Question

Describe the temperature coefficient of the resistance of the material of a conductor?

Answer 1

Hint: The variation in the resistance occurring at $0{}^\circ C$ can be defined as the temperature coefficient of the material. Temperature coefficient of the resistance has been defined as the measure of variation in the electrical resistance of any of the substances per degree of the variation in temperature. This will help you in answering this question.

Complete answer:
The temperature coefficient of resistance can be defined as the variation in resistance per unit resistance per degree rise in the temperature based upon the resistance of $0{}^\circ C$.
This can be written as an equation given as,
$R\left( T \right)={{R}_{0}}\left( 1+\alpha \Delta T \right)$
Where $R\left( T \right)$ be the resistance at any temperature, ${{R}_{0}}$ be the resistance at $0{}^\circ C$ temperature, $\alpha $ be the temperature coefficient of resistance and $\Delta T$ be the change in temperature.
From the above mentioned equation, after rearranging this equation, we can write that,
$\left( 1+\alpha \Delta T \right)=\dfrac{R\left( T \right)}{{{R}_{0}}}$
That is we can write that,
$\left( \alpha \Delta T \right)=\dfrac{R\left( T \right)}{{{R}_{0}}}-1$
Expanding this equation will be given as,
$\left( \alpha \Delta T \right)=\dfrac{R\left( T \right)-{{R}_{0}}}{{{R}_{0}}}$
The change in resistance can be shown as,
$R\left( T \right)-{{R}_{0}}=\Delta R$
Substituting this in the equation, we can write that,
$\alpha =\dfrac{\Delta R}{{{R}_{0}}\Delta T}$
The second equation will be the mathematical expression of the temperature coefficient of resistance of the material of a conductor. Therefore the temperature coefficient of the material of the conductor has been calculated.

Note:
A positive coefficient for a material means that its resistance will increase in temperature. Pure metals will be having a positive temperature coefficient of resistance. The materials whose resistance will increase with enhancement in temperature. Even though there are many elements whose electrical resistance of which decreases with a decrease in temperature. In metal when the temperature will increase, the random motion of the free electrons and the interatomic vibration inside the metal also increase which will cause more collisions. More collisions prevents the smooth flow of electrons through the metal, therefore the resistance of the metal will increase with the increase in temperature.