The displacement current ($I_d$) inside the capacitor is equal to the conduction current ($I$) flowing in the connecting wires.

1. Charge on Capacitor: The charge $q$ on the capacitor at any time $t$ is given by $q = CV$. Substituting the given voltage $V = V_0 \sin \omega t$: $q = C(V_0 \sin \omega t)$

2. Calculate Current: The current is the rate of change of charge. $I_d = \frac{dq}{dt} = \frac{d}{dt}(C V_0 \sin \omega t)$ $I_d = C V_0 \frac{d}{dt}(\sin \omega t)$ $I_d = C V_0 (\omega \cos \omega t)$ $I_d = V_0 \omega C \cos \omega t$

Therefore, the displacement current is $V_0 \omega C \cos \omega t$.