The resistivity \( r \) of a material is an essential property that indicates how strongly it opposes the flow of electric current; this property is temperature dependent. For metallic conductors, the general formula for resistivity as it relates to temperature is given by \( r = r_0 [1 + a(T - T_0)] \), where \( r_0 \$ is the resistivity at the reference temperature \$ T_0 \$ and \$ a \$ is the temperature coefficient of resistivity. This relationship indicates that for metals, the resistivity increases linearly with temperature, leading to a positive temperature coefficient \$ (a > 0) \$ due to increased thermal vibrations of atoms at higher temperatures, which impedes the flow of electrons. Conversely, semiconductors exhibit a negative temperature coefficient where their resistivity decreases with increasing temperature, owing to the increased mobility of charge carriers as thermal energy facilitates electron movement across the band gap. The section is significant as it outlines the implications of temperature on material properties, especially in applications such as resistors, sensors, and electrical components utilized in various temperatures.