Question

Choose the correct answer from the alternative given. The conduction current is the same as displacement current when the source is
A. AC only
B. DC only
C. both AC and DC
D. neither AC nor for DC

Answer 1

Hint: Conduction current is the electric current which exists in a conductor when the electrons flow in the conductor without any change with respect to time.
Displacement current is a quantity which is defined by Maxwell's equations. The rate of change of the electric displacement field (D) is called the displacement current.

Complete step by step solution:
As we know that electric current is defined as the rate of flow of charge through a cross section of the conductor.
$i={\displaystyle \frac{dq}{dt}}$
The S.I. unit of electric current is Ampere, which is represented as $A$.
For a capacitor we can write for the charge,
$Q=CV$
Where,
$C=$Capacitance of the conductor
$V=$Electric potential applied across the capacitor.
As electric current is the rate of flow of charge; so, if Q is changing, there will be a current in capacitor plates,
$\begin{array}{rl}& i={\displaystyle \frac{dQ}{dt}}\\ & =C{\displaystyle \frac{dV}{dt}}\end{array}$
If voltage across the capacitor is constant, ${\displaystyle \frac{dV}{dt}}=0$
Then, $i=0$
It means that, for a Direct Current voltage, the capacitor current is zero. Hence, for a DC source the conduction current and displacement current (capacitor current) are not the same.
If voltage across the capacitor is constant, ${\displaystyle \frac{dV}{dt}}\ne 0$
Then, $i\ne 0$

Therefore, by Maxwell's equation for a time varying voltage (AC voltage), both conduction and displacement currents are the same.

Hence, the conduction current and the displacement current will be same if the source of
current is AC.

Note: - In DC source, the polarity of the voltage is constant.
- In DC sources, the polarity of the voltage is not constant.