To determine which graph represents the variation of resistivity $(\rho)$ with temperature $(T)$ for copper, we need to understand the behavior of metals.$\\$For metals like copper, resistivity increases with temperature. This is because as temperature rises,$\\$the lattice vibrations increase, causing more collisions for the electrons and thus increasing resistivity.$\\$The relationship is approximately linear over a moderate temperature range and can be expressed as:$\\ \rho = \rho_0 (1 + \alpha T) \\$where $\rho_0$ is the resistivity at a reference temperature, and $\alpha$ is the temperature coefficient of resistivity.$\\$Analyzing the options:$\\$• Option 1 shows a decreasing curve, which is typical for semiconductors, not metals.$\\$• Option 2 shows an increasing curve, which is consistent with the behavior of metals.$\\$• Option 3 shows a decreasing curve, similar to Option 1, and is incorrect for metals.$\\$• Option 4 shows a linear increase, which is also consistent with metals, but the curve in Option 2 is more typical.$\\$Therefore, the correct graph representing the variation of resistivity with temperature for copper is Option 2.