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Temperature coefficient of resistance

Short answer

Temperature coefficient of resistance is fractional change in resistance per °C. Using R = R0(1+α0 t) with R20=4.6Ω, R80=5.88Ω: subtract to get R0α0=0.021333, then R0=4.173Ω, α0=0.00511 per °C. R60 = 4.173 + 60×0.021333 = 5.45Ω. (a) α0 ≈ 0.00511/°C, (b) R60 ≈ 5.45Ω.

Define temperature coefficient of resistance. The resistance of a certain length of wire is 4.6Ω at 20°C and 5.88Ω at 80°C. Determine (a) The temperature coefficient of resistance of the wire at 0° (b) The resistance of the wire at 60°C.

Definition

The temperature coefficient of resistance (α) is the fractional change in resistance per degree rise in temperature, measured from a stated reference temperature. For a rise from t₀: R_t = R₀ [1 + α₀ (t − t₀)]. Unit: per °C.

(a) α at 0°C

Let R₀ be the resistance at 0°C and α₀ its coefficient.

R₂₀ = R₀ (1 + 20 α₀) = 4.6 R₈₀ = R₀ (1 + 80 α₀) = 5.88

Subtract: 60 R₀ α₀ = 1.28, so R₀ α₀ = 0.021333

From the first: R₀ = 4.6 − 20 × 0.021333 = 4.1733 Ω

α₀ = 0.021333/4.1733 = 0.005112 per °C

(b) Resistance at 60°C

R₆₀ = R₀ (1 + 60 α₀) = 4.1733 + 60 × 0.021333 = 5.453 Ω

Answer: (a) α₀ ≈ 0.00511 per °C; (b) R₆₀ ≈ 5.45 Ω

✓ Answer checked by Claude Opus 5.5 (high effort)

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