Q.An AC circuit carries an rms voltage of $200\ \text{V}$ and an rms current of $5\ \text{A}$, with the current lagging the voltage by a phase angle of $60^\circ$. Calculate the power factor of the circuit and the average power consumed.

Given: $V_{rms}=200\ \text{V}$, $I_{rms}=5\ \text{A}$, $\phi=60^\circ$.

Power factor.

Average power.

Check against apparent power. The apparent power is $V_{rms}I_{rms}=1000\ \text{VA}$; with a power factor of only $0.5$, exactly HALF of this apparent power is delivered as genuine average power, the other half being wattless (reactive), ex …

Compute the power factor $\cos\phi$ directly from the given phase angle, then substitute …

• Using the apparent power $V_{rms}I_{rms}=1000\ \text{W}$ directly as the answer, forgetting to multiply by $\cos\phi$. …