Temperature Dependence on Resistance

Temperature is the measure of hotness or coldness of material and it can be determined in various scales including Kelvin, Celsius, etc. It indicates the direction in which the heat energy will flow. While resistance can be defined as the measure of the opposition of the current flow in an electrical circuit and it is measured in ohms(Ω).

The formula is ρ = RA/L, where R is the resistance in ohms, A is the area of cross-section in square meters and L is the length in meters

In this particular topic, we will try to understand the correlation between temperature and resistance. 

Resistivity Variation with Temperature

The temperature dependence of resistance has an impact on material resistivity. The equation  ⍴(T) =  ⍴(0) [1 + 𝛼(T – T0)] depicts the relationship between temperature and material resistivity. In the equation,  ⍴(0) represents the resistivity at a standard temperature; ⍴(T) represents the resistivity at temperature T; T0 represents the reference temperature and 𝛼 is the temperature coefficient of resistance.

The variation of resistance due to temperature in conductors:

In the conductors, the gap between the conduction band and valence band is null and due to that valence electrons are not tightly bound to the nucleus. Whenever the temperature goes up, the vibrations of the metal ions in the lattice structure increase and this results in the atoms starting to vibrate with higher amplitude. Because of these vibrations there are frequent collisions and every collision drains out some energy of the free electrons and their movement is completely restricted, literally, they can’t move and because of this, the delocalized electrons cannot move either. 

This, in turn, results in the decrease of the drift velocity of electrons due to collisions. The resistivity of the metal increases and therefore the current flow in the metal decreases. 

Most metals are good conductors and have a positive temperature coefficient. Examples of good conductors are silver, gold and copper.

The variation of resistance due to temperature in Semiconductors:

As the name itself indicates semiconductors are the materials that are in between conductors and insulators. Under regular conditions, semiconductors are poor conductors.  At 0K the conduction band can be completely empty and the valence band is completely filled. But when a small amount of energy is applied the electrons move easily towards the conduction band.

Silicon is the primary example of semiconductors.

When the temperature is increased the gap gets smaller and the electrons move from valence to conduction band. Thus some electrons from the covalent bonds between the SI atoms are free to move within the structure. This results in the increased conductivity of the material. 

The conductivity increases mean the resistivity decreases. Therefore whenever there is an increase in the temperature of a semiconductor, the density of the charge carriers also increases and the resistivity decreases. Semiconductors have a negative temperature coefficient. So the value of the temperature coefficient of resistivity, α is negative.

The variation of resistance due to temperature in Insulators:

In the case of insulators, the forbidden gap between the valence band and the conduction band is extremely high and due to which the valence band is completely filled with electrons.  Automatically there is a requirement of high energy for the electrons to move from valence band to conduction band. The electrons are very tightly attached to the nucleus, and all the electrons are involved in the formation of covalent bonds hence conduction doesn’t happen.

Whenever the temperature increases, the atoms of the material start vibrating extensively. Whenever the conductivity of the material increases, it means that the resistivity decreases and so the current flow increases. This makes some insulators at room temperatures change to conductors at high temperatures.  Because of the above-mentioned reasons, insulators have a negative temperature coefficient. So the value of the temperature coefficient of resistivity, α is negative

Superconductors:

The materials with zero resistance are called superconductors. At zero resistance the material conducts current without any loss of energy. 

Factors affecting Resistivity:

As we know that the resistivity, ρ = m/ne²ԏ, where e is the charge on an electron, ԏ is the average time taken between each collision or the relaxation time of electrons and m is the mass of the electron, n is the charge density.

Therefore it’s evident that the resistivity depends on a number of factors like the relaxation time between the collisions and the charge density. From the above explanations, it is clear that when the temperature is increased the average speed of the electrons increases and thus more collisions occur. Thus the relaxation time between each collision decreases.

Conclusion

Metals and conductors are correctly described as having a positive temperature coefficient. Although, furthermore, it has a positive value in the range of 500K, the resistivity of most metals increases in a linear pattern as the temperature rises.

When the dependence of resistivity on the temperature of metal or conductor rises, the metal’s resistivity increases. As a result, the current flow in the metal diminishes. A positive temperature coefficient causes this phenomenon. In this scenario, the value is positive.