Question

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

Answer 1

Hint: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.