If you need a refresher, this web page by Jason Starck has an excellent overview of the Standard Model version.
Impedance is the net sum of the capacitive and inductive reactances and resistance in the circuit. The equations for capacitive and inductive reactance are:
- Xc = 1 / 2pi * freq * capc
- Xl = 2pi * freq * indc
in the APM, the inverse of frequency times capacitance is magnetic flux, as is frequency times inductance. In the present form of the impedance equation resistance adds to magnetic flux, which is not supposed to happen in math. The units must be the same when adding.
It is interesting that the imaginary number has to be introduced into the equation in order to force the correct answer. The imaginary number is the square root of -1. It would seem that the incorrect units force the invention of the imaginary number. I'll need to give this more thought and try to verify it with experiment, but the charge dimensions in magnetic flux is the square root of the charge dimensions in resistance.
I find it also interesting that the phase angles of the inductance and capacitance have to be accounted for in the impedance equation. In the APM, the electrons have a definite magnetic structure with poles. It would seem the magnetic structure of the electrons is again verified, this time by the impedance equation.
I also notice that 2pi occurs frequently in Standard Model equations involving resonance, but APM equations suggest the value should be 4pi. This is something I've been wanting to investigate for some time. I'll give it some more thought.