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GATE 2023 BM – Question 55

Sensors and Bioinstrumentation · Sensors and Signal Conditioning · 2 marks · Numerical answer

A thermistor has resistance 1 kΩ at 25°C and 500 Ω at 50°C. Find its temperature coefficient of resistance at 35°C, in °C⁻¹ to three decimals.

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Correct answer: -0.03 to -0.025

Explanation

Use the standard thermistor model R(T)=R₀exp[β(1/T−1/T₀)], with absolute temperatures in kelvin. The two readings give β=ln(2)/(1/298.15−1/323.15)≈2671 K. Its fractional temperature coefficient is α=(1/R)dR/dT=−β/T². At 308.15 K this is approximately −0.0281 °C⁻¹, rounded to −0.028.

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