Ncert Exercises & Solutions

The relaxation time $τ$ is nearly independent of the applied E field whereas it changes significantly with temperature T. First fact is (in part) responsible for Ohm's law whereas the second fact leads to a variation of $ρ$ with temperature. Elaborate why?

Hint: The drift velocity depends merely on the electric field applied.

Step 1:

Relaxation time is inversely proportional to the velocities of electrons and ions. The applied electric field produces an insignificant change in velocities of electrons at the order of 1 mm/s, whereas the change in temperature (T), affects velocities at the order of 10 m/s.

Step 2:

This decreases the relaxation time considerably in metals and consequently resistivity of metal or conductor increases as

$ρ = \frac{1}{σ} = \frac{m}{{ne}^{2} τ}$

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