#### What is Conductance?

Conductance is the measure of how easily electricity flows along a certain path through an electrical element, and since electricity is so often explained in terms of opposites, conductance is considered the opposite of resistance. The higher the electrical conductivity within a material, the greater the current density for a given applied potential difference.

#### Unit of Conductance

The SI (International System) derived unit of conductance is known as the Siemens (Sm), named after the German inventor and industrialist Ernst Werner von Siemens. Since conductance is the opposite of resistance, it is usually expressed as the reciprocal of resistance.
In terms of resistance and conductance, the reciprocal relationship between the two can be expressed through the following equation:

$$ G=1/R \,(Sm) \tag{1}$$

where R equals resistance and G equals conduction.

#### Resistivity and conductivity

we have read that conductance is the opposite of resistance as shown in the above equation. but resistance in terms of length and area can be formulated as:

$$ R = \rho {L \over A}\,(ohm) \tag{2} $$

where rho ($ \rho $) is the resistivity of resistance in ohm-metre, $ Ω -m$. $L$ is the length and $A$ is the cross sectional area of conductor.

Now we can put resistance value in eq.1.

$$ G= {1 \over R}\,(Sm) $$

$$ G= {1 \over (\rho {L \over A})} = {1 \over \rho} {A \over L}\,(Sm) $$

$$ G= \sigma {A \over L}\,(Sm) \tag{3}$$

where sigma ($ \sigma $) is the conductivity of conductor in siemens per metre, $Sm/m$. $L$ is the length and $A$ is the cross sectional area of conductor.

The factors that affect the magnitude of resistance are exactly the same for conductance, but they affect conductance in the opposite manner. Therefore, conductance is directly proportional to area, and inversely proportional to the length of the material.

Resistivity and conductivity are interrelated. Conductivity is the inverse of resistivity. Accordingly it is easy to express one in terms of the other.

$$ \text{conductivity} \, \text{(sigma)}\, (\sigma)= {1 \over \rho} \,(Sm/m) \tag{4}$$

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