Question

Which one is given as the correct diagram for Resistivity vs Temperature for Metals?

Answer 1

Resistivity which is also called as specific resistance is the measure of resistance provided to a conducting material of unit length and unit area of cross section. It is a basic property of material and depends on the nature of material. It is also dependable on the temperature of a conductor. It is enhanced when the temperature is higher.

Complete answer:

The electrical resistivity of a conductor is given as the measure of the strength at which the material prevents the flow of electric current through it. The resistivity factor is also known as the specific resistance which makes it possible to compare the resistance of different types of conductors one another at a certain temperature in accordance to their physical properties without making considerations to their lengths or their cross-sectional areas. Therefore we can say that higher the resistivity value, the more will be the resistance and vice versa. A good conductor has less resistivity. At the same time, a bad conductor or insulator will have high resistivity. In the materials such as metals which are basically conductors are having lots of free electrons for conduction.

The resistivity of the metal is given by the equation,

$\rho =\dfrac{m}{n{{e}^{2}}\tau }$

Where $e$ be the charge of an electron, $\tau$ be the relaxation time, $n$ be the charge density and $m$ be the mass of the electron. As the temperature increases, the collision will take place faster than before which will reduce the relaxation time. Therefore the resistivity increases.

The relationship between the resistivity and the temperature is explained using the equation,

${{\rho }_{t}}={{\rho }_{0}}\left[ 1+\alpha \left( T-{{T}_{0}} \right) \right]$

Where ${{\rho }_{t}}$be the resistivity at $t{}^\circ C$, ${{\rho }_{0}}$ be the original resistivity, $\alpha$ be the coefficient of resistivity and ${{T}_{0}}$ be the reference temperature. From this we can see that the resistivity increases with temperature. Therefore these materials can easily conduct current at low temperature, because they will be having less resistance. Metals are offering high electrical resistance with increase in temperature. Therefore the resistivity of the metals also highly depends on their temperature and it gets enhanced with the enhancement in temperature.

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Therefore the correct answer is figure 1.

Note: Electrical conductivity is the reciprocal of the electrical resistivity. It is the measure of the strength of the conductors to allow the passage of current through it. This is also increasing as the temperature increases. The figure 2 shows that the resistivity is inversely proportional to the temperature which is wrong.