--- title: "Temperature rise from resistance change" subject: "Basic Electrical Engineering" chapter: 1 key: "semester_1/basic_electrical_engineering:coil-resistance-temperature-rise-100-124" source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/coil-resistance-temperature-rise-100-124 site: BCT Engineering --- # Temperature rise from resistance change Basic Electrical Engineering · Chapter 1: General Electric System - Asked in: 2073 Shrawan, 6 marks - Video: [Temperature Dependence of Resistance | Hindi](https://www.youtube.com/watch?v=65tQNrVtyzA) — Ashiesh Kapoor - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/coil-resistance-temperature-rise-100-124 - Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-1 ## Question A coil has a resistance of 100 ohms, when the temperature is 20°C and 110 ohms when the temperature is 45°C. Find temperature rise when its resistance is 124 ohms, and surrounding temperature is 15°C. ## Short answer Temperature coefficient α20 = 0.004/°C. When resistance is 124 Ω, temperature = 80°C. With surrounding at 15°C, temperature rise = 65°C. ## Answer **Step 1: Temperature coefficient at 20°C** R₄₅ = R₂₀ [1 + α₂₀ (45 − 20)] 110 = 100 (1 + 25 α₂₀) α₂₀ = 0.1/25 = 0.004 per °C **Step 2: Temperature at which R = 124 Ω** 124 = 100 [1 + 0.004 (t − 20)] 0.004 (t − 20) = 0.24 t − 20 = 60 t = 80°C **Step 3: Temperature rise** The surrounding (ambient) temperature is 15°C. Temperature rise = 80 − 15 = 65°C **Answer: Final temperature = 80°C; temperature rise above the surroundings = 65°C** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. From 100 ohm at 20 degC and 110 ohm at 45 degC, what is alpha at 20 degC? A. 0.004 per degC B. 0.0004 per degC C. 0.1 per degC D. 0.0045 per degC Answer: A. 110 = 100 (1 + 25 alpha), so alpha = 0.1/25 = 0.004. (Key point: Finding alpha) 2. Using 124 = 100 [1 + 0.004 (t - 20)], what is t? A. 60 degC B. 65 degC C. 80 degC D. 95 degC Answer: C. 0.004 (t - 20) = 0.24 so t - 20 = 60 and t = 80 degC. (Key point: Temperature for 124 ohm) 3. Why is the temperature rise 65 degC and not 60 degC? A. Rise is measured from 20 degC, the reference B. Rise is measured from the surroundings at 15 degC: 80 - 15 C. Rise is measured from 0 degC D. Rise equals alpha x 124 Answer: B. The rise is relative to the ambient temperature given, 15 degC, so 80 - 15 = 65 degC. (Key point: Temperature rise) ## Related in Basic Electrical Engineering - [Transformer coil temperature and power rating](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Atransformer-coil-temperature-rise) — Basic Electrical Engineering, chapter 1 - [Temperature rise of machine field winding](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Afield-winding-temperature-rise-160-185) — Basic Electrical Engineering, chapter 1 - [Coil in series with non-inductive resistance](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Acoil-series-30ohm-voltmeter-180v) — Basic Electrical Engineering, chapter 6 - [Coil inductance and resistance from two frequencies](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Acoil-resistance-inductance-127hz-456hz) — Basic Electrical Engineering, chapter 6 - [Temperature coefficient of resistance](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Atemperature-coefficient-resistance-wire-4-6) — Basic Electrical Engineering, chapter 1 - [Temperature coefficient and effect on resistance](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Atemperature-coefficient-effect-on-resistance) — Basic Electrical Engineering, chapter 1 ## Related in other subjects - [Nominal-T 100 km line, 20 MW at 110 kV](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Anominal-t-100km-20mw) — Power System Analysis I, chapter 5 - [Arch 100 m rise 15 m: rolling UDL 10 m, section 60 m](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Aarch-100m-rise15-udl-10m-60m-section) — Theory of Structures I, chapter 6 - [AC with 50% of Carnot COP: max surrounding temperature](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aac-cop-50-percent-max-surrounding-temp) — Fundamental of Thermodynamics & Heat Transfer, chapter 5, asked 2× - [Heat pump at 50% of ideal: minimum surrounding temperature](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aheat-pump-50-percent-min-surrounding-temp) — Fundamental of Thermodynamics & Heat Transfer, chapter 5