**Resistance** and **Resistivity** are both important concepts for electrical engineering.

**Resistance gives the ratio of the potential difference to current across a conductor at a given time**, whereas **Resistivity is the ratio of electric field to current density** for a material **at a specific temperature**.

## What is Resistance

**Resistance (****) **across a conductor is the ratio of the potential difference () across the conductor to the current () flowing through the conductor:

An electric current is made of a flow of charges. For simplicity, we will consider cases where electrons flow across a uniform piece of cylindrical wire in response to a potential difference across the wire. As the electrons flow through the wire, the vibrating nuclei from the wire’s atoms often knock the electros off their path. This is the origin of resistance. Resistance is measured in units of ohms (Ω).

In experiments, it can be shown that the resistance across a metal wire is:

- Directly proportional to the length ().
- Inversly proportional to the cross-sectional area ().

## What is Resistivity

The two conditions and can be combined into an equation with an appropriate constant of proportionality, :

The constant (the greek letter “rho”) is called **resistivity**. It describes the resistive properties of the *material**, regardless of its dimensions*. Resistivity *does* depend on the temperature. Nevertheless, a particular material at a given temperature has the same resistivity.

Resistivity is more generally *defined* as the ratio of the electric field () driving the current to the current density ():

However, it can be shown that the in both these equations is, in fact, the same. The unit for measuring resistance is the ohm metre (Ω m).

Metals typically have low , of the order of ~10^{-8} Ω m at room temperature. As temperature increases, the resistivity increases in metals. The resistivity of **semiconductors** with a so-called “negative temperature coefficient” *decreases* as temperature increases. If a **superconductor** is cooled below a critical temperature, its resistivity drops to 0.

## Difference Between Resistance and Resistivity

### Definition of Resistance and Resistivity

**Resistance** across a conductor is the ratio of the potential difference across it to the current flowing through it.

**Resistivity** of a material is the ratio of electric field strength to the current density at a specific temperature.

### Units

**Resistance **is measured in units of **ohms** (Ω).

**Resistivity **is measured in units of **ohm metres** (Ω m).

### Dependence

**Resistance** is a property of a particular object. It depends on the object’s material, temperature as well as its dimensions (directly proportional to length, inversely proportional to the cross-sectional area for the case of a uniform metal wire).

**Resistivity** is a property of a particular *material*. It is *not* dependent on the dimensions. It is, however, dependent on temperature.

**Image courtesy**

“Showing a resistor component with 330 Ω and a tolerance of 5%” by Nunikasi (Own work) [], via