Question

how does the resistivity of a material change with temperature? write the expression for the resistivity at a given temperature T?

Answer 1

as d resistivity of material is given by
ρ=m/ne2t

This shows that the resistivity is related to the number density n of free electrons in the material and relaxation time t. The variation of resistivity of material with temperature is different in different materials and it is discussed below:

(a)    Metals: In most metals, number density n of free electrons does not change with temperature but an increase in temperature increases the amplitude of vibration of lattice ions of the metal. Therefore, the Collision of free electrons with ions or atoms while drifting towards the positive end of the conductor becomes more frequent, resulting in a decrease in relaxation time. Thus resistivity of conductor increases with increase in temperature. At low temperature, resistivity increases at a higher power of T.

It is found that the temperature dependence of resistivity of a metal is given by the relation

ρ = ρ 0[1+αt(T-T­0)]

Where ρ and ρ0 are the resistivity at temperature T and T0 respectively and αt is called temperature coefficient of resistivity.

Or                              αr= (ρ – ρ 0)/ ρ 0(T-T0)=d ρ / ρ0(1/dT)

Thus, αris defined as the fractional change in resistivity (dρ / ρ0) per unit change in temperature (dT)

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Answer 2

Answer:

Resistivity or specific resistance:-

• Resistivity is defined as the measure of a material’s resistance to the flow of an electric current.

• Electrical resistivity is an intrinsic property of a material.
• Resistivity is denoted as ρ (rho).
• Resistivity or specific resistance is the reciprocal of conductivity i.e., higher the conductivity, lower will be the resistivity of the material.

Resistivity of the material can be altered by changing its temperature.

• Resistivity is kind of indirectly proportional to the temperature. Because when we increase temperature, resistivity increases. It could be true for one kind of substance but all materials do not have the same dependence on temperature.
• The resistivity of metallic conductor with temperature are given by the following equation:-

        $\rho _T=\rho_o[1+a(T-T_o)]$

where, $\rho_T$ = resistivity at a temperature T

And, $\rho_o$ =resistivity at a reference temperature T₀

And, a = temperature coefficient of resistivity and have the dimension of (Temperature)⁻¹.

When we plot the graph of this equation, the resistivity of a metallic conductor increases with increasing temperature.

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