Question

Choose the correct answer from the alternatives given.
The conduction current is the same as displacement current when the source is

• A. $\text{AC}$ only
• B. $\text{DC}$ only
• C. both $\text{AC}$ and $\text{DC}$ (Transition phase)
• D. neither $\text{AC}$ nor for $\text{DC}$

Answer 1

The correct option is C both $\text{AC}$ and $\text{DC}$ (Transition phase)

We know that the displacement current in a capacitor is equal to the conduction current flowing in the connecting wires.
Therefore, as long as conducting current is flowing, displacement current will also flow in the capacitor.

We know that for a capacitor :

$Q=CV$

Now if $Q$ is changing, conduction current will flow in the wires and therefore, the displacement current will also flow in the capacitor plates.

$I_d=I_C=\frac{dQ}{dt}=C\frac{dV}{dt}$

We know that after long time, potential drop across a capacitor becomes constant when it is connected with $\text{DC}$ supply source.

When voltage across the capacitor is constant, i.e. $\frac{dV}{dt}=0$,

therefore, $I_c=I_d=0$.

It implies that, for $\text{DC}$, as voltage is constant, the capacitor current is zero.

Hence, for a $\text{DC}$ source the conduction current and displacement current (capacitor current) are not the same.

Whereas, by Maxwell's equation for a time varying voltage ($\text{AC}$ voltage), both conduction and displacement currents will always be the same.

Hence, option $\left(\text{A}\right)$ is correct.