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Electrical conductance
 
 
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Electrical conductance is a measure of how easily electricity
Electricity

Electricity is a general term that encompasses a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena such as lightning and static electricity, but in addition, less familiar concepts such as the electromagnetic field and electromagnetic induction....
 flows along a certain path through an electrical element
Electrical element

The concept of electrical elements is used in the circuit analysis of electrical networks. Any electrical network can be modeled by decomposing it down to multiple, interconnected electrical elements in a Schematic diagram#Electronic industry or circuit diagram....
. The SI derived unit
SI derived unit

SI derived units are part of the SI system of measurement Units of measurements and are derived from the seven SI base units.Note that while the names of all SI units are in lowercase, the symbols of units named after people are written with an initial capital letter ....
 of conductance is the Siemens
Siemens (unit)

The siemens is the SI SI derived unit of electric conductance. It is equal to inverse ohm. It is named after the Germany inventor and industrialist Ernst Werner von Siemens, and was previously called the #Mho....
 (also called the mho, because it is the reciprocal of electrical resistance, measured in Ohms). Oliver Heaviside
Oliver Heaviside

Oliver Heaviside was a autodidact English electrical engineering, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's equations in terms of electric and magnetic forces and flux, and independently co-f...
 coined the term in September 1885.

Electrical conductance
Conductance

Conductance can refer to:*Electrical conductance*Fluid conductance*Thermal_conductivity#Thermal_Conductance*Conductance *Conductance ...
 is related to but should not be confused with conduction
Electrical conduction

Electrical conduction is the movement of electric charge particles through a transmission medium . The movement of charge constitutes an Current ....
, which is the mechanism by which charge flows, or with conductivity
Electrical conductivity

Electrical conductivity or specific conductance is a measure of a material's ability to electrical conduction an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current....
, which is a property of a material.

entioned, conductance is related to resistance by: for purely resistive circuits.

where:
G is the electrical conductance (for gate),
R is the electrical resistance
Electrical resistance

The electrical resistance of an object is a measure of its opposition to the passage of a steady electrical current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material....
,
I is the electric current
Electric current

Electric current is the flow of electric charge. The electric charge may be either electrons or ions.The International System of Units unit of electric current intensity is the ampere....
,
V is the voltage
Voltage

Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
.


(Note: this is not true where the impedance is complex)

Furthermore, conductance is related to susceptance
Susceptance

In electrical engineering, the susceptance is the imaginary part of the admittance. In SI units, the susceptance is measured in siemens . Oliver Heaviside first defined this property, which he called permittance, in June 1887....
 and admittance
Admittance

In electrical engineering, the admittance is the multiplicative inverse of the Electrical impedance . The SI unit of admittance is the siemens ....
 by the equation:

or

where:
Y is the admittance
Admittance

In electrical engineering, the admittance is the multiplicative inverse of the Electrical impedance . The SI unit of admittance is the siemens ....
,
is the imaginary unit
Imaginary unit

In mathematics, physics, and engineering, the imaginary unit is denoted by  or the Latin   or the Greek iota . It allows the real number system, to be extended to the complex number system,   Its precise definition is dependent upon the particular method of extension....
,
B is the susceptance
Susceptance

In electrical engineering, the susceptance is the imaginary part of the admittance. In SI units, the susceptance is measured in siemens . Oliver Heaviside first defined this property, which he called permittance, in June 1887....
.


Kirchhoff's circuit laws
Kirchhoff's circuit laws

Kirchhoff's circuit laws are two Equality that deal with the Charge conservation and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff....
 we can deduce the rules for combining conductances.






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Encyclopedia


Electrical conductance is a measure of how easily electricity
Electricity

Electricity is a general term that encompasses a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena such as lightning and static electricity, but in addition, less familiar concepts such as the electromagnetic field and electromagnetic induction....
 flows along a certain path through an electrical element
Electrical element

The concept of electrical elements is used in the circuit analysis of electrical networks. Any electrical network can be modeled by decomposing it down to multiple, interconnected electrical elements in a Schematic diagram#Electronic industry or circuit diagram....
. The SI derived unit
SI derived unit

SI derived units are part of the SI system of measurement Units of measurements and are derived from the seven SI base units.Note that while the names of all SI units are in lowercase, the symbols of units named after people are written with an initial capital letter ....
 of conductance is the Siemens
Siemens (unit)

The siemens is the SI SI derived unit of electric conductance. It is equal to inverse ohm. It is named after the Germany inventor and industrialist Ernst Werner von Siemens, and was previously called the #Mho....
 (also called the mho, because it is the reciprocal of electrical resistance, measured in Ohms). Oliver Heaviside
Oliver Heaviside

Oliver Heaviside was a autodidact English electrical engineering, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's equations in terms of electric and magnetic forces and flux, and independently co-f...
 coined the term in September 1885.

Electrical conductance
Conductance

Conductance can refer to:*Electrical conductance*Fluid conductance*Thermal_conductivity#Thermal_Conductance*Conductance *Conductance ...
 is related to but should not be confused with conduction
Electrical conduction

Electrical conduction is the movement of electric charge particles through a transmission medium . The movement of charge constitutes an Current ....
, which is the mechanism by which charge flows, or with conductivity
Electrical conductivity

Electrical conductivity or specific conductance is a measure of a material's ability to electrical conduction an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current....
, which is a property of a material.

Relation to other quantities

As mentioned, conductance is related to resistance by: for purely resistive circuits.

where:
G is the electrical conductance (for gate),
R is the electrical resistance
Electrical resistance

The electrical resistance of an object is a measure of its opposition to the passage of a steady electrical current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material....
,
I is the electric current
Electric current

Electric current is the flow of electric charge. The electric charge may be either electrons or ions.The International System of Units unit of electric current intensity is the ampere....
,
V is the voltage
Voltage

Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
.


(Note: this is not true where the impedance is complex)

Furthermore, conductance is related to susceptance
Susceptance

In electrical engineering, the susceptance is the imaginary part of the admittance. In SI units, the susceptance is measured in siemens . Oliver Heaviside first defined this property, which he called permittance, in June 1887....
 and admittance
Admittance

In electrical engineering, the admittance is the multiplicative inverse of the Electrical impedance . The SI unit of admittance is the siemens ....
 by the equation:

or

where:
Y is the admittance
Admittance

In electrical engineering, the admittance is the multiplicative inverse of the Electrical impedance . The SI unit of admittance is the siemens ....
,
is the imaginary unit
Imaginary unit

In mathematics, physics, and engineering, the imaginary unit is denoted by  or the Latin   or the Greek iota . It allows the real number system, to be extended to the complex number system,   Its precise definition is dependent upon the particular method of extension....
,
B is the susceptance
Susceptance

In electrical engineering, the susceptance is the imaginary part of the admittance. In SI units, the susceptance is measured in siemens . Oliver Heaviside first defined this property, which he called permittance, in June 1887....
.


Combining conductances


The conductance G of an object of cross-sectional area A and length can be determined from the material's conductivity
Electrical conductivity

Electrical conductivity or specific conductance is a measure of a material's ability to electrical conduction an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current....
 s by the formula,

From Kirchhoff's circuit laws
Kirchhoff's circuit laws

Kirchhoff's circuit laws are two Equality that deal with the Charge conservation and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff....
 we can deduce the rules for combining conductances. For two conductances and in parallel the voltage across them is the same and from Kirchoff's Current Law the total current is

.


Substituting Ohm's law for conductances gives



and the equivalent conductance will be,

.


For two conductances and in series the current through them will be the same and Kirchhoff's Voltage Law tells us that the voltage across them is the sum of the voltages across each conductance, that is,

.


Substituting Ohm's law for conductance then gives,



which in turn gives the formula for the equivalent conductance,



This equation can be rearranged slightly,

.


Small-signal device conductances

The term conductance is applied to electronic devices such as transistor
Transistor

In electronics, a transistor is a semiconductor device commonly used to Electronic amplifier or switch Electronics signals. A transistor is made of a solid piece of a semiconductor material, with at least three terminals for connection to an external circuit....
s and diode
Diode

In electronics, a diode is a two-terminal device .Diodes have two active electrodes between which the signal of interest may flow, and most are used for their unidirectional electric current property....
s, where it usually refers to a small-signal model that is a linearization of the underlying device equations about a selected DC operating point or Q-point. This conductance is the reciprocal of the small-signal device resistance. See Early effect
Early Effect

The Early effect is the variation in the width of the base in a Bipolar junction transistor due to a variation in the applied base-to-collector voltage, named after its discoverer James M....
 and channel length modulation
Channel length modulation

One of several short channel effects in MOSFET#MOSFET scaling scaling, channel length modulation is a shortening of the length of the inverted channel region with increase in drain bias for large drain biases....
.

See also

  • SI electromagnetism units
    SI electromagnetism units

    See also* SI units* Speed of light* meter* ampere* secondReferences...
  • Electrical conductivity
    Electrical conductivity

    Electrical conductivity or specific conductance is a measure of a material's ability to electrical conduction an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current....
  • Siemens
    Siemens (unit)

    The siemens is the SI SI derived unit of electric conductance. It is equal to inverse ohm. It is named after the Germany inventor and industrialist Ernst Werner von Siemens, and was previously called the #Mho....
  • Hybrid-pi model
    Hybrid-pi model

    The hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of transistors. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate inter-electrode capacitances and other parasitic elements....
  • Small-signal model