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The relaxation time $\tau$ is nearly independent of applied $\mathrm{E}$ field whereas it changes significantly with temperature $T$. First fact is (in part) responsible for Ohm's Law whereas the second fact leads to variation of $p$ with temperature. Elaborate why?
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Relaxation time $(\tau)$ is inversely proportional to the velocities electrons and ions. The applied electric field produces the insignificant change in drift velocities of electrons at the order of $1 \mathrm{~mm} / \mathrm{s}$, whereas the change in temperature (T), affects velocities at the order of $10^2 \mathrm{~m} / \mathrm{s}$.
As, the drift velocity increase, this decreases the relaxation time considerably in metals and consequently resistivity of conductor increases as
$$
\rho=\frac{1}{\sigma}=\frac{\mathrm{m}}{\mathrm{ne}^2 \tau}
$$
As, the drift velocity increase, this decreases the relaxation time considerably in metals and consequently resistivity of conductor increases as
$$
\rho=\frac{1}{\sigma}=\frac{\mathrm{m}}{\mathrm{ne}^2 \tau}
$$
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