GATE 2025 BM – Question 53
A thermistor obeys $R(T)=R_0\exp[\beta(1/T-1/T_0)]$, with β=3100 K. A resistance measurement has 10% relative error. Estimate relative error in measuring T=310 K, as an integer percentage.
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Correct answer: 1 to 1
Explanation
Logarithmic differentiation gives dR/R=−β dT/T². Thus |dT|/T=(T/β)|dR|/R=(310/3100)×0.10=0.01. The temperature relative error is therefore one percent, so the numerical answer is one.