Resistivity
Before you go through this article, make sure that you have gone through the previous article on Resistivity of Conductor.
We have learnt
 Resistivity of a conductor is defined as the resistance of a unit cube of the material of the conductor.
 It depends upon the nature of material and temperature of the conductor.
In this article, we will discuss the temperature dependence of resistivity for
 Metals
 Alloys
 Semiconductors & Insulators
 Electrolytes
Temperature Dependence of Resistivity
The resistivity of any material depends upon the number density (n) of free electrons and the mean collision time (τ) as
Also Read Deriving Formula For Resistivity of Conductor
For Metals (Conductors)
 For metals, the number density (n) of free electrons is almost independent of temperature.
 As temperature increases, the thermal speed of the free electrons increases and also the amplitude of vibration of the metal ions increases.
 Consequently, the free electrons collide more frequently with the metal ions.
 Thus, the mean collision time (τ) decreases.
Hence,
On increasing the temperature,
the resistivity of metals (conductors) increases. 
For most of the metals, resistivity increases linearly with the rise in temperature.
In such cases, resistivity at any temperature T (>T_{0}) is given by
where
 ρ_{T} = Resistivity at temperature T
 ρ_{0} = Resistivity at a reference temperature T_{0}
 α = Temperature coefficient of resistivity
Temperature Coefficient of Resistivity
The temperature coefficient of resistivity (α) may be defined as the increase in resistivity per unit resistivity per unit rise in temperature.

For metals, the value of α is positive meaning that the resistivity increases with the increase in temperature.
At low temperatures, the resistivity of metals increases as a higher power of temperature.
The following graph shows the variation of resistivity (ρ) of copper as a function of temperature T
For Alloys
 When two or more metals are mixed together to form an alloy, a complex crystalline structure is formed.
 This is because of what alloys have very high resistivity than their constituent metals.
ρ_{alloys} > ρ_{metals}
Alloys have very weak dependence on temperature.
For alloys, α → 0 
Example
The resistivity of nichrome has weak temperature dependence as shown in the following graph while that of manganin is almost independent of temperature.
α_{alloys} < α_{metals}
For Semiconductors and Insulators
For semiconductors and insulators, the relaxation time does not change with temperature but the number density (n) of free electrons increases exponentially with the rise in temperature.
Hence,
On increasing the temperature, the resistivity of semiconductors and insulators decreases.
Thus, for semiconductors and insulators, α is negative. 
For Electrolytes
As the temperature increases, the interionic attractions (solutesolute, solventsolute and solventsolvent types) decreases and also the viscous forces decreases and therefore the ions are able to move more freely.
Hence,
As the temperature of electrolytic solution increases,
the resistivity of electrolyte decreases. 
Test Your Concepts
Quiz on Temperature Dependence of Resistivity
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