- 2073 Shrawan · 6 marks
Temperature rise from resistance change
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.
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.
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
✓ Answer checked by Claude Opus 5.5 (high effort)
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