Difference Between Resistance and Resistivity

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 ( $\mathbf{R}$ ) across a conductor is the ratio of the potential difference ( $V$ ) across the conductor to the current ( $I$ ) flowing through the conductor:

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

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).

Difference Between Resistance and Resistivity – A Resistor

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

Directly proportional to the length $l$ ( $R\propto l$ ).
Inversly proportional to the cross-sectional area $A$ ( $R\propto \frac{1}{A}$ ).

What is Resistivity

The two conditions $R\propto l$ and $R\propto \frac{1}{A}$ can be combined into an equation with an appropriate constant of proportionality, $\rho$ :

$R=\rho \frac{l}{A}$

The constant $\rho$ (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 ( $E$ ) driving the current to the current density ( $J$ ):

$\rho=\frac{E}{J}$

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

Metals typically have low $\rho$ , 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) [CC BY-SA 3.0], via Wikimedia Commons