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At room temperature (27 °C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 137 Ω, given that the temperature coefficient of the material of the resistor is 1.35×10⁻⁴ °C⁻¹?

Asked in GUJCET 2022 · Temperature dependence of resistance

• (1) 2767 °C
• (2) 1227 °C
• (3) 1027 °C
• (4) 2327 °C

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 1227 °C. Check: a rise of 1200 °C would add only 100×1.35×10⁻⁴×1200=16.2 Ω, taking the element to 116.2 Ω, not 137 Ω.
• (3) Is the answer to the textbook example this question is adapted from (117 Ω with 1.70×10⁻⁴ °C⁻¹), not to these numbers; here the rise is (37)/(1.35×10⁻²)≈2741 °C.
• (4) No single slip gives 2327 °C. Check: a rise of 2300 °C would add 100×1.35×10⁻⁴×2300=31.05 Ω, giving 131.05 Ω, not 137 Ω.

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