NEET 2020 Physics Question 163 Solution

For metals, resistivity is given by Drude-Lorentz model: $$\rho = \frac{m}{n e^2 \tau}$$, where $$n$$ is the free electron density and $$\tau$$ is relaxation time. As temperature increases, lattice vibrations (phonons) increase, shortening $$\tau$$ and increasing $$\rho$$.

For pure metals such as copper, at temperatures close to absolute zero ($$0\text{ K}$$ to $$50\text{ K}$$), resistivity increases non-linearly with temperature (proportional to $$T^5$$ according to quantum electron-phonon scattering theory).

As temperature exceeds $$100\text{ K}$$, the rate of increase settles into a nearly linear dependence ($$\rho = \rho_0 [1 + \alpha(T - T_0)]$$). Thus the full plot starting from $$0\text{ K}$$ curves upward initially.

- Graph 1: Decreasing exponential (typical of intrinsic semiconductors). - Graph 2: Constant horizontal line (temperature-independent ideal resistor). - Graph 3: Curved upward non-linear plot starting near origin (exact NCERT plot for Copper). - Graph 4: Pure straight line passing through origin (neglects quantum low-temperature non-linearity). Therefore, Graph 3 is the correct representation.