Understanding Power Factor: Cosine of Power Angle

The question asks for the term that represents the cosine of the angle between useful power and total power in an electrical system.

Defining Key Electrical Power Terms

In AC circuits, there are three types of power:

• Real Power (P): This is the actual power consumed by the load to do useful work. It is measured in Watts (W). This is also referred to as useful power.
• Reactive Power (Q): This power is required by inductive or capacitive loads to establish and sustain magnetic or electric fields. It does not perform useful work but is necessary for the operation of certain equipment. It is measured in Volt-Amperes reactive (VAR).
• Apparent Power (S): This is the vector sum of Real Power and Reactive Power. It represents the total power that the circuit appears to be delivering. It is measured in Volt-Amperes (VA).

The Power Triangle and Power Factor

These three powers can be represented in a right-angled triangle, known as the power triangle, where:

• Apparent Power (S) is the hypotenuse.
• Real Power (P) is the adjacent side.
• Reactive Power (Q) is the opposite side.

The angle ($\phi$) between the Real Power (P) and the Apparent Power (S) is the phase angle difference between the voltage and the current in the circuit.

The Power Factor (PF) is defined as the ratio of Real Power (P) to Apparent Power (S).

Mathematically, it is expressed as:

$$ PF = \cos(\phi) = \frac{\text{Real Power}}{\text{Apparent Power}} = \frac{P}{S} $$

Therefore, the cosine of the angle between useful power (Real Power) and total power (Apparent Power) is the Power Factor.

Analyzing the Options

• Diversity Factor: This factor relates to the maximum demands of different loads within a system. It is the ratio of the sum of individual maximum demands to the overall maximum demand of the installation. It doesn't represent the cosine of the power angle.
• Load Factor: This is the ratio of the average load over a period to the maximum load during that period. It indicates how consistently loads are utilized but is not related to the cosine of the power angle.
• Power Factor: As explained above, this is the cosine of the angle between voltage and current, or equivalently, the ratio of real power to apparent power. This matches the question's description.
• Demand Factor: This is the ratio of the maximum demand of a system or part of a system to the total connected load which produces that demand. It is used for system design but doesn't represent the cosine of the power angle.

Conclusion

The cosine of the angle between useful power (Real Power) and total power (Apparent Power) is precisely the definition of the power factor.