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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