Question

A capacitor has been charged by a dc source. What are the magnitudes of conduction and displacement currents, when it is fully charged?

Answer 1

We know,

Conduction current $I_c=C.\frac{dv}{dt}⟶\left(i\right)$

[Fully charged means, voltage and charge is constant]

so, $\frac{dv}{dt}=0⟶\left(ii\right)$

By equation $\left(i\right)$ & $\left(ii\right)$

$I_c=0$

Displacement current $I_D={\epsilon }_o\frac{d\varphi }{dt}$

$={\epsilon }_o\frac{d\left(\frac{q}{{\epsilon }_o}\right)}{dt}$

$=0(\frac{dq}{dt}=0)$