# Resistivity

### What is resistivity?

Resistivity is a measure of the resistance to an electrical conductor for a given size of a specific material.

Every material resists the flow of electrical current but some do more than others. We can use resistivity to compare different materials opposition to the flow of current.

Materials that conduct electricity easily are called conductors and they have a low resistivity. Materials that do not conduct electricity easily are called insulators and they have a high resistivity.

The unit of resistivity is the ohm-metre or Ω⋅m. This is represented by the Greek letter ρ.

### Calculating resistivity

We can calculate resistivity by using the formula:  ρ = E / J

ρ is the resistivity of the material in ohms metre, in Ω⋅m

E is the magnitude of the electric field in volts per metre, V⋅m^-1

J is the magnitude of the current density in amperes per square metre, A⋅m^-2

If a material has a uniform cross-section, with a uniform flow of current (such as a wire), we can use this formula: ρ = R A / l

R is the electrical resistance of a uniform specimen of material, in ohms

L is the length of the material, in metres

A is the cross-sectional area of the material, in m^2

### Factors that affect resistivity

Looking at these formulas, we can see that if we increase the length or decrease the cross-section, the resistance will increase. Also, if we increase the resistivity, we increase the resistance. The resistivity is at a specific temperature, as temperature affects the resistivity of a material. This is because as temperature increases, particles vibrate more and the chances of this getting in the way of current flow is greater.

Resistivity is very important, as we need to choose the material that’s suitable for the task. If we need a material to be a conductor in a wire, then we need to choose a material with a low resistivity. Copper is often used for this role as it has a low resistivity, typically around 16.8 nΩm. PVC (polyvinyl chloride), is a common insulator that is used for wire insulation, it has a typical resistivity of around 1014 Ω.

Note that resistivity is one of a number of considerations, there are others, such as cost! Gold has a lower resistivity than copper but is more expensive! Gold is used sometimes but only when the cost can be justified!

If we need a material to be an insulator in a wire, then we need to choose a material with a high resistivity.

### Resistivity vs Resistance

Resistivity and resistance are not the same thing! Resistance is a property of the opposition to electric current, that is dependant on length and cross-section. Resistivity is the resistance of a material per length, per cross-section.