Power Factor

Compare AC voltage with the lagging current of an inductive load, and distinguish real, reactive and apparent power.

V1 supplies 10 V peak at 50 Hz to R1 = 100 Ω in series with L1 = 318.31 mH. At this frequency the inductive reactance equals the resistance.

$$X_L=2\pi fL\approx100\,\Omega$$ $$\phi=\tan^{-1}\frac{X_L}{R}=45^\circ$$ $$\mathrm{PF}=\cos\phi=\frac{P}{S}\approx0.707$$

The RMS source voltage is 7.071 V and the uncorrected RMS current is 50 mA. The load consumes 0.25 W of real power and exchanges 0.25 var of inductive reactive power; its apparent power is 0.3536 VA.

Read the chart. Vin is green and Iload blue. The final two cycles are shown after startup. Current peaks follow voltage peaks by 2.5 ms, one eighth of the 20 ms period. Stacked axes separate volts from amperes.

Try it. Set L1’s Inductance to 636.619772 mH. Reactance doubles, current falls and the phase lag grows to about 63.43°. Power factor falls to about 0.447. Restore 318.309886 mH. Compare with Power Factor Correction to see how a parallel capacitor changes source current.

Model limits. These calculations assume sinusoidal voltage, a linear ideal inductor and a pure resistor. With harmonics, total power factor also includes waveform distortion and is not simply the cosine of one phase angle.