Question

A parallel plate capacitor is composed of two rectangular plates with length 5mm and width 3 mm. The thickness of the insulating material is 0.5 mm. Find the permittivity of the insulating material if the capacitance is 2 μF

Answer 1

Length of rectangular plate, $L=5\space mm=5\times10^{-3}\space m$

Breadth of plate, $B=3\space mm=3\times10^{-3}\space m$

Area of plate, $A=15\times10^{-6}\space m^2$

Thickness of plate, $d=0.5\space mm=0.5\times10^{-3}\space m$

Capacitance, $C=2\space\mu F=2\times10^{-6}\space F$

Let permittivity of plate be $\epsilon$

Capacitance of parallel plate capacitor is given by

$C=\dfrac{\epsilon A}{d}$

Since, parallel plate capacitor is composed of two rectangular plates

$C=\dfrac{\epsilon A}{2d}$

$\epsilon=\dfrac{C\times2d}{A}$

$\epsilon=0.133\times10^{-3}\space C^2/N\space m^2$