Draw the resistivity versus temperature $(\rho \to T)$ graph for metals, alloys, and semiconductors.

(N/A) $1$. For metals: The resistivity $\rho_T$ at temperature $T$ is given by $\rho_T = \rho_0 [1 + \alpha(T - T_0)]$. For a limited range of temperatures, this graph is a straight line. At very low temperatures, the graph deviates from linearity and shows a non-linear behavior as shown in the provided figure for copper.
$2$. For alloys: Alloys like nichrome, manganin, and constantan have a very high resistivity compared to pure metals. Their resistivity shows a very weak dependence on temperature, resulting in a nearly flat, slightly increasing straight-line graph.
$3$. For semiconductors: The resistivity of semiconductors decreases exponentially with an increase in temperature. The relation is given by $\rho_T = \rho_0 e^{E_g / k_B T}$, where $E_g$ is the band gap energy. The graph is a downward-sloping curve.