Power in AC Circuit

In a DC circuit, electrical power is simply the product of the (constant) voltage and current: $P=VI$. In an AC circuit, however, both the instantaneous voltage e and instantaneous current i are continuously changing with time, so the INSTANTANEOUS power $P=ei$ also constantly fluctuates throughout each cycle -- sometimes even becoming momentarily negative, when energy flows briefly back from the circuit element toward the source. Because of this constant fluctuation, a single instantaneous power value is not a meaningful description of how much energy an AC circuit actually consumes over time; instead, what matters physically is the AVERAGE power dissipated over one complete cycle, $P_{av}=\dfrac{1}{T}\displaystyle\int_0^T P\,dt$. The next four subsections work this average out in turn for a pure resistor, a pure …