Theoretical Investigation of Temperature-Dependent Resistivity in Metallic Conductors

The electrical resistivity of metallic conductors is a fundamental property that depends on temperature. This paper presents a theoretical investigation into the temperature-dependent resistivity of metallic conductors using both classical and quantum mechanical models. The derivation of resistivity as a function of temperature is provided, along with a discussion on electron-phonon interactions that contribute to scattering mechanisms. Furthermore, a simple experiment to measure resistivity variations with temperature is described. While classical models provide a general understanding, quantum mechanics further refines the predictions, particularly at low temperatures. This paper is written for high school and early university students, ensuring accessibility to fundamental concepts with a rigorous mathematical foundation.