Question

We are given three copper wires of different lengths and different areas of cross-section. Which one of the following would have highest resistivity ?
1. Copper wire of 50 cm length and 1 mm diameter
2. Copper wire of 25 cm length and 0-5 mm diameter
3. Copper wire of 10 cm length and 2-0 mm diameter
4. All the wires would have same resistivity

Answer 1

Correct Answer - Option 4 : All the wires would have same resistivity

The correct answer is All the wires would have the same resistivity.

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 = ρL/A

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

EXPLANATION:

• The resistivity of the material will not change (remain the same, ρ) as it is independent of the length or cross-section of the wire. 
• So, All the wires would have the same resistivity.

EXTRA POINTS:

• The resistivity of copper is generally given as  1.72 x 10-8 Ωm.

Difference between resistivity and resistance:

Sl.No.	RESISTANCE	RESISTIVITY
1	The property of any conductor that opposes the flow of electric current through it and depends on the shape and size (length and area) of the materials, temperature, and nature of the materials is called resistance.	The property of a conductor that opposes the flow of electric current through them and is independent of the shape and size (length and area) of the materials but depends on the nature and temperature of the materials is called resistivity.
2	It is denoted by R.	It is denoted by ρ.
3	The SI unit is the ohm(Ω).	The SI unit is ohm-meter (Ω-m).
4	It is not a constant term for a given material. It can be changed by changing the length or cross-sectional area of that material.	It is a constant term for a given material. It doesn't change by changing the length and cross-sectional area of the material.