Question

The relationship between conductivity σ and resistivity ρ of a material is
1. σ² = ρ^-1
2. σ = ρ-1
3. σ -1 = ρ-1
4. √σ = ρ

Answer 1

Correct Answer - Option 2 : σ = ρ-1

The correct answer is option 2) i.e. σ = ρ-1

CONCEPT:​

• The resistivity of a material is defined as the resistance offered by a material of unit cross-sectional area and unit length. 

It is represented as:

\(\Rightarrow ρ = \frac{RA}{l}\)

Where R is the resistance, l is the length of the material and A is the area of cross-section.

• Resistivity is an intrinsic property i.e. it is the same for a given type of material.
• Conductivity (σ) is the reciprocal of electrical resistivity.

​EXPLANATION:

Since conductivity is the reciprocal of resistivity, \(σ = \frac{1}{\rho} = \rho^{-1}\)