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Asked in GUJCET 2026 · Temperature dependence of resistance
Idea: a free electron in a metal has two quite different speeds. Its random thermal motion is set by the temperature; its slow drift along the wire is set by the field and by how long it survives between collisions.
Thermal motion: 1/2mvᵣₘₛ²=3/2k_BT, so vᵣₘₛ=√(3k_BT)/m, which grows with the temperature.
Faster random motion means the electrons meet the vibrating ions more often, so the relaxation time τ gets shorter.
Mobility μ=(eτ)/m and drift velocity v_d=μ E both follow τ downwards, which is why a metal's resistance rises as it is heated.
So of the four, the thermal speed is the one that increases.
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