Which of the following does resistivity NOT depend on?

CONCEPT:

Resistivity (ρ):

• The property of a conductor that opposes the flow of electric current through them and 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).
• Materials that conduct electrical current easily are called conductors and have a low resistivity.
• Materials that do not conduct electricity easily are called insulators and these materials have a high resistivity.
• Resistivity is inversely proportional to the number of free electrons per unit volume of the conductor and to the average relaxation time of the free electrons in the conductor.

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 = ρL/A

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

EXPLANATION:

From the above discussion, we can say that

• The resistivity depends on the nature of the material.
• The resistivity depends on the average relaxation time and the number of free electrons per unit volume. 
• The resistivity doesn't depend on the dimensions (length and area) of the material. So option 3 is correct.

EXTRA POINTS:

Difference between resistivity and resistance: