8.9 APPARENT POWER, ACTIVE POWER, REACTIVE POWER AND
POWER FACTOR
Consider a sinusoidal voltage source v(t) V
m
cos
ω
tdelivering power to a resistive load R.
The current in the resistor is i(t) I
m
cos
ω
t, where I
m
V
m
/R.
The instantaneous power is p(t) V
m
I
m
cos
2
ω
t 0.5V
m
I
m
0.5V
m
I
m
cos2
ω
t 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 0.5V
m
I
m
0.5V
m
2
/R 0.5I
m
2
R. The average
power can be expressed as V
rms
I
rms
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 ...
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