# Resistivity, Conductivity, Resistance and Conductance

## Resistivity

**Resistivity** is an attribute of a material, such as copper for example, which is **proportional **to how **strongly it resists **an **electric current** flowing through it.

Hence a material with a **high resistivity **strongly **opposes **electric current flowing through it and conversely a material with a **low resistivity** **permits **electric current and makes a better conductor.

Resistivity is given the symbol **ρ** (pronounced rho) and has units of **Ohm metre [Ωm].**

## Conductivity

**Conductivity** is a related property of a material which is the **reciprocal of resistivity** and reflects **how strongly** a material **conducts **an **electric current**.

**Copper **is a material which has **high conductivity** and **low resistivity**.

Conductivity is given the symbol **σ** (pronounced sigma) and has units of **Siemens per metre [S/m].**

## Resistance and Conductance

**Electrical resistance** is a measure of an objects *opposition* to an electric current.

It has units of **ohms (Ω)** and depends on three factors: **resistivity (ρ)**, **length (L)** and **cross sectional area (A)** and is qualitatively described with the equation below:

And shown diagrammatically as:

Intuitively from this we can see that *longer *objects will have an *increased ***resistance **which is understandable as the charges have *more *resistance to get through and a *smaller *cross section area also *increases *resistance as less charges will be able to **pass through it per second** and there are also **less charges** in the material itself to help conduction.

A related measurement to resistance is **conductance** which has the units of **Siemens (S)**. Similar to resitivity and conductivity, conductance is the **reciprocal of resistance**.

Objects with a **larger conductance** allow **higher currents** to flow.

### Example:

**Q. **What is the resistance of a 15cm long wire with an area of 100mm^{2} and resisitivity of 1.68*10^{-8}Ωm?

**dimensional analysis**where we check the

**units**on both sides of the equation. In our case we want to confirm that if all units are in

**m**, then the final result will be in

**Ω's**: Which proves that we will achieve the desired result by converting the length and area into

**base units of m**. Now to calculate each of the parameters in units of m and then substitute them into the formula for resistance: When possible it is best practice to express the final answer in the units which will

**simplify**the result. Unless the question specifically asks for an answer in

**specific units**, for example: "Provide the answer in Ω's", be careful of this especially in

**exams**and

**assignments!**

### Questions:

**1.** An object has a resistance of 5Ω, a length of 40cm and an area of 10mm^{2}. What is its resistivity?

#### Answer

**2.** An object has a resistance of 2mΩ, a length of 40cm and a resistivity of 1.79*10^{-5}Ωm. What is its area?