Summarizing Resistance and Resistivity

Summary

• The resistance \(R\) of a cylinder of length \(L\) and cross-sectional area \(A\) is \(R=\cfrac{\mathrm{\rho L}}{A}\), where \(\rho \) is the resistivity of the material.
• Values of \(\rho \) in this table show that materials fall into three groups—conductors, semiconductors, and insulators.
• Temperature affects resistivity; for relatively small temperature changes \(\Delta T\), resistivity is \(\rho ={\rho }_{0}(\text{1}+\alpha \Delta T)\), where \({\rho }_{0}\) is the original resistivity and \(\text{α}\) is the temperature coefficient of resistivity.
• This table gives values for \(\alpha \), the temperature coefficient of resistivity.
• The resistance \(R\) of an object also varies with temperature: \(R={R}_{0}(\text{1}+\alpha \Delta T)\), where \({R}_{0}\) is the original resistance, and \(R\) is the resistance after the temperature change.

Glossary

resistivity

an intrinsic property of a material, independent of its shape or size, directly proportional to the resistance, denoted by ρ

temperature coefficient of resistivity

an empirical quantity, denoted by α, which describes the change in resistance or resistivity of a material with temperature