Why does resistivity depend on temperature

The general rule says with resistance increases in conductors with increasing temperature and decreases with increasing temperature in insulators. In the case of semiconductors, typically, the resistance of the semiconductor decreases with the increasing temperature. But there is no simple mathematical relation to describe this relationship between resistance and temperature for different materials with graphs.

For Conductor: The valence band and conduction band overlap with one another in the case of a conductor. So, a conductor's conduction band contains excess electrons. By absorbing the energy, more electrons will go from the valence band to the conduction band when you raise the temperature.

Image to be added soon. For Semiconductor: The conductivity of the semiconductor material increases with temperature increases. As temperature increases, outermost electrons acquire energy, and thus by acquiring energy, the outermost electrons leave the atom's shell. Resistivity is basically the quantitative value of the resistance offered by any material. Although materials resist electrical current flow, some are better than others to conduct it. The amount of energy loss varies depending on the resistance of the material.

In some scientists cooled a sample of mercury down to 4. Thus the resistance of the material changed to zero. Thus the first super conductor was discovered. Thus the scientists found that in some circumstances some materials do not show any resistance.

The materials with zero resistance are called super conductors. At zero resistance the materials conducts current without any loss of energy. When the temperature of such materials are decreased, the free electrons stop colliding with the positive ions and thus it offers zero resistance. The temperature at which the resistance falls to zero is called Critical Temperature.

When the superconductor is placed in the magnetic field, the magnetic field bends around the material as it does not allow the magnetic field to pass through them.

When the intensity of the magnetic field is increased, at a certain point the field is able to penetrate through the super conductor and thus its behavior is destroyed.

Consider an electric current is passed through the superconductor. Suppose the density of the current is increased, at a particular value of current density, it loses its superconductivity and finally behaves like a normal material.

The current density above which the material loses its superconductivity is called the critical current density. High temperature, high magnetic field and high current density will destroy the behavior of superconductivity of a material.

Now a days these materials are used in MRI machines. The resistivity of materials like nichrome, manganin and constantan does not depend much on temperature and show a very low dependence. Hence these materials are used in wire bound standard resistors as the variation in the value of resistance is negligible when the temperature changes.

Thus it shows that the resistivity depends on the number of factors like the relaxation time between the collisions and the charge density. From the above scenarios it is clear that when the temperature is increased the average speed of the electrons increases and thus more collision occurs. Thus the relaxation time between each collisions decreases. In case of metals the charge density does not depend on temperature to a certain extent. For semiconductors and insulators, the charge density n increases when the temperature is increased.

Hence the resistivity decreases when the temperature decreases. The resistivity is the resistance offered by a conductor having unit length and unit area of cross section. For metals or conductors, when the temperature increases and the resistivity of the metal increases and thus current flow in the metal is decreased.

They have a positive temperature co — efficient. For semiconductors, when the temperature is increased the conductivity of the material is increased. It means that the resistivity of the material is decreased and so the current flow is increased. For semiconductors they have a negative temperature co — efficient. For insulators the conductivity of the material is increased, when the temperature is increased. When the conductivity of the material is increased, we know that the resistivity decreases and the current flow thus increases.

So some insulators at room temperatures changes to conductors at high temperature. The temperature at which the resistance drops to zero is called the critical temperature. Where does this idea belong? Nichrome was invented in , which made electric toasters possible. The general rule is resistivity increases with increasing temperature in conductors and decreases with increasing temperature in insulators.

Unfortunately there is no simple mathematical function to describe these relationships. From the equation 2. Its unit is per oC. If the temperature of a conductor increases, the average kinetic energy of electrons in the conductor increases. This results in more frequent collisions and hence the resistivity increases. The graph of the equation 2. Even though, the resistivity of conductors like metals varies linearly for wide range of temperatures, there also exists a non-linear region at very low temperatures.

The resistivity approaches some finite value as the temperature approaches absolute zero as shown in Figure 2.