27.784}=5998.5m=6km$