Originally Posted by bb
I'll freely admit, I'm a 3rd year student and I'm just starting to understand all of this theory. I know that there is inductive and capacitive reactance in a circuit that is shown by power factors. I have also never seen any of these differential equations or the AC equations shown by Steve. My question is this: Do the DC equations still correctly show the basic relationship between Power, Voltage, Current and Resistance, or does AC change all of this as Steve seems to be suggesting? If I'm missing something big, I would welcome someone pointing me in the right direction.
Watt's Law and Ohm's Law hold true, but only for instantanous measurements we never make in the real world- whenever you start dealing with harmonics and power correction, the easy rules of thumb (EG, taking RMS voltage and multiplying by peak current) are not accurate. In practice, you won't actually need to integrate or use any calculus because we're working with constant frequencies like 60Hz (and 60Hz harmonics) with GREATLY simplifies things! (And yes, that wiseass diffeq I put down was wrong. Shame on me- should all be simply dt. If you have to work in the wonderful world of RF, acoustics, vibration, etc, all the frequencies are different and it can get excrutiatingly painful very quickly!)

For instance, lets say you had a resistive load of 1 Ohm and a capacitive load of 0.5j Ohms (j=i= the square roof of negative 1) in series. This would give you an equivilent complex impedance of (1+.5j) which would be 1.118<26.5° in phasor notation.

Now, the apprentice might put his handy-dandy fluke on this and say "aha, I've got 107A, 120V x107A = 12.8kW!" but he'd be wrong. In this case, you'd have 12.8kVA, which is simply RMS volts x peak amps taken from your meter, but to actually determine power, phase angle has to be considered.
E = 120<0° Volts
R = 1.118<26.5° Ohms
I=E/R= 120<0 / 1.118<26.5 = 107<-26.5° Amps

-26.5° is a PF of .88 leading.

E = 120<0° Volts
I = 1.118<-26.5° Amps
P=ExR= 120<0° x 1.118<-26.5° = 12.8 x cos(-26.5°) = 12.8 x .88 = 11.2kW.

Last edited by SteveFehr; 01/04/08 08:17 AM.