What is the power factor in an R-L circuit with a 45 degree phase angle between voltage and current?

In an R-L circuit, the power factor is determined by the cosine of the phase angle between the voltage and the current. When the phase angle is 45 degrees, the power factor can be calculated using the cosine function:

Power Factor (PF) = cos(θ)

For a phase angle of 45 degrees:

PF = cos(45°) = √2/2 ≈ 0.707

This indicates that the circuit is utilizing approximately 70.7% of the power supplied for useful work, while the remainder is reactive power, which does not perform any work but is necessary for creating the magnetic fields in inductors.

The other values listed do not correspond to the cosine of a 45-degree angle. A power factor of 0.5 corresponds to a phase angle of 60 degrees, 0.866 corresponds to a phase angle of 30 degrees, and a power factor of 1 corresponds to a purely resistive circuit (0 degrees phase angle). Thus, the calculation confirms that 0.707 is indeed the correct power factor for an R-L circuit with a 45-degree phase angle.