Name: Temperature Dependence of Resistivity
Uploaded: 2019-07-19
Duration: 3 min 27 s
Description: It seems intuitive to think that the resistance of a given material changes at different temperatures, but in which direction does this change occur? We find...

Question

Discuss the variation of resistivity with temperature

Accepted Answer

The variation of resistivity of a conductor can be expressed in terms of the temperature coefficient of resistivity as

$α = \frac{△ ρ}{ρ_{0} △ T}$ where $ρ_{0}$ =initial resistivity and $△ ρ$ is the change in resistivity with $△ T$ change in the temperature.

In the case of conductors: The graph between resistivity and temperature is shown in the diagram.

When the temperature increases the vibrations of the metal ions in the lattice structure increases. These vibrations in turn cause frequent collisions between the free electrons and the other electrons. Each collision causes them unable to move. Thus, it restricts the movement of the electrons. This means that the resistivity of the metal increases

In the case of semiconductors: the curve is shown in the following diagram:

In semiconductors the forbidden gap between the conduction band and the valence band is small. When a small amount of energy is applied, the electrons easily move to the conduction band. Thus, some electrons from the covalent bonds between the atoms are free to move within the structure. This increases the conductivity of the material. The conductivity increases mean the resistivity decreases. Thus, when the temperature is increased in a semiconductor, the density of the charge carriers also increases and the resistivity decreases.

The curve is non-linear for a wide range of temperature.

Discuss the variation of resistivity with temperature

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