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Asked in GSEB Board March 2022 · Temperature dependence of resistance
Idea: in a metal the number of free electrons per unit volume hardly changes with temperature.
On heating, the ions vibrate more strongly, so the electrons collide more often and the relaxation time τ becomes shorter.
Since ρ = m/(ne²τ), a smaller τ means a larger ρ.
The resistivity therefore rises with temperature, ρ_T = ρ₀[1 + α(T - T₀)] with α > 0.
So α is positive for metals.
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