How do we find the Power Factor (PF) of a circuit?

The Power Factor (PF) of a circuit is a measure of how effectively the current is being converted into useful work and is defined as the cosine of the phase angle between the voltage and the current in an AC circuit. This phase angle, denoted as θ, reflects the difference in timing between when the voltage and current waveforms reach their peaks.

When the circuit is purely resistive, the voltage and current are in phase, resulting in a PF of 1, indicating that all the power is being effectively used. However, in circuits with reactive components (inductive or capacitive), this angle results in a lower power factor, which signifies that not all the supplied power is being converted into useful work. The PF can be calculated using the cosine of the phase angle, which is why the correct definition is PF = cos(θ).

The other options do not accurately describe the PF. For instance, using the sine of the phase angle or ratios of voltage to current does not capture the direct relationship between voltage, current, and their phase difference as it relates specifically to real power consumption versus apparent power in AC circuits.