Conductivity and Temperature Dependence

Electrical conductivity, represented by the letter $\sigma$, is a measure of a material's ability to conduct an electric current. Resistivity, represented by $\rho$, is the inverse quantity, $\rho =\frac{1}{\sigma }$, and it quantifies how strongly the material opposes the flow of the current. In some contexts, such as experiments, it is more convenient to consider the resistivity, while in others, such as the theory presented in this project, it is useful to consider the conductivity. These values are temperature dependent. In metals the resistivity decreases as temperature is reduced, $\frac{\partial \rho }{\partial T}>0$. In other materials resistivity increases as temperature is reduced, $\frac{\partial \rho }{\partial T}<0$.