If the inductive reactance of a given circuit is −Q, what must be done to correct the power factor to a value of 1?

To correct the power factor to a value of 1, it is crucial to understand the relationship between inductive reactance and capacitive reactance in an AC circuit. Inductive reactance is represented as a negative imaginary component, hence if the inductive reactance is denoted by -Q, it indicates that the circuit is predominantly inductive and is consuming reactive power.

To bring the power factor to unity (1), the circuit must be made to balance out the reactive power. This can be achieved by introducing capacitive reactance, which provides opposite reactive power that can cancel out the inductive effects. By adding capacitive reactance equal to +Q, the negative inductive reactance of -Q will be neutralized, leading to a net reactance of 0. This results in improved power factor because the circuit will now have both real power and reactive power balanced, allowing for all the power to be used effectively.

This adjustment harmonizes the phase relationship between voltage and current, thus bringing the total power factor to 1. In essence, capacitive reactance serves to counteract the effects of excess inductance, achieving the desired correction.