Explanation:
For a capacitor, we have:
Q = CV
If Q is changing, there will be a current in capacitor plates,
$\text{I}=\frac{\text{dQ}}{\text{dt}}=\frac{\text{CdV}}{\text{dt}}$when voltage across the capacitor is constant, $\frac{\text{dV}}{\text{dt}}=0$
therefore, I = 0
It implies that, for a DC (constant) voltage, the capacitor current is zero.
Hence, for a DC source the conduction current and displacement current (capacitor current) are not same.
Whereas, by Maxwell's equation for a time varying voltage (AC voltage), both conduction and displacement currents are same.
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