siemens

SI coherent derived unit with special name and symbol
Name Symbol Derived quantity Expressed in terms of SI base units
siemens S electrical
conductance
kg-1 m-2 s3 A2

Definition

The siemens, symbol S, is the SI coherent derived unit of electrical conductance.

For a device with a conductance of one siemens, the electric current through the device will increase by one ampere for every increase of one volt of electric potential difference across the device.

The siemens is named after the German engineer Ernst Werner von Siemens (1816 – 1892).

Conductance

The electrical conductance of an object is a measure of the ease with which an electric current passes through it. The conductance of an object is defined as the ratio of the current passing through it to the voltage across it. Conductance is the reciprocal of resistance:

$G = \dfrac{I}{V} = \dfrac{1}{R}$

Using SI coherent units,

• G is the conductance, measured in siemens, symbol S,
• I is the current, measured in amperes, symbol A,
• V is the voltage, measured in volts, symbol V,
• R is the resistance, measured in ohms, symbol Ω,

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

The electrical conductance of an object depends on:

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

For example, a thick copper wire has a higher conductance than a thin copper wire.

Conductivity

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

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

Using SI coherent units, the proportionality constant, sigma, is the conductivity of the material, measured in siemens per metre, symbol S/m:

$G = \sigma \ \dfrac{A}{\ell}$

Temperature

At temperatures of around 20 °C, an increase in temperature typically results in a decrease of a metal’s conductivity, and an increase in a semiconductor’s conductivity. 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 decreasing the conductance of the strained section of conductor. Under compression, the conductance of the strained section of conductor increases. This effect is made use of in the design of strain gauges.

Photoconductivity

Some materials, particularly those made from semiconductors, exhibit photoconductivity, That is, the magnitude of their conductance depends on the amount of incident light. When light is absorbed by such materials, the number of free electrons and electron holes increases causing an increase in conductivity. This effect is made use of in basic light detectors.

Admittance

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

Superconductivity

Superconductors are made of materials that have infinite conductance.

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.