Conductors And Ohmic Behaviour

Question

When the temperature of a pure metallic conductor is raised, which statement correctly describes the resulting change in its electrical conductivity?

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Electrical conductivity in a metal is governed by how freely its abundant conduction electrons move between collisions, expressed through $\sigma = \frac{ne^2\tau}{m}$, where $\tau$ is the mean time between collisions. In a pure metal the free-electron density $n$ is essentially fixed, so the temperature behaviour is controlled by $\tau$. Raising the temperature makes the lattice ions vibrate more vigorously, so electrons collide more often and $\tau$ decreases, lowering the conductivity and equivalently raising resistivity. Hence the first statement is correct. The second is wrong because, unlike semiconductors, metals do not gain appreciable extra carriers on heating. The third is wrong because charge conservation says nothing about how easily charge moves. The fourth confuses cause and effect, since increased scattering actually reduces the average drift, not increases it. This reflects the NCERT free-electron treatment of metallic conduction. A plausibility check confirms it: experimentally, metals are known to grow more resistive when heated, which is exactly a fall in conductivity, consistent with the chosen statement.

Conductors And Ohmic Behaviour

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