The resistivity of a conductor depends on temperature. For most metals, the resistivity increases with temperature and the change is linear over a limited range of temperature.
ρ = ρ0[1 + α(T – T0)]
where ρ and ρ0 are the resistivities at temperatures T and T0, respectively. The temperatures are taken in °C and T0 is the reference temperature. α is called the temperature co-efficient of resistivity. Its unit is per degree celcius.
Resistance of a conductor is proportional to its resistivity. Therefore, temperature variation of resistance can written as
R = R0[1 + α(T – T0)]
Temperature coefficient of resistance is numerically equal to the change in resistance of a wire of resistance 1Ω at 0°C when the temperature changes by 1°C. This property of metals is used in making resistance thermometers.
Resistivity of Alloys
The resistivity of alloys also increases with increase in temperature. But the increase is very small compared to that for metals. For alloys such as manganin, constantan and nichrome, the temperature coefficient of resistivity is vanishingly small and resistivity is high. That is why these materials are used for making resistance wires or standard resistances.
Resistivity of Semiconductors
Semiconductors such as germanium and silicon have resistivities which lie between those of metals and insulators. The resistivity of semiconductors usually decreases with increase in temperature.