What is the average power supplied to a capacitor over one complete cycle when an AC voltage is applied across it?
The context clearly states, 'So, as in the case of an inductor, the average power $P_C = \frac{1}{2} i_m v_m \langle \sin(2\omega t) \rangle = 0$ since $\langle \sin(2\omega t) \rangle = 0$ over a complete cycle.' (Equation 7.19 and accompanying text). Also, point 4 under summary confirms 'the average power supplied to a capacitor over one complete cycle is zero.'.