Temperature Dependence Of Resistance

In a metallic conductor, resistivity rises with temperature because the lattice ions vibrate more vigorously when heated, so drifting electrons collide with them more often, and this idea underpins the discussion in NCERT Class 12, Chapter 3 (Current Electricity). Since resistivity is given by $\rho =\frac{m}{n{e}^2\tau }$, a shorter mean relaxation time $\tau$ directly increases $\rho$ and hence resistance. The number density $n$ of free electrons in a metal is essentially fixed, so the dominant temperature effect works through $\tau$. The option claiming that free electrons fall sharply is wrong because that behaviour describes semiconductors, not metals, where the carrier concentration barely changes with temperature. The option about the wire physically shrinking is wrong because metals actually expand on heating, and in any case thermal expansion is far too small to account for the observed change in resistance. The option that electrons gain charge is unphysical, since the charge of an electron is a fixed fundamental constant that never varies with temperature. A plausibility check aligns with experience: an incandescent bulb filament shows a much higher resistance when glowing white hot than when cold at switch-on, and the large inrush current seen at turn-on is a direct everyday demonstration of exactly the collision mechanism this explanation predicts.