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In the figure, the voltages are v1(t) = 100 cos (ωt), v2(t) = 100 cos (ωt + π/18) and v3(t) = 100 cos (ωt + π/36). The circuit is in sinusoidal steady state, and R << ωL. P1, P2 and P3 are the average power outputs. Which one of the following statements is true?

In the figure, the voltages are v1(t) = 100 cos (ωt), v2(t) = 100 cos (ωt + π/18) and v3(t) = 100 cos (ωt + π/36). The circuit is in sinusoidal steady state, and R << ωL. P1, P2 and P3 are the average power outputs. Which one of the following statements is true? Correct Answer P<sub>1</sub> &lt; 0, P<sub>2</sub> &gt; 0, P<sub>3</sub> &lt; 0

Given that,

V1 (t) = 100 cos ωt

V2(t) = 100 cos(ωt + π/18) = 100 cos(ωt +10∘)

V3(t) = 100 cos(ωt + π/36) = 100 cos(ωt + 5°)

Phasor diagram of all the three voltages as shown in  below fig,

[ alt="F1 Raviranjan 19-01-22 Savita D2" src="//storage.googleapis.com/tb-img/production/22/01/F1_Raviranjan_19-01-22_Savita_D2.png" style="width: 214px; height: 159px;">

From the above diagram,

V2 (t) is leading V1(t) by 10° and

V3 (t) is leading V1(t) by 5°

V2 (t) is leading V3 (t) by 5°.

We know that active power always flows from a leading angle to a lagging angle.

Hence, current flows from V2 (t) to V1 (t) and V3 (t).

Hence, P2 > 0, P1 < 0 P3 < 0.

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