Question

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

Answer 1

Change in resistance at $0^\circ C$ is called the temperature coefficient.

Complete step by step solution:
The temperature coefficient of resistance is defined as the Change in resistance per unit resistance per degree rise in temperature based upon the resistance of $0^\circ C$.
$R\left( T \right) = {R_0}\left( {1 + \propto \Delta T} \right)$ ….(1)
Where, R (T) =Resistance at any temperature
${R_0}$= resistance at temperature $0^\circ$
$\propto$ = temperature coefficient of resistance
$\Delta T$=change in temperature
From equation …(1)
$1 + \propto \Delta T = \dfrac{{R\left( T \right)}}{{{R_0}}}$
$\propto \Delta T = \dfrac{{R\left( T \right)}}{{{R_0}}} - 1$
$\propto \Delta T = \dfrac{{R\left( T \right) - {R_0}}}{{{R_0}}}$
$\propto = \dfrac{{\Delta T}}{{{R_0}\Delta T}}$ …(2)
$\left[ {R\left( T \right) - {R_0} = \Delta R} \right]$
Where $\Delta R$ = change in resistance

The equation (2), is the mathematical expression of temperature coefficient of resistance of the material of a conductor.

Note: A positive coefficient for a material means that its resistance increases with an increase in temperature. Pure metals typically have positive temperature coefficient of resistance.