Question

Write the definition of specific conductivity and its unit.

Hint:

It is the reciprocal of resistivity; think of the unit of \(1/\rho\).

Answer 1

Step 1: Recall specific resistance (resistivity).
The resistance of a wire is \(R=\rho\dfrac{l}{A}\), where \(l\) is length, \(A\) is cross-sectional area and \(\rho\) is the specific resistance (resistivity) of the material. Rearranging, \(\rho=\dfrac{RA}{l}\), so \(\rho\) is the resistance of a conductor of unit length and unit area of cross-section.

Step 2: Define specific conductivity.
Specific conductivity (also called conductivity), denoted \(\sigma\), is defined as the reciprocal of the specific resistance (resistivity) of the material:
\[ \sigma=\frac{1}{\rho} \]
Physically, it measures how easily a material allows electric current to pass through it; a good conductor has a large \(\sigma\).

Step 3: Derive the unit.
Since \(\rho\) has the unit ohm-metre \((\Omega\,\text{m})\), its reciprocal has the unit
\[ \sigma=\frac{1}{\Omega\,\text{m}}=\Omega^{-1}\text{m}^{-1} \]
This is written as siemens per metre \((\text{S m}^{-1})\) or mho per metre \((\text{mho m}^{-1})\).

Result:
\[\boxed{\sigma=\dfrac{1}{\rho}\ ;\quad \text{unit}=\text{S m}^{-1}\ (\Omega^{-1}\text{m}^{-1})}\]