Power in Alternating-Current Circuits — Question 7

Question 7

Inductive and capacitive loads combine by adding signed reactive power

Two parallel loads share a 200-V rms source. Load 1 has $P_1=800$ W and $Q_1=+600$ var. Load 2 has $P_2=600$ W and $Q_2=-800$ var. Both operate sinusoidally at the same frequency.

1. Find total real, reactive, and apparent power.

2. Find source current and total power factor with its leading or lagging designation.

Question 7 - Solution

Inductive and capacitive loads combine by adding signed reactive power

(a) Method and calculation

$$P=P_1+P_2=1400\,W,\quad Q_r=Q_1+Q_2=-200\,var.$$$$\boxed{S=\sqrt{P^2+Q_r^2}=1414.21\,VA}.$$

(b) Interpretation and further calculation

$$I=S/V=1414.21/200=7.07107\,A.$$$$\boxed{\mathrm{pf}=P/S=.989949\quad\text{leading}}.$$

Physical check

Apparent powers do not generally add as scalar magnitudes; signed reactive contributions can cancel.