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GATE 2017 EE – Question 44

Electrical and Electronic Measurements · Measurement of voltage, current, power, energy and power factor · 2 marks · Multiple choice

The load shown in the figure is supplied by a 400 V (line-to-line), 3-phase source (RYB sequence). The load is balanced and inductive, drawing 3464 VA. When the switch S is in position N, the three watt-meters $W_1$, $W_2$ and $W_3$ read 577.35 W each. If the switch is moved to position Y, the readings of the watt-meters in watts will be:

A 400 V three-phase source with lines R, Y, B and neutral N feeds a load through three wattmeters $W_1$, $W_2$ and $W_3$ in lines R, Y and B. The common point of the voltage coils is connected through a switch S either to the neutral N or to line Y.
  1. $W_1 = 1732$ and $W_2 = W_3 = 0$
  2. $W_1 = 0$, $W_2 = 1732$ and $W_3 = 0$
  3. Option C (cut off at the page edge in the source PDF)
  4. Option D (cut off at the page edge in the source PDF)

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Correct answer: (D) Option D (cut off at the page edge in the source PDF)

Explanation

The line current is $\frac{3464}{\sqrt{3} \times 400} = 5$ A, and the power per phase is $577.35 = 230.9 \times 5 \cos\phi$, so $\cos\phi = 0.5$ and the load lags by 60°. With the switch at Y, all the voltage coils are referred to line Y. Wattmeter $W_2$ then reads 0 because its voltage is zero. Wattmeter $W_1$ sees $V_{RY}$, which leads the current by 90° in this load, so it also reads 0. Wattmeter $W_3$ sees $V_{BY}$, which is 30° from its current, so it reads $400 \times 5 \times \cos 30° = 1732$ W. The readings are 0 W, 0 W and 1732 W, and the official key marks option D as the answer.