If resistance is cut in half, what happens to the power factor?

In electrical systems, the power factor is a measure of how effectively electrical power is being converted into useful work output. It is defined as the cosine of the angle between the current and voltage waveforms in an AC circuit, indicating the relationship between real power (used to do work) and apparent power (the total power in the circuit).

When resistance is halved in a resistive load, given that the circuit's voltage remains constant, this change impacts the current flowing through the circuit. According to Ohm's Law (V = I × R), if resistance decreases, current must increase to maintain the same voltage level.

As the resistance is halved, the current increases, leading to a greater power output. The formula for power in a resistive circuit is given by P = I²R. If the resistance is reduced, with a constant voltage, the increase in current will lead to an increase in overall power. As a result, if resistance decreases while voltage remains constant, the power factor must increase, as more of the apparent power is being used effectively (the real power increases).

Thus, halving the resistance results in an increase in the power factor, demonstrating a more efficient conversion of electrical power into work.