Resistivity and Temperature Dependence of Resistivity

Specific electrical resistance or electrical resistivity is an intrinsic property of a material. It is defined as the measure of a material’s resistance to the flow of an electric current and is denoted as ρ (rho). Resistivity is the reciprocal of conductivity i.e.,higher the conductivity, lower will be the resistivity of the material and vice versa. However, it is found that resistivities of the materials can be altered by changing the temperature. Let’s learn more about the temperature dependence of resistivity.

Temperature Dependence of Resistivity

Based on the conductivity of the materials, they are classified into three – conductors, semiconductors and insulators. Conductors have low resistivities ranging from 10-8Ωm to 10-6 Ω m while insulators have high resistivities which can be 1018 times greater than metals. Resistivity is indirectly proportional to the temperature. In other words, as you increase the temperature of  materials, their resistivities will decrease. But this is not true for every material i.e.,all materials do not have same dependence on temperature.

The resistivities of metallic conductors within a limited range of temperature is given by the following equation:

ρT= ρ0 [1 + a(T–T0)]

Here,

ρT= resistivity at a temperature T

ρ0 =resistivity at a reference temperature T0

a= temperature coefficient of resistivity; the dimension of a is (Temperature)-1

According to the above equation, a graph of ρT plotted against T would be a straight line i.e., the resistivity of a metallic conductor increases with increasing temperature.

As we mentioned, different materials have a different dependence on temperature. For example, materials like Nichrome, Manganin and constantan are less likely to change their resistivities with temperature. Hence, they are employed in wire bound standard resistors. However, semiconductors exhibit an indirect relation with temperature. Resistivities of semiconductors decrease with increasing temperatures.

In terms of ‘n’

We know resistivity, ρ is given by

ρ= 1/σ = m/ne2ζ

Here, n (no. of free electrons) and ζ (the average time between collisions) are inversely proportional to ρ.

In metals, ‘n’ does not change with temperature. However, the increase in temperature can increase the collision of electrons. This reduces the ζ and implies that increase in temperature increases the ρ. However in insulators and semiconductors, ‘n’ increases with the increasing temperature. Thus an increase in temperature decreases the ‘ρ’ in them.