ABSTRACT
From the double angle formula, cos2 θ = 1 + cos 2θ 2
Hence:
p = V 2 m
R
( 1 + cos (2ωt)
) = V
2R + V
2 m cos (2ωt)
2R (i)
This is an important result. From equation (i) we can infer that the power waveform (i.e. the waveform of p plotted against t) will take the form of a cosine function at twice the frequency of the voltage (see Figure 31.1) as shown in Chapter 29. Furthermore, if we apply our recently acquired knowledge of Fourier series, we can infer that the mean value of the power waveform (over a complete cycle of the voltage or current) will be the same as its amplitude. The values of the Fourier coefficients are:
A0 = V 2m 2R
(the mean power over one complete cycle
of the power waveform)
A2 = V 2m 2R
(the amplitude of the term in cos 2ωt
– at twice the frequency of the voltage)
Note that no other components are present.
