Power Factor

The power factor of a circuit can be defined equivalently in any of three ways: (i) as $\cos\phi$, the cosine of the phase angle of lead or lag between voltage and current; (ii) as the ratio R/Z of resistance to impedance; or (iii) as the ratio $P_{av}/(V_{RMS}I_{RMS})$ of true power to apparent power. All three definitions are algebraically equivalent and give the same numerical value for any given circuit.

Special cases, following directly from Table 4.1: for a PURELY RESISTIVE circuit, the phase angle is zero, so $\cos\phi=1$ and $P_{av}=V_{RMS}I_{RMS}$ -- true power equals apparent power exactly, the best possible case. For a PURELY INDUCTIVE or PURELY CAPACITIVE circuit, the phase angle is $\pm\pi/2$, so $\cos(\pm\pi/2)=0$ and $P_{av}=0$ -- despite a real current flowing, no true power is consumed at all (matching the wattless-current result of section 4.8.2). For a general SERIES RLC circuit, $\phi=\tan^{-1}\left[(X_L-X_C)/R\right]$, and $P_{av}=V_{RMS}I_{RMS}\cos\phi$ lies somewhere between these two extremes. Finally, for a series RLC circuit specifically AT RESONANCE, the phase angle is exactly zero (since $X_L=X_C$ there), so $\cos\phi=1$ and on …