I've been deriving transmission line theory from scratch, out of curiosity, and I'm a bit hung up on one seemingly insignificant point.
When determining the real power drop on a reactive load with a reactive transmission line attached (and supplied by a voltage source), it is commonly accepted that the current amplitude in the loop should be multiplied by only the real part of the load impedance. This does not make sense to me. I think the current amplitude in the loop should be multiplied by the magnitude of the load impedance (r^2 + x^2)^(0.5).
What the hell is going on here!?
Best Answer
Go back to the time domain and see that, for the real part of the load impedance, power is always absorbed. The average power is, thus, non-zero.
However, for the imaginary (reactive) part of the impedance, power is alternately absorbed and then delivered (the power alternates from positive to negative). For the reactive part, the average power is, thus, zero.