The GATE Grind

GATE 2026 IN – Question 29

Measurements · Errors and uncertainty · 1 mark · Multiple select

In a linear element, the measured current is $100\ \mathrm{mA}\pm2.5\%$ and the measured voltage is $5\ \mathrm V\pm5\%$. Which of the following options show(s) the consumed power?

  1. $(500\pm37.5)\ \mathrm{mW}$
  2. $(500\pm12.5)\ \mathrm{mW}$
  3. $500\ \mathrm{mW}\pm7.5\%$
  4. $500\ \mathrm{mW}\pm2.5\%$

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Show answer and explanation

Correct answer: (A) $(500\pm37.5)\ \mathrm{mW}$; (C) $500\ \mathrm{mW}\pm7.5\%$

Explanation

The nominal power is $P=VI=5\times0.100=0.500\ \mathrm W=500\ \mathrm{mW}$. For first-order worst-case uncertainty in a product, $\Delta P/P\approx\Delta V/V+\Delta I/I=5\%+2.5\%=7.5\%$.

The absolute uncertainty is $0.075\times500=37.5\ \mathrm{mW}$. Options **A and C** are equivalent. This conventional linear approximation omits the second-order product of the two uncertainties.