In an A C circuit the emf (e) and the current (i) at any instant...

Key Idea: The power is defined as the rate at which work is being done in the circuit. Power = rate of work done in one complete cycle. $$\begin{aligned} & P_{a \nu}=\frac{W}{T} \\ & P_{a \nu}=\frac{\left(E_0 I_0 \cos \phi\right) T / 2}{T} \\ & P_{a \nu}=\frac{E_0 I_0 \cos \phi}{2} \end{aligned}$$ where $\cos \phi$ is called the power factor of an AC circuit.