On increasing the temperature of a conductor, | vedclass

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Question

(A) The resistance $R$ of a conductor is given by the formula $R = \frac{ml}{ne^2 	au A}$,where $m$ is the mass of the electron,$l$ is the length,$n$

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Relaxation time decreases

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(A) The resistance $R$ of a conductor is given by the formula $R = \frac{ml}{ne^2 	au A}$,where $m$ is the mass of the electron,$l$ is the length,$n$ is the electron density,$e$ is the charge,$A$ is the cross-sectional area,and $	au$ is the relaxation time.From this relation,we see that $R \propto \frac{1}{	au}$.When the temperature of a conductor increases,the thermal velocity of the free electrons increases.This leads to more frequent collisions between the electrons and the lattice ions.Consequently,the average time between two successive collisions,known as the relaxation time $	au$,decreases.Since $R$ is inversely proportional to $	au$,a decrease in $	au$ results in an increase in the resistance $R$.

On increasing the temperature of a conductor,its resistance increases because

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