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Power factor is given by
S/P
P/S
P/Q
Q/S
P/S
The power factor of an A.C. circuit is defined as the cosine of the phase angle between the voltage and current vectors, which mathematically equates to the ratio of real power (P) to apparent power (S). It represents the efficiency with which the electrical equipment converts apparent power into useful work.
The power factor of an A.C. circuit is defined as the cosine of the phase angle between the voltage and current vectors, which mathematically equates to the ratio of real power (P) to apparent power (S). It represents the efficiency with which the electrical equipment converts apparent power into useful work.
pf=cos(╧Х)=SPтАЛ тАФ Basic definition of power factor
S=P2+Q2тАЛ тАФ Relation between power components
In an A.C. circuit, the power triangle consists of Real Power (P in Watts), Reactive Power (Q in VARs), and Apparent Power (S in VA). The power factor is the projection of the current vector onto the voltage vector, resulting in cos(╧Х)=SPтАЛ. When the phase angle ╧Х between voltage and current is zero (resistive load), the power factor is unity, meaning all apparent power is consumed as real power.
A power factor of 1.0 (unity) indicates purely resistive load.
A lagging power factor is caused by inductive loads, while a leading power factor is caused by capacitive loads.
Low power factor increases distribution losses and reduces the capacity of electrical equipment.
The range of power factor is always between 0 and 1.
High power factor reduces the current drawn for the same amount of real power.
Improves system efficiency and reduces voltage drops in transmission lines.
Low power factor requires larger conductor sizes and increases energy costs.
Poor power factor results in heavy penalties from utility companies.
Power system load management
Design of electrical machines (motors and transformers)
Industrial energy auditing
Power factor correction is usually achieved by installing capacitor banks in parallel with inductive loads.
Option A (S/P) is the reciprocal of the power factor.
Option C (P/Q) represents the reciprocal of the tangent of the phase angle, often used to calculate capacitor size for power factor correction.
B is correct тАФ Power factor is defined as the ratio of Real Power (P) to Apparent Power (S).
Always remember the mnemonic 'P-I-V' (Power-In-Vector) or look at the power triangle: P is the base, S is the hypotenuse, and cos(╧Х)=HypotenuseAdjacentтАЛ=SPтАЛ.