Current Electricity

Question

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If the temperature of a good conductor decreases, how does the relaxation time of electrons in the conductor change?

Solution

When the temperature of a good conductor decreases, the number of collisions of electrons also decreases. Hence, the time of free travel increases or relaxation time increases.
OR
If the temperature of a good conductor decreases, its resistance decreases. Since,

R = ρ \frac{l}{A}

R = \frac{m}{{ne}^{2} τ} \frac{l}{A} \leq 0, R \propto 1 / τ \Rightarrow τ \propto 1 / R;

so time of relaxation increases.

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Current Electricity

If the temperature of a good conductor decreases, how does the relaxation time of electrons in the conductor change?

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