Eq. 24.22

PF = TP/APAP= Apparent PowerTP= True Power or Real Power

A number that represents the portion of the apparent power dissipated as true power.

(Number represented as a decimal fraction or percentage.)

• 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:

IR2R / IT2Z = PF

In series circuits, the current is the same, and IR equals IT. Therefore this power factor equation becomes:

•Eq. 24.23

IR2R / IT2Z R / Z = PF

Eq. 24.23 is modified as:

Eq. 24.24IR / IZ = PF

(Note: IZ = IT)

Eq. 24.25

PF = Cos θ

S= Apparent PowerP= True PowerQ= Reactive Power

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

Find the power factor of a series circuit when R=5kΩ, Z=7.07kΩ, θ= 45°, VS= 20V, and IT = 2.82mA

Eq. 24.26

TP = ITVS Cos θ

Combining the previous equations gives us an equation for true power that is universal. Can be used for any type of circuit.

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