Question

A wire of length 1 m and cross section 10 cm², has a resistance of 100 Ω. Its resistivity is-
1. 10 Ω-m
2. 1 Ω-m
3. 0.1 Ω-m
4. 0.01 Ω-m

Answer 1

Correct Answer - Option 3 : 0.1 Ω-m

Concept:

Resistivity (ρ): The property of a conductor that opposes the flow of electric current through them and is independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.

• The unit for resistivity is the ohm-meter (Ω-m).
• The resistivity of a material depends on its nature and the temperature of the conductor.
• The resistivity of a material doesn't depend on its shape and size (length and area).

Resistance: The property of any conductor that opposes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.

• It is denoted by R and the SI unit is the ohm (Ω).

The resistance is given by:

\(R = ρ \frac {L}{A}\)

where ρ is resistivity, L is the length and A is the area of the cross-section. 

Calculation:

Given:

L = 1 m, A = 10 cm² = 10 × 10^-4 m², R = 100 Ω 

Using \(R = ρ \frac {L}{A}\)

\(100 = ρ \frac {1}{10\times 10^{-4}}\)

ρ = 0.1 Ω-m