In the figure, the voltages are v_{1}(t)=100 \cos (\omega t), v_{2}(t)=100 \cos (\omega t+\frac{\pi}{18}) and v_{3}(t)=100 \cos (\omega t+\frac{\pi}{36}). The circuit is in sinusoidal steady-state, and R ≪ \omega L P_{1}, P_{2} and P_{3} are the average power outputs. Which one of the following statements is true?

Correct Answer is : P1<0,P2>0,P3<0

GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 28 of 65

Marks: +1, -0

In the figure, the voltages are

v_{1}(t)=100 \;\; \cos (ω t), v_{2}(t)=100 \cos (ω t+\;{π}/{18})

and

v_{3}(t)=100 \cos (ω t+\;{π}/{36})

.
The circuit is in sinusoidal steady-state, and

R ≪ ω L P_{1}, P_{2}

and

P_{3}

are the average power outputs. Which one of the following statements is true?

Solution:

V_{2}: \;{π}/{18}=\;{180^{∘}}/{18}=10^{∘}

V_{3}: \;{π}/{36}=\;{180^{∘}}/{36}=5^{∘}

V_{2}

leads

V_{1}

and

V_{3}

So, current will flow from

v_{2}

towards

v_{1}

and

v_{3}

.
Hence,

P_{1}<0, P_{2}>0, P_{3}<0

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