Question

The resistance of a wire is R. When the length of the wire is increased by 20% and the cross-sectional area is decreased by 5%, the resistivity of the wire will:
1. Remain constant
2. Increase by 26.32%
3. Decrease by 26.32%
4. None of the above

Answer 1

Correct Answer - Option 1 : Remain constant

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).
• 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:

\(\Rightarrow R=\frac{\rho l}{A}\)

Where R = resistance , ρ = resistivity, l = length of the wire and A = cross-sectional area

EXPLANATION:

• Resistivity is a material property so it does not depend on the length, area, size, and shape of the wire.
• So when the length of the wire is increased and the area is decreased, its specific resistance will not change.
• So the resistivity of the wire will remain constant. Hence, option 1 is correct.