In an alternating current circuit the average value of the current over a full cycle is zero, yet the average power dissipated is not zero. Why not?

1. In an alternating circuit the current is positive for half of each cycle and negative for the other half. 2. Averaging those two halves gives zero, which is why the root mean square value is used for current. 3. Power in a resistive circuit is the product of the current and the potential difference. 4. In such a circuit the current and the potential difference always carry the same sign as each other. 5. Two positive quantities multiply to a positive product, and two negative quantities also multiply to a positive product. 6. So the power is positive during both halves of the cycle and never cancels itself out. 7. The average power is therefore not zero, and no root mean square value is needed for the power itself. 8. The claim that current or voltage never becomes negative describes direct current, not alternating current, and power is measured in watts rather than volts. _Source: Siyavula Physical Sciences Grade 12 (Everything Science, CC BY 4.0), Chapter 11: Electrodynamics_