>[!summary] Resistivity is a material that reduces (or stops) the flow of electrons Conductivity allows this flow. > Key equations: > Resistivity in general: $\rho=\frac{\vec E}{J}$ > Resistance in a material: $R=\rho\frac{L}{A}$ > Conductivity in a material: $\sigma = \frac{J}{E}$ >[!info]+ Read Time **⏱ 1 min** # What is Resistivity Resistivity is how much the structure of a material reduces the flow of electrons ([[Resistance & Ohm Law]]). Materials can do this because they can affect how many electrons are in **some area** ([[Current#Current Density]]), and effect **the [[Electric Field]].** We define Resistivity as: $\rho=\frac{\vec E}{J}$ If we let E = V/L and J = i/A $\rho = \frac{E}{J}$ End with the result: $R=\rho\frac{L}{A}$ # Conductivity Unlike Resistivity, conductivity is how much electrons can move through a material ([[Current#Current Density]]) and how that material effect the [[Electric Field]]. Conductivity is the inverse of resistivity $\frac{1}{\rho} = \sigma$ $\sigma = \frac{J}{E}$ --- > 📚 Like this note? [Star the GitHub repo](https://github.com/rajeevphysics/Obsidan-MathMatter) to support the project and help others discover it! ---