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GATE 2022 BM – Question 53

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

A wire material has linear temperature coefficient x×10⁻⁴ °C⁻¹. Its resistance is 50 Ω at 25°C and 60 Ω at 75°C. Find x to two decimals.

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Correct answer: 44.35 to 44.55

Explanation

The published key uses the coefficient referenced to zero Celsius: R(T)=R₀(1+α₀T). The slope is (60−50)/(75−25)=.2 Ω/°C, giving R₀=50−.2×25=45 Ω. Thus α₀=.2/45=.00444444 °C⁻¹ and x=44.44. A coefficient referenced to twenty-five Celsius would differ; the official interpretation uses zero.

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