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(C) The displacement current $I_D$ in a capacitor is equal to the conduction current flowing through the circuit,which is defined as the rate of chang

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$2\pi n q_0 \cos(2\pi nt)$

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(C) The displacement current $I_D$ in a capacitor is equal to the conduction current flowing through the circuit,which is defined as the rate of change of charge on the plates.$I_D = \frac{dq}{dt}$Given $q = q_0 \sin(2\pi nt)$.Differentiating with respect to time $t$:$I_D = \frac{d}{dt} [q_0 \sin(2\pi nt)]$$I_D = q_0 \cdot \cos(2\pi nt) \cdot \frac{d}{dt}(2\pi nt)$$I_D = 2\pi n q_0 \cos(2\pi nt)$.

The charge on a capacitor varies with time as $q = q_0 \sin(2\pi nt)$. What is the displacement current produced in the dielectric of the capacitor?

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