Question

A cylindrical rod has resistivity $\mathbf{\rho }$. If we triple its length and diameter, what is its resistivity in terms ofrole="math" localid="1655715631515" $\mathbf{\rho }$ .

Short answer

Resistivity remains constant.

Step-by-step solution

Definition of resistivity

The term resistivity is opposition offered by the particular electric conductor to the flow the charges. It depends on the type of material used, while the resistance will depend on the length and the area of the conductor.

The expression for the resistance is,

$\mathbf{R}\mathbf{=}\frac{\mathbf{\rho L}}{\mathbf{A}}$

Here, $\mathbf{\rho }$is the resistivity, Ris the resistance, L is the length and A is the area of the cross section.

Calculation of resistivity

Resistivity does not depend upon the length and cross section area it’s depend upon the temperature and the conductor material so resistivity no change if length and cross section area are changed.

Hence, resistivity remains constant.