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GATE 2015 EE (EE2) – Question 16

Electrical and Electronic Measurements · Measurement of voltage, current, power, energy and power factor · 1 mark · Multiple choice

A balanced three-phase load consumes 5 kW at pf 0.707, measured by the two-wattmeter method. The readings are

  1. 3.94 kW and 1.06 kW
  2. 2.50 kW and 2.50 kW
  3. 5.00 kW and 0.00 kW
  4. 2.96 kW and 2.04 kW

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Show answer and explanation

Correct answer: (A) 3.94 kW and 1.06 kW

Explanation

The readings satisfy W1+W2=P=5 kW and tanφ=√3(W1−W2)/(W1+W2). With cosφ≈0.707, φ≈45° and tanφ≈1.

Thus W1−W2≈5/√3=2.88675 kW. Adding and subtracting gives W1≈3.9434 and W2≈1.0566 kW. Hence **A**; exchanging instrument labels swaps the pair without changing the answer.

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