# Conductance and Conductivity

The conductance is a property of a substance due to which it facilitates the flow of current through it when a voltage is applied across the substance. It is the opposite property of resistance. Because the resistance is the property of a substance by which the substance opposes the flow of current through it. The conductance of a substance is represented by reciprocal of its resistance. If R is the resistance of a substance then conductance of the substance would be 1/R.

## Unit of Conductance

The unit of conductance is named as mho. One mho is the reciprocal of one ohm where ohm is the unit of resistance. From Ohm’s Law we know that ohm is voltage/current. So mho is current/voltage.

## Laws of Conductance

If the length of a conductor is increased the conductance of the conductor decreases. The conductance of a conductor is inversely proportional to the length of the conductor.

If the cross-section of the conductor gets increased, the conductance of the conductor increases and this relationship is also linear. Hence the conductance of the conductor is directly proportional to the cross-section of the conductor.

The conductance of a conductor also depends on the material by which the conductor is made of. Because of this reason, conductors of the same dimensions, made of different materials have different conductance.

The conductance also depends on the temperature of the conductor.

This is the reason, during expressing the conductance of a conductor, the temperature of the conductor must be mentioned.

## Conductivity

As we have already told that conductance of a conductor is directly proportional to the cross-section (A) of the conductor and it is inversely proportional to the length (L) of the conductor. If the conductance is denoted as G, at a constant temperature, we can write

Here, the constant of proportionality is σ. This is called conductivity. If we put the unit of length and unit cross-section in the equation, we get,

From here we can say, conductivity of a conductor is defined as the conductance between two opposite faces of a cube of unit volume of the material by which the conductor is made of.

## Unit of Conductivity

From the above expression of conductance, we can write the expression of conductivity as below,

If we put the unit of length, unit of area and unit of conductance in the above equation, we get

Hence we may write unit of conductivity as mho/meter.

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