Temperature Dependence of Resistance

Introduction

Resistivity is also known as volume resistivity or specific electrical resistance. It can be defined as a material’s intrinsic attribute that demonstrates its resisting current flow. It’s also known as the resistance provided by a conductor with a unit length and cross-section area. As a result, the temperature dependence of resistance is unaffected by the length and area of a material’s cross-section. However, its length and cross-sectional area determine a material’s resistance, where R is the resistance in ohms; A is the cross-section area in square meters; and L is the length in meters. The resistivity is given as ⍴ = R A/L. The ohmmeter is the unit of 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.

Resistivity Variation in Conductors

When there is a potential difference, we know that current is the movement of free electrons from one atom to the next. There is no forbidden gap between the conduction and valence bands in conductors. In many circumstances, the two bands overlap. In conductors, the valence electrons are freely connected to the nucleus. Because metals and conductors have low ionization energy, they lose electrons quickly. The delocalized electrons can travel around when an electric current is supplied to the structure. This is what happens when the temperature is average.

The vibrations of the metal ions in the lattice structure increase as the temperature rises. The vibrations of the atoms begin to increase in amplitude. The free electrons and other electrons frequently collide because of these oscillations. Each impact saps some energy from the liberated electrons, rendering them immobile. As a result, the delocalized electrons’ mobility is restricted. The electrons’ drift velocity reduces because of the collision. This indicates that when the metal’s resistivity rises, the current flow in the metal decreases; when the substance’s resistance increases, the material’s conductivity drops.

Resistivity Variation in Semiconductors

An example of a semiconductor is silicon. The prohibited gap between the conduction and valence bands in semiconductors is tiny. The valence band is filled at 0K, whereas the conduction band is possibly empty. However, when a modest amount of energy is applied, the electrons migrate easily to the conduction band. As an example, silicon is a semiconductor. Each silicon atom is connected to four other silicon atoms by four bonds. Covalent bonds, in which the electrons are in fixed positions, exist between these atoms. As a result, the electrons in the lattice structure do not move at 0K.

The prohibited gap between the two bands narrows as the temperature rises, and electrons flow from the valence band to the conduction band. As a result, certain electrons from the Si atoms’ covalent bonds can roam within the structure. This improves the material’s conductivity. When the conductivity rises, the resistance falls. As a result, as the temperature of a semiconductor increases, the density of charge carriers rises, lowering the resistivity. It is said that semiconductors have a negative temperature coefficient. As a result, the temperature coefficient of resistivity has a negative value.

Resistivity Variation in Insulators

The electrons have filled the valence band. More than 3eV will be the forbidden gap between the two bands. As a result, moving the valence electron to the conduction band demands a significant amount of energy. An excellent example of an insulator is a diamond. Conduction does not occur because all the valence electrons create a covalent bond. The nucleus is strongly connected to the electrons.

When the resistance depends on the temperature of a raised material, the atoms vibrate, causing the valence electrons in the valence band to move into the conduction band. As a result, the material’s conductivity improves. Conversely, when a material’s conductivity rises, the resistance falls, and the current flow increases.

In the case of metals, the charge density is primarily independent of temperature. As a result, additional parameters such as are influenced, implying that as the temperature rises, the average time between collisions reduces, causing the resistivity to rise.

When the resistance depends on the temperature in some materials (such as silicon) is negative, implying that resistance decreases as temperature rises. Therefore, the increasing temperature in such materials can free more charge carriers, increasing current.

Electrical Resistance as a Concept

Temperature dependence of resistivity is the phenomenon of a material’s particular electrical resistance or volume resistivity. It can also be defined as a material’s intrinsic attribute that shows how the substance opposes current flow through it. The resistance produced by a conductor with unit length and unit area of the given cross-section can also be defined as the notion.

As a result, the temperature dependence of resistivity is unaffected by the cross-sectional length and area of a material. The resistance of a material, on the other hand, is determined by the length and area of its cross-section.

ρ = RA/L,

where R is the resistance in ohms; A is the cross-section area in square meters; and L is the length in meters. The ohmmeter is the widely recognized unit of resistivity.

Getting to Know the Formula

When there is a potential difference between two atoms, an electric current transfers free electrons from one to the other. There is no gap between the conduction band and the valence band of electrons in conductors. These bands usually overlap in most circumstances.

The valence electrons in a specific atom are loosely connected to the nucleus of a conducting material. Metals and conductors frequently have low ionization energy, and as a result, they lose electrons quickly. When an electric current is applied to the structure, the electrons can move around independently. This occurs when a material’s typical temperature is exceeded.

Each of these collisions drains some of the energy from the free-moving electrons, rendering them immobile. As a result, the movement of the delocalized electrons is restricted.

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.