Electrical conductance

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Categories: Physics stubs | Physical quantity | Electricity

Electrical conductance is related to but should not be confused with conduction, which is the mechanism by which charge flows, or with conductivity, which is a property of a material.

1 Relation to other quantities
2 Combining conductances
3 Small-signal device conductances
4 References
5 See also
6 External links

Relation to other quantities

As mentioned, conductance is related to resistance by:

Failed to parse (Missing texvc executable; please see math/README to configure.): G = \frac{1}{R} = \frac{I}{V} \,

for purely resistive circuits

where:

G is the electrical conductance,

R is the electrical resistance,

I is the electric current,

V is the voltage.

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

Furthermore, conductance is related to susceptance and admittance by the equation:

Failed to parse (Missing texvc executable; please see math/README to configure.): Y = G + j B \,

Failed to parse (Missing texvc executable; please see math/README to configure.): G = Re(Y) \,

where:

Y is the admittance,

Failed to parse (Missing texvc executable; please see math/README to configure.): j

is the imaginary unit,

B is the susceptance.

Combining conductances

The conductance G an object of cross-sectional area A and length Failed to parse (Missing texvc executable; please see math/README to configure.): \ell

can be determined from the material's conductivity σ by the formula,

Failed to parse (Missing texvc executable; please see math/README to configure.): G=\frac{\sigma \, A}{\ell}

From Kirchhoff's circuit laws we can deduce the rules for combining conductances. For two conductances Failed to parse (Missing texvc executable; please see math/README to configure.): G_1

and Failed to parse (Missing texvc executable; please see math/README to configure.): G_2
in parallel the voltage across them is the same and from Kirchoff's Current Law the total current is

Failed to parse (Missing texvc executable; please see math/README to configure.): I_{Eq} = I_1 + I_2\ \,

Substituting Ohm's law for conductances gives

Failed to parse (Missing texvc executable; please see math/README to configure.): G_{Eq} V = G_1 V + G_2 V\ \,

and the equivalent conductance will be,

Failed to parse (Missing texvc executable; please see math/README to configure.): G_{Eq} = G_1 + G_2\ \,

For two conductances Failed to parse (Missing texvc executable; please see math/README to configure.): G_1

and Failed to parse (Missing texvc executable; please see math/README to configure.): G_2
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,

Failed to parse (Missing texvc executable; please see math/README to configure.): V_{Eq} = V_1 + V_2\ \,

Substituting Ohm's law for conductance then gives,

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac {I}{G_{Eq}} = \frac {I}{G_1} + \frac {I}{G_2}

which in turn gives the formula for the equivalent conductance,

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac {1}{G_{Eq}} = \frac {1}{G_1} + \frac {1}{G_2}

This equation can be rearranged slightly,

Failed to parse (Missing texvc executable; please see math/README to configure.): G_{Eq} = \frac{G_1 G_2}{G_1+G_2}

Small-signal device conductances

The term conductance is applied to electronic devices such as transistors and diodes, 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 and channel length modulation.