EXAMPLE 7 6
7 7  POWER IN AC CIRCUIT: THE POWER FACTOR
We have seen that a voltage v = vm sinwt applied to a series RLC circuit
drives a current in the circuit given by i = im sin(wt + f) where
m
m
v
i
=Z
  and φ =
−


−
tan 1
X
X
R
C
L
Therefore, the instantaneous power p supplied by the source is
Rationalised 2023-24
191
Alternating Current
(
) [
]
sin
sin(
)
m
m
p
v i
v
t
i
t
ω
ω
φ
=
=
×
+
[
]
cos
cos(2
)
2
m m
v i
t
φ
ω
φ
=
−
+
(7 29)
The average power over a cycle is given by the average of the two terms in
R