Question

The resistance of a metal wire at 20°C is 1.05 Ω and at 100°C is 1.38 Ω. Determine the temperature coefficient of resistivity of this metal.

Answer 1

Given: R₁ = 1.05 Ω

T₁ = 20°C

R₂ = 1.38 Ω

T₂ = 100°C

∆T = T₂ − T₁

= 100 − 20 

= 80°C

Resistance variation with temperature (R_t) = R₀(1 + α ∆T)

R₂ = R₁(1 + α ∆T)

1.38 = 1.05(1 + 80 α)

`1.38/1.05` = 1 + 80 α

1.314 = 1 + 80 α

80 α = 1.314 − 0.314

80 α = 0.314

α = `0.314/80`

= 3.93 × 10⁻³ °C⁻¹

α ≈ 3.9 × 10⁻³ °C⁻¹