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GATE 2017 EE – Question 19

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 1 mark · Multiple choice

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $v_{an} = 220\sin(100\pi t)$ V and $i_a = 10\sin(100\pi t)$ A, respectively. Similarly for phase-b, the instantaneous voltage and current are $v_{bn} = 220\cos(100\pi t)$ V and $i_b = 10\cos(100\pi t)$ A, respectively.

[Figure: A source connected to a load by three wires a, b and n. The currents $i_a$ and $i_b$ flow in wires a and b towards the load, and the voltages $v_{an}$ and $v_{bn}$ are measured from each of those wires to the neutral wire n.]

The total instantaneous power flowing from the source to the load is

Diagram for GATE 2017 EE question 19
  1. 2200 W
  2. $2200\sin^2(100\pi t)$ W
  3. 4400 W
  4. $2200\sin(100\pi t)\cos(100\pi t)$ W

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Correct answer: (A) 2200 W

Explanation

The instantaneous power is the sum of the powers in the two phases: $p = v_{an}i_a + v_{bn}i_b = 2200\sin^2(100\pi t) + 2200\cos^2(100\pi t) = 2200$ W. The total power is constant at 2200 W.