Question

A wire of resistivity $\rho$ is stretched to double its length what will be its new resistivity?

Answer 1

Hint: Resistivity only depends on the material of the conductor. It is defined as the ability of a conductor to oppose the current to flow through it. In our case, considering the wire to be Ohmic conductor means it follows Ohm’s law for the purpose of this problem.

Complete step by step solution:
Resistance depends on resistivity of the material, length and area of the conductor. On the other hand, resistivity only depends on the material properties of the conductor. Higher the resistivity, lesser will be its conducting nature.

Resistivity does not depend on the length of the conductor. Hence, doubling the length will not change its resistivity.
In short, $\operatorname{R} = \rho \dfrac{l}{A}$

Where,
R is resistance of material
$\rho$ is resistivity of material
$l$ is length of material
$A$ is cross section area of material

Additional Information:
- Resistivity of material is intrinsic property but it’s not constant for all material in all situations for example. In case of transistor effective resistance in transistor depends on voltage applied. With rise in temperature, resistivity changes and so the resistance of material changes.
- Resistivity has a dual called conductivity. Unlike resistivity it is defined as the ability of the conductor to let the current through it. Analogous to resistivity there is dual of resistance as well. We call it conductance of the material.

Note: In questions like these, remember the difference between resistance and resistivity. Resistivity is intrinsic property whereas resistance depends on several other factors like configuration of circuit, length, and cross section area as well.