ohm

SI coherent derived unit with special name and symbol

Name

Symbol

Derived quantity

Expressed in terms of SI base units

ohm

electrical
resistance

kg m² s⁻³ A^-2

Definition

The ohm, symbol Ω, is the SI coherent derived unit of electrical resistance.

One ohm is defined as the electrical resistance between two points of a conductor when a constant potential difference of one volt, applied to these points, produces in the conductor a current of one ampere, the conductor not being the seat of any electromotive force.

The ohm is named after the German physicist Georg Simon Ohm.

Resistance

The electrical resistance of an object is a measure of its opposition to the flow of electric current. The resistance of an object is defined as the ratio of voltage across it to current passing through it:

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

Using SI coherent units,

R is the resistance, measured in ohms, symbol Ω,
V is the voltage, measured in volts, symbol V,
I is the current, measured in amperes, symbol A.

$1\ \Omega = 1\ \dfrac{\text{V}} {\text{A}}$

The electrical resistance of an object depends on:

the material it is made of,
cross-sectional area,
length.

For example, a thick copper wire has a lower resistance than a thin copper wire.

Resistivity

The resistance of an object made of a given material is directly proportional to the length of the object, and inversely proportional to its cross-sectional area;

$R \propto \dfrac{\ell}{A}$

Using SI coherent units, the proportionality constant, ρ, is the resistivity of the material, measured in ohm metres, symbol Ω m:

$R = \rho \ \dfrac{\ell}{A}$

Temperature

At temperatures of around 20 °C, an increase in temperature typically results in an increase of a metal’s resistivity, and a decrease in a semiconductor’s resistivity. This effect is made use of in the design of resistance thermometers, or thermistors.

Strain

When a conductor is placed under tension, leading to strain in the form of stretching of the conductor, the length of the section of conductor under tension increases and its cross-sectional area decreases. Both these effects contribute to increasing the resistance of the strained section of conductor. Under compression, the resistance of the strained section of conductor decreases. This effect is made use of in the design of strain gauges.

Photoresistance

Some resistors, particularly those made from semiconductors, exhibit photoconductivity, That is, the magnitude of their resistance depends on the amount of incident light. Resistors made from such materials are called photoresistors. This effect is made use of in basic light detectors.

Impedance

Impedance extends the concept of resistance to AC circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude. When a circuit is driven with direct current (DC), there is no distinction between impedance and resistance. Resistance can be thought of as impedance with zero phase angle.

Superconductivity

Superconductors are made of materials that have zero resistance.

Superconductors only exhibit superconductivity at very low temperatures. Metallic superconductors generally require cooling to temperatures near 4 K with liquid helium. Some “high temperature” ceramic superconductors remain superconductive near 77 K, and thus cooling with liquid nitrogen is sufficient.

When a current passes through a superconductor, there is no joule heating, and no dissipation of electrical energy. Superconductors would therefore be ideal for power transmission, were it not for the impracticalities of their low temperature requirements.