September 2008
Beginner
834 pages
37h 13m
English
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8.9 APPARENT POWER, ACTIVE POWER, REACTIVE POWER AND POWER FACTOR
Consider a sinusoidal voltage source v(t) = Vm cosωt delivering power to a resistive load R. The current in the resistor is i(t) = Im cosωt, where I m = Vm/R.
The instantaneous power is p(t) = VmIm cos2ωt = 0.5 VmIm + 0.5 VmIm cos2ωt W. The first term is a constant and the second term produces an average of zero over a cycle. Therefore, the average power delivered to the resistor is 0.5 VmIm = 0.5Vm2/R = 0.5Im2R. The average power can be expressed as VrmsIms in terms of rms values of voltage and current. Thus, a sinusoidal voltage/current is only as effective as a DC voltage/current of magnitude that is only 70.7% of the amplitude of the sinusoid. The presence of the second term ...
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