Q.Define power factor. State its value, and hence the average power consumed, for

Definition. Power factor is the quantity $\cos\phi$ appearing in $P_{avg}=V_{rms}I_{rms}\cos\phi$ -- the fraction of the apparent power $V_{rms}I_{rms}$ that is actually delivered as real, usable average power.

1. Pure resistive circuit. Here $\phi=0$ (voltage and current in phase), so $\cos\phi=1$, and

   $P_{avg} = V_{rms}I_{rms}$

   the maximum possible power for a given $V_{rms}$ and $I_{rms}$ -- every bit of the apparent power is delivered as real power.
2. Pure inductive circuit. Here $\phi=90^\circ$ (current lags by a quarter-cycle), so $\cos\phi=0$, and

   $P_{avg} = 0$

   despite genuine rms voltage and current both being present.
3. Pure capacitive circuit. Here too $\phi=90^\circ$ (current leads by a quarter-cycle), so $\cos\phi=0$, and again $P_{avg} = 0$ …

Define power factor from the average-power formula, then substitute the known phase angle ($0^\circ$ or $90^\ …

• Assuming a pure inductive/capacitive circuit consumes NO power at all in any sense -- instantaneous power is nonzero throughout, only the AVERAGE (net) power is zero. …