D

In a pure inductor, the average power dissipated can be analyzed using the relationship between voltage across the inductor and the current through it. For an AC current of the form i(t) = I_0 \sin(\omega t), the voltage across the inductor v(t) can be represented as v(t) = L \frac{di}{dt} = L I_0 \omega \cos(\omega t). The instantaneous power is given by p(t) = v(t) \cdot i(t) = (L I_0 \omega \cos(\omega t))(I_0 \sin(\omega t)). This product will yield terms that oscillate with time, leading to an average power over one complete period being zero because the positive and negative contributions cancel out. Therefore, the average power dissipated in a pure inductor when an AC current flows through it is zero.