Which one of the following schematic graphs correctly represents qualitatively the variation of resistivity ρ with respect to temperature T for a semiconductor?

For a semiconductor, resistivity generally decreases as temperature increases. This is because increasing thermal energy excites more electrons into the conduction band and creates more holes in the valence band, increasing the number of free charge carriers available for conduction. More charge carriers lead to higher conductivity and thus lower resistivity. Graph (b) qualitatively shows this inverse relationship where resistivity decreases with increasing temperature.