Question

Show that the displacement current in the dielectric of a parallel-plate capacitor is equal to the conduction current in the connecting leads.

Answer 1

The capacitance of a parallel-plate capacitor is given by

where A is the area of the plate and d is the plate separation. 

At any instant if V is the voltage across the capacitor then the charge on the plate of the capacitor is

q = CV

Now, the electric field in the dielectric is (neglecting the fringe effect)

where vector D → is normal to the plates. The displacement current is

where i_C is the conduction current.