Resistance and temperature

The resistance of a metal rises with temperature. Hotter atoms vibrate more, and the drifting electrons collide with them more often.

For moderate temperature changes:

R_T = R₀[1 + α(T – T₀)]

R₀ is the resistance at temperature T₀, and α is the temperature coefficient of resistance (unit °C⁻¹). It tells you the fraction by which R grows for each degree.

Example: a wire of 10 Ω at 20 °C, with α = 0.004 °C⁻¹. At 70 °C: R = 10(1 + 0.004 × 50) = 12 Ω.

To find a temperature from a resistance, rearrange: T – T₀ = (R_T – R₀) / (R₀ α).

Different materials behave differently:

• Metals: α is positive; R rises with temperature.
• Alloys like nichrome, manganin and constantan: α is very small, so R hardly changes. That makes them good for heater coils and standard resistors.
• Semiconductors (silicon, germanium): α is negative; R falls as they warm up, because heat frees more charge carriers.

Uses: a platinum resistance thermometer measures temperature by measuring resistance.

A heater or bulb takes a bigger current the moment it is switched on, while the wire is cold and its R is low. As it heats up, R rises and the current settles at a lower value.