The GATE Grind

GATE 2021 IN – Question 15

Measurements · Errors and uncertainty · 1 mark · Multiple choice

In an AC mains, measured rms voltage is 100 V ±1%, rms current 1 A ±1%, and power 50 W ±2%, with errors relative to readings. The percentage limiting error in the calculated power factor is ______.

  1. 1%
  2. 2%
  3. 3%
  4. 4%

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Show answer and explanation

Correct answer: (D) 4%

Explanation

Power factor is W/(VI). For worst-case small relative errors, the magnitudes add even for denominator quantities: |δPF/PF|≤|δW/W|+|δV/V|+|δI/I|.

Thus 2%+1%+1%=**4%, D**; an RSS uncertainty is not the requested limiting-error calculation.