# The Conjugate Match

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!?

• Note that an impedance has a magnitude even if it has no real part, and without any real parts, a circuit is lossless. E.g. lossless transmission line out to infinity.
– Kaz
May 12, 2013 at 0:27
• Current x impedance gives voltage across the load but it doesn't tell you the power taken by the load. If the load is X + R, the power taken by the load is I^2.R - it has nothing to do with X. May 12, 2013 at 10:13