Ratio R/Z

Another way to compute the power factor is to find ratio of resistance R to the absolute value impedance Z. In the figure given below, this is visually apparent. A right triangle can be formed by the resistance vector R (base), the reactance vector jX (height) and the absolute value impedance Z (hypotenuse). The cosine of phase angle is equal to the ratio of base length to hypotenuse length; this represents R/Z.

Problem:

A circuit has the absolute value impedance Z of 100 Ω, with the resistance R=80 Ω. What will be the power factor?

Resistance and reactance

At times you will get data which tells you the resistance and reactance components in the circuit. To compute the power factor from this, you can find the phase angle and take its cosine, or find absolute value impedance and take ratio R/Z.

Simply find ratio: PF = R/Z = 80/100 = 0.8 = 80 %. Note that it does not matter whether the reactance in the circuit is capacitive or inductive. Actually, you do not even have to worry about value of the reactance here.