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 of the conductor and temperature of the conductor.
In this article, we will discuss the temperature dependence of resistivity.
Temperature Dependence of Resistivity-
The resistivity of any material depends upon the number density (n) of free electrons and the mean collision time () as-
For Metals (Conductors)-
- For metals, the number density (n) of free electrons is almost independent of temperature.
- As temperature increases, the thermal speed of 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 () decreases.
|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 is given by-
- ρT = Resistivity at temperature T
- ρ0 = Resistivity at a reference temperature T0
- 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 degree rise in temperature.
For metals, the value of α is positive meaning that resistivity increases with increasing 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-
- When two or more metals are mixed together to form an alloy, complex crystalline structure is formed.
- This is because of what alloys have very high resistivity than their constituent metals.
ρalloys > ρmetals
|Alloys have very weak dependence on temperature.
For alloys, α → 0
The resistivity of nichrome has weak dependence as shown in the following graph while that of manganin is almost independent of temperature.
αalloys < αmetals
For Semiconductors and Insulators-
In case of insulators and semiconductors, the relaxation time does not change with temperature but the number density (n) of free electrons increases exponentially with the rise in temperature.
|On increasing the temperature, the resistivity of semiconductors and insulators decreases.
For semiconductors and insulators, α is negative.
As the temperature increases, the inter-ionic attractions (solute-solute, solvent-solute and solvent-solvent types) decreases and also the viscous forces decreases and therefore the ions move more freely.
|As the temperature of electrolytic solution increases,
the resistivity of electrolyte decreases.
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