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GATE 2026 BM – Question 56

Measurements and Control Systems · Measurement Errors and Uncertainty · 2 marks · Numerical answer

Resistance is 60±2 Ω and measured voltage across it is 120±10 mV. Estimate uncertainty of dissipated power in mW, rounded to one decimal place.

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Correct answer: 0.0 to 0.1

Explanation

Nominal power is V²/R=(0.120)²/60=0.00024 W=0.24 mW. For worst-case first-order propagation, ΔP/P≈2ΔV/V+ΔR/R=2×10/120+2/60=0.20. Thus ΔP≈0.048 mW, which rounds to 0.0 mW at one decimal place and lies in the published 0.0–0.1 range. The unrounded value clarifies why the reported precision looks coarse.

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