Question #42716

This question tests the student's ability to link microscopic kinetic theory with macroscopic steady-state conduction and spatially varying fields.

The primary trap is assuming resistivity scales linearly with temperature ($\rho \propto T$), which is true for real metals at high temperatures due to phonon scattering, but contradicts the explicitly stated classical Drude model ($\tau \propto 1/v_{rms} \propto T^{-1/2}$).

A secondary trap is calculating resistance using the average temperature or average resistivity instead of integrating the local electric field $E(x) = J\rho(x)$ over the non-uniform conductor.

Students who bypass the integration by using $T_{avg}$ or $\rho_{avg}$ will incorrectly arrive at Option B, failing to recognize that series resistance requires integrating the local resistivity profile.