4 Temperature Dependence of Resistivity
Temperature Dependence of Resistivity
For Metallic conductor
In terms of relaxation time, the resistivity of the material of a conductor is given by,
Where, the letters have their usual meanings
If the temperature increases, the amplitude of the vibrations of the +ve ions in the conductor also increases. Due to this, the free electrons collide more frequently with the vibrating ions and as a result, the average relaxation time decreases. Since ρ ∝ 1/τ, the resistivity of a metallic conductor increases with increase in temperature.
- Resistivity of a metallic conductor is given by, ρT = ρ0 [1 + α (T − T0)]
Where,
ρT→ Resistivity at temperature T
ρ0 → Resistivity at reference temperature T0
α → Temperature co-efficient of resistivity
- α is + ve for metals.
- Graph of ρT plotted against T should be a straight line. At temperature lower than 0°C, the graph deviates from a straight line.
For Alloys
In case of an alloy, the resistivity is very large and it has very weak
dependence on temperature.
- Nichrome (an alloy) exhibits weak dependence of resistivity with temperature.
For Semi-conductors
- Resistivity of a semi-conductor decreases with temperature.