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Temperature coefficient and effect on resistance

Short answer

Temperature coefficient of resistance α is the change in resistance per ohm per °C: α₀ = (R_t − R₀)/(R₀·t). For pure metals α is positive and resistence rises with temperature; for semi-conductors, insulators, carbon it is negative; for alloys like manganin it is nearly zero.

Define the temperature coefficient of resistance and explain the effect of temperature on resistance of a substance.

Temperature coefficient of resistance

The temperature coefficient of resistance (α) is the change in resistance per ohm of original resistance per degree rise in temperature:

α₀ = (R_t − R₀)/(R₀ · t), so R_t = R₀ (1 + α₀ t)

Unit: per °C. The value depends on the reference temperature: α_t = α₀/(1 + α₀ t).

Effect of temperature on resistance

MaterialαEffect of rising temperature
Pure metals (Cu, Al, Fe)positiveResistance increases nearly linearly
Semiconductors, insulators, carbon, electrolytesnegativeResistance decreases
Alloys (manganin, constantan)almost zeroResistance almost unchanged

Reason for metals: at a higher temperature the atoms vibrate more, so free electrons collide more often and their drift is opposed more. Reason for semiconductors: heat frees more electron-hole pairs, and this increase in charge carriers outweighs the effect of the extra collisions, so conductivity rises.

   Metal            Alloy             Semiconductor
 R |      /       R |               R |\
   |    /           |---------        |  \
   |  /             |                 |    \____
   +-------- T      +-------- T       +---------- T

Examples: a lamp filament has a much lower resistance when cold than when hot; manganin is used for standard resistors because of its near-zero α.

✓ Answer checked by Claude Opus 5.5 (high effort)

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