question_answer

The relaxation time \[\tau \] is nearly independent of applied E whereas it changes significantly with temperature T. First fact is responsible for Ohm's law whereas second fact leads to variation of \[\rho \] with temperature. Elaborate why?

Answer:

Relaxation time \[(\tau )\]is inversely proportional to the velocities of electrons (e) and ions. The applied electric field produces an insignificant change in velocities of electrons at the order of 1m/s whereas the change in temperature T affects velocities at the order of \[{{10}^{2}}\,\,m\,/\,s.\] This decreases the relaxation time considerably in metals and consequently resistivity (\[\rho \]) of metal or conductor. \[\rho =\frac{M}{n{{e}^{2}}\tau }\] Where, \[n=\]electron density.