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Gate 2016 EE -Set 2 - Question 41

Given that the rating is 500kvA and \cos \phi =0.8

Active power, P_{1}=500\times 0.8=400kW

Reactive power, Q_{1}=500\times 0.6=300kvAR

To raise the power factor to unity, the motor should supply 300kvAR

The motor ratings are now, 100kW, 300kvAR

\phi =\tan ^{-1}\left ( \frac{Q}{P} \right )=\tan ^{-1}\left ( \frac{300}{100} \right )

\Rightarrow \phi =71.56^{\circ}

\cos \phi =\cos (71.56)=0.316

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