Temperature coefficient
(E5.4.1) E5.4 · Resistance and Temperature →An approximately linear rise with temperature over a moderate range.
| resistivity at temperature T | Ω·m | |
| resistivity at the reference temperature | Ω·m | |
| temperature coefficient | (°C)⁻¹ (Cu 3.9×10⁻³) | |
| reference temperature | °C | |
| temperature | °C |
Metals, over a moderate temperature range.
Written for metals over a moderate temperature range — semiconductors have a negative temperature coefficient instead, since heat frees more carriers than it costs in collisions.
From the conduction model, resistivity is set by the collision time:
Heating makes the lattice vibrate harder, so collisions come more often and τ falls — pushing ρ up.
Over a limited range the rise is close to linear, so expand about a reference temperature:
For a fixed piece of wire, R follows ρ directly:
α = 3.92 × 10⁻³ °C⁻¹ and R₀ = 100 Ω at 0 °C:
Repeatable and nearly linear, which is why the Pt100 is an industrial standard.
Semiconductors go the other way — α is negative, because heat frees far more carriers than it costs in collisions.
<b>Superconductors</b> break the pattern entirely: below a critical temperature the resistance is exactly zero, not merely small. A current started in a superconducting loop circulates for years with no source.