ABSTRACT
Alternating currents and voltages change their polarity during each cycle. It is not surprising therefore to find that power also pulsates with time. The product of voltage v and current i at any instant of time is called instantaneous power p, and is given by:
p = vi
26.2 Determination of power in a.c. circuits
(a) Purely resistive a.c. circuits Let a voltage v=Vm sinωt be applied to a circuit comprising resistance only. The resulting current is i= Im sin ωt, and the corresponding instantaneous power, p, is given by:
p= vi = (Vm sinωt)(Im sinωt) i.e. p=VmIm sin2 ωt From trigonometrical double angle formulae, cos 2A= 1-2 sin2A, from which,
sin2A = 12 (1 − cos 2A) Thus sin2ωt = 12 (1− cos 2ωt) Then power p=VmIm
[ 1 2 (1− cos 2ωt)
] i.e. p= 12VmIm(1− cos 2ωt) The waveforms of v, i and p are shown in Figure 26.1. The waveform of power repeats itself after π/ω seconds and hence the power has a frequency twice that of voltage and current. The power is always positive, having a maximum value of VmIm. The average or mean value of the power is 1 2VmIm. The rms value of voltage V = 0.707Vm, i.e.
