Consider the following circuit:
VR = V0sin(ωt)
i = v/R = V0sin(ωt)/R
The maximum current, I0, is when sin(ωt)=1, so
I0 = V0/R
i = I0sin(ωt)
If p is instantaneous power, and P0 is maximum power, then
p = iv = i2R = (I0sin(ωt))2R = I02R sin2(ωt) P0 = I02R p = P0sin2(ωt)
The following graph shows the relationship between the instantaneous values of voltage (v), current (i), and power (p):
Fischer-Cripps. A.C., The Electronics Companion. Institute of Physics, 2005.
Copyright © 2014 Barry Watson. All rights reserved.