# 6.8A: Electrical Conductivity and Resistivity

Electrical resistivity and conductivity is an important property for materials. Different materials have different conductivity and resistivity. Electrical conductivity is based on electrical transport properties. These can be measured with multiple techniques by using a variety of instruments. If electricity easily flows through a material, that material has high conductivity. Some materials that have high conductivity include copper and aluminum. Electrical conductivity is the measure of how easily electricity flows through a material.

## Conductivity vs Resistivity

Conductivity and resistivity are inversely proportional to each other. When conductivity is low, resistivity is high. When resistivity is low, conductivity is high. The equation is as follows:

$\rho = \dfrac{1}{\sigma}$

where

• Resistivity is represented by $$\rho$$ and is measured in Ohm-meters ($$Ωm$$),
• Conductivity is represented by $$\sigma$$ and is measured in Siemens ($$1/Ωm$$).

Since conductivity is the measure of how easily electricity flows, electrical resistivity measures how much a material resists the flow of electricity.

## Electrical Transport Properties

Simply put, electricity is the movement of electrons through a material. As electrons move through a material, it comes into contact with atoms in the material. Collisions slow the electrons down. Each collision increases the resistivity of the material. The easier the electrons continue through a material, the fewer collisions that take place and the higher the conductivity.

When temperature increases, the conductivity of metals usually decreases, while the conductivity of semiconductors increases. This of course assumes that the material is homogenous, which is not always the case. You can calculate resistivity using the following equation

$\dfrac{E}{J} = ρ$

As you already read, ρ is the symbol for resistivity. $$E$$ is the electric field and has units of Volts per meter (V/m). J is the current density and has units of amps per meter squared (A/m2). The electric field is calculated by dividing the Voltage by the length, l, that voltage is applied.

$E=\dfrac{V}{l}$

The current density is calculated by the equation below

$J=\dfrac{I}{A}$

I is the current and is divided by the cross sectional area, A, over which the current flows.

## Resistivity vs Resistance

Resistivity and resistance are two different things. Resistivity does not depend on size or shape. Resistance, however, does. You can calculate resistance with the equation below.

$R=\dfrac{V}{I}$

R refers to resistance and is measured in Ω. $$V$$ is the voltage and is measured in volts. I measures the current and its unit is amps (A).

## References

1. Electrical Conductivity and Resistivity, Heaney, Michael, Electrical Measurement, Signal Processing, and Displays. Jul 2003
2. Levy, Peter M., and Shufeng Zhang. "Electrical Conductivity of Magnetic Multilayered Structures." Physical Review Letters 65.13 (1990): 1643-646. Print.