How is the relationship between true power and apparent power expressed?

The relationship between true power and apparent power is expressed through power factor. Power factor is a dimensionless number that represents the fraction of total power that is used effectively to perform work. It is calculated as the cosine of the phase difference between the current and voltage waveforms in an AC circuit.

True power (measured in watts) represents the actual power consumed by the circuit to perform useful work, while apparent power (measured in volt-amperes) is the product of the voltage and current in the circuit without considering their phase relationship. The power factor provides a clear indication of how effectively electrical power is being converted into useful work output, which is critical for understanding the efficiency and performance of electrical systems.

By expressing power factor as the ratio of true power to apparent power, it becomes easier to evaluate and optimize the efficiency of electrical systems, making it a key concept in power systems engineering.