GATE 2022 EE – Question 33

Power Electronics · Power factor and Distortion Factor of AC to DC converters · 1 mark · Numerical answer

The voltage at the input of an AC-DC rectifier is given by $v(t)=230\sqrt2\sin\omega t$ where $\omega=2\pi\times50$ rad/s. The input current drawn by the rectifier is given by

$$i(t)=10\sin\left(\omega t-\frac\pi3\right)+4\sin\left(3\omega t-\frac\pi6\right)+3\sin\left(5\omega t-\frac\pi3\right).$$

The input power factor, (rounded off to two decimal places), is, ________ lag.

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Correct answer: 0.44 to 0.46

Explanation

Only the fundamental current produces real power. $P=V_{rms}I_{1,rms}\cos60^\circ=230\times\frac{10}{\sqrt2}\times0.5=813$ W. The rms current is $I=\sqrt{\frac{10^2+4^2+3^2}{2}}=7.906$ A, so $S=230\times7.906=1818$ VA. The power factor is $\frac{813}{1818}=0.447\approx0.45$.