Question

Write the definitions of electrical conductivity and specific conductivity.

Hint:

Conductance is the reciprocal of resistance (\( 1/R \), unit siemens); specific conductivity is the reciprocal of resistivity (\( 1/\rho \), unit S/m).

Answer 1

Step 1 (Electrical conductance / conductivity of a conductor): The electrical conductance of a conductor is the reciprocal of its resistance. It measures how easily current flows through that particular conductor.
\[ G = \frac{1}{R} \]
where \( R \) is the resistance. Its SI unit is \( \text{ohm}^{-1} \) or siemens (S), also called mho.
Step 2 (Specific conductivity / conductivity of the material): The specific conductivity (simply called conductivity) is the reciprocal of the specific resistance (resistivity) of the material. It depends only on the material and not on its shape or size.
\[ \sigma = \frac{1}{\rho} \]
where \( \rho \) is the resistivity. Its SI unit is \( \text{ohm}^{-1}\,\text{m}^{-1} \) (siemens per metre, S/m).
Step 3 (Relation): For a wire of length \( l \) and area \( A \), \( R = \rho\dfrac{l}{A} \), so the two quantities are linked by
\[ G = \sigma\,\frac{A}{l} \]
\[\boxed{G=\tfrac{1}{R}\ (\text{S}),\qquad \sigma=\tfrac{1}{\rho}\ (\text{S/m})}\]