Question

Resistivity does not change if
A. The material is changed
B. The temperature is changed
C. The shape of the resistor is changed
D. Both material and temperature are changed.

Answer 1

In order to deal with this question first we will derive the expression of resistivity then we will proceed further by finding the factors upon which the resistivity depends on the basis of the formula of resistivity.
Formula used:
$R = \dfrac{{\rho l}}{A}$, where $R$= Resistance of the material, ${\rho}$= Resistivity of the given material, $l$= Length of the material or wire, ${A}$= Cross-sectional Area of the material.

Complete answer:
We assume that the resistance for a substance is proportional to the material's resistivity, proportional to the length and inversely proportional to the cross-sectional area of the material.
$R = \dfrac{{\rho l}}{A}$
Where $\rho$ is the resistivity of the material or wire
Re- arranging the terms we will get,
$\rho = \dfrac{{AR}}{l}$
Hence, resistivity will depend on the area, length of the material.
As there is no shape factor involved in the formula derived, which shows Resistivity of the material does not depend on the shape of the resistor. Its SI unit is ohm-meter$(\Omega m)$.
“The shape of the resistor is changed”.

So, the correct answer is “Option C”.

Note:
Resistivity is a measure of the resistance to electrical conduction of a specific substance of a given thickness. Materials that easily perform electrical current are called conductors and have low resistivity. Some that do not conduct electricity quickly are considered insulators and are extremely resistant to these materials.