What is the power factor?
A number that
represents the
portion of the
apparent power
dissipated as true
power.
(Number
represented as a
decimal fraction or
percentage.)

Eq. 24.22
PF = TP/AP
AP= Apparent Power
TP= True Power or Real Power
• In an electric power system, a load with a low power
factor draws more current than a load with a high power
factor for the same amount of useful power transferred.
• The higher currents increase the energy lost in the
distribution system, and require larger wires and other
equipment.
• Because of the costs of larger equipment and wasted
energy, electrical utilities will usually charge a higher cost
to industrial or commercial customers where there is a
low power factor.
• An automatic power factor correction unit consists of a
number of capacitor that are switched by means of
contactors. These contactors are controlled by a regulator
that measures power factor in an electrical network.

Substituting the equations for TP and AP in
the Power Factor equation will yield:
2
2
IR R / IT Z
= PF
For Series Circuits
Only!!
In series
circuits, the
current is the
same, and IR
equals IT.
Therefore
this power
factor
equation
becomes:
•Eq. 24.23
IR
2R
/
2
IT Z
R / Z = PF
Eq. 24.23 is modified as:
Eq. 24.24
IR / IZ = PF
(Note: IZ = IT)
Eq. 24.25
S= Apparent Power
P= True Power
Q= Reactive Power
PF = Cos θ

Find the power factor of a series circuit when
R=5kΩ, Z=7.07kΩ, θ= 45°, VS= 20V, and IT =
2.82mA
Find the power factor of a series circuit when R=5kΩ,
Z=7.07kΩ, θ= 45°, VS= 20V, and IT = 2.82mA
PF = (2.82mA)2*5kΩ/(2.82mA)2*7.07k Ω = .707
PF = 5kΩ/7.07kΩ = .707
PF = Cos 45° = .707
Last equation to know
Combining the
previous
equations gives
us an equation for
true power that is
universal. Can be
used for any type
of circuit.

Eq. 24.26
▪TP = ITVS Cos θ
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vol_2/chpt_11/4.html