The charge on a parallel plate capacitor varies as $\mathrm{q}=\mathrm{q}_0 \cos 2 \pi \mathrm{vt}$. The plates are very large and close together (area = A, separation = d). The displacement current through the capacitor is:

$-\mathrm{q}_0 2 \pi \mathrm{v} \sin 2 \pi \mathrm{vt}$

Displacement current, $\mathrm{I}_{\mathrm{D}}=$ conduction current, $\mathrm{I}_{\mathrm{C}}$

∴  $\frac{\mathrm{dq}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left[\mathrm{q}_0 \cos 2 \pi \mathrm{vt}\right]=-\mathrm{q}_0 2 \pi \mathrm{v} \sin 2 \pi \mathrm{vt}$