Electrical conductance

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Electrical conductance is the real part of the reciprocal of electrical impedance. It is a measure of how easily electricity flows along a certain path through an electrical element. The SI derived unit of conductance is the siemens (formerly referred to as the reciprocal ohm or mho). Oliver Heaviside coined the term in September 1885^{[citation needed]}.

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 References
4 See also
5 External links

As mentioned, conductance is related to resistance by:

$G = \frac{1}{R} = \frac{I}{V} \,$

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:

$Y = G + j B \,$

$G = Re(Y) \,$

where:

Y is the admittance,

j

is the imaginary unit,

B is the susceptance.

The conductance an object of cross-sectional area A and length $\ell$ can be determined from the material's conductivity σ by the formula,

$G=\frac{\sigma \, A}{\ell}$

From Kirchhoff's circuit laws we can deduce the rules for combining conductances. For two conductances $G 1$ and $G 2$ in parallel the voltage across them is the same and from Kirchoff's Current Law the total current is

$I_{Eq} = I_1 + I_2\ \,$ .

Substituting Ohm's law for conductances gives

$G_{Eq} V = G_1 V + G_2 V\ \,$

and the equivalent conductance will be,

$G_{Eq} = G_1 + G_2\ \,$ .

For two conductances $G 1$ and $G 2$ 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,

$V_{Eq} = V_1 + V_2\ \,$ .