A parallel plate capacitor made of circular plates each of radius $\mathbf{R}=\mathbf{6 . 0} \mathbf{~ c m}$ has a capacitance $C=100 \mathrm{pF}$. The capacitor is connected to a $230 \mathrm{~V}$ ac supply with an (angular) frequency of $300 \mathrm{rad} \mathrm{s}^{-1}$.
(a) What is the rms value of the conduction current?
(b) Is the conduction current equal to the displacement current?
A parallel plate capacitor made of circular plates each of radius $\mathbf{R}=\mathbf{6 . 0} \mathbf{~ c m}$ has a capacitance $C=100 \mathrm{pF}$. The capacitor is connected to a $230 \mathrm{~V}$ ac supply with an (angular) frequency of $300 \mathrm{rad} \mathrm{s}^{-1}$.
(a) What is the rms value of the conduction current?
(b) Is the conduction current equal to the displacement current?

Solution:

Radius of each circular plate is given as $0.06m$

Capacitance of a parallel plate capacitor is given as $\mathrm{C}=100 \mathrm{pF}=100 \times 10^{-12} \mathrm{~F}$

Supply voltage is given as $V=230 \mathrm{~V}$

Angular frequency is given as $\omega=300 \mathrm{rad} \mathrm{s}^{-1}$

(a) Rms value of conduction current is represented by the equation,

$I=\frac{V}{X_{c}}$

Where,

$X_{c}=$ Capacitive reactance $=\frac{1}{\omega C}$

$\therefore I=V \times \omega C$

$=230 \times 300 \times 100 \times 10^{-12}$

$=6.9 \times 10^{-6} \mathrm{~A}$

$=6.9 \mu \mathrm{A}$

As a result, $6.9 \mu \mathrm{A}$ is the rms value of conduction current.

(b) Yes, conduction current is equivalent to displacement current.