What is the power factor in an R-L circuit with a 30 degree phase angle between voltage and current?

In an R-L (resistive-inductive) circuit where the phase angle between the voltage and current is 30 degrees, the power factor can be determined using the cosine of the phase angle. The power factor is defined as the cosine of the phase angle (φ), which indicates the ratio of the real power used in the circuit to the apparent power flowing in the circuit.

For a phase angle of 30 degrees, the power factor is calculated as:

[ \text{Power Factor} = \cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.866 ]

This value reflects that in the circuit, a significant portion of the apparent power is being converted into real power, which is essential for understanding efficiency in AC circuits. A power factor of 0.866 indicates that the circuit is reasonably efficient, with most of the power being used effectively.

Other choices represent different levels of efficiency: a power factor of 0.5 suggests a less efficient circuit, while 1 indicates a purely resistive load where all power is effectively used. Therefore, identifying the power factor as 0.866 shows a balanced understanding of the R-L circuit dynamics in the context of AC electrical