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and the rainfall
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Yeah, I know. It’s just a joke on the complexity of the formula for the equivalent single impedance. It doesn’t look so bad if you define intermediate variables to take it one step at a time. But if you try condensing it all to a single function written in terms of the original unknown impedances in the diagram above, it’s unwieldy as hell. Try it.
This must be what you people see when I talk about math.
Of course, one can approach simplifying as in series parallel simplification, I meant simplifying as obtaining a transfer function at some arbitrary port. Or did you mean simplifying as some sort of Thevenin/Norton source exercise?
Once you do all that, you obtain a single impedance seen from the AC source (the circle with the squiggly thing). It will have a complex symbolic expression, but you can then model that circuit as a single source and a single complex-valued resistor across it. That’s what simplifying means in electrical circuits.
And actually, you can simply add all impedances in series and use (1/Z_1 + 1/Z_2)^(-1) to calculate impedances in parallel to get to that last impedance equation. No need for all that KVL/KCL bull. SpaceCowboy is partly trolling you.
…Jesus Christ. I said “simplify,” man, not “combine into a hulking 12-variable polynomial.” But if you wanna go for it, hey, knock yourself out.
(Who am I kidding? I’ll probably try my hand at it later on.)
Symbolically.
Take some Laplace transforms and you get
Z_R = R_i, Z_C = 1/(sC_i) and Z_L = sL_i,
now do some KCL, KVL and Y-Delta transforms and you’re on your way LOL.
Well lol, Impedance generalizes resistances to include complex phase shifts imparted by reactive passive components such as inductors and capacitors.
Well sure if you want to be all alternative about it.
You mean impedance, right?
mouere*