Question 2.6: Power Triangle for a Motor. A 230-V induction motor draws 25......
Power Triangle for a Motor. A 230-V induction motor draws 25 A of current while delivering 3700 W of power to its shaft. Draw its power triangle.
Step-by-Step
\begin{matrix}\quad \quad \text{Real power} \ P & = & 3700 \ W \ = \ 3.70 \ kW \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ \\ \text{Apparent power} \ S & = & 25 \ A \ \times \ 230 \ V \ = \ 5750 \ \text{volt-amps} \ = \ 5.75 \ kVA \quad \quad \ \ \ \\ \ \ \text{Power factor} \ PF & = & \frac{\text{Real power}}{\text{Apparent power}} \ = \ \frac{3700 \ W}{5750 \ VA} \ = \ 0.6435 \quad \quad \quad \quad \quad \quad \quad \quad \quad \\ \ \quad \ \text{Phase angle} \ \theta & = & \cos ^{-1} \left(0.6435\right) \ = \ 50° \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \\ \text{Reactive power} \ Q & = & S \ \sin \theta \ = \ 5750 \ \sin 50° \ = \ 4400 \ VAR \ = \ 4.40 \ kVAR \end{matrix}
The power triangle is therefore
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