Question

The resistivity of a wire varies with its
$A)$Length
$B)$Cross-section
$C)$Mass
$D)$Material

Answer 1

We must know that resistivity is an intrinsic property and it is always a constant for a particular material. Resistivity of a conductor and resistance of a conductor are completely different. Resistance depends upon area, length and nature of material but resistivity is a proportionality constant in the formula for resistance.

Complete answer:
Before discussing the question, we shall know what resistivity is. Resistivity is also called specific resistivity. For a particular temperature, the resistance of a conductor depends on its length, area of cross section and nature of material from it made.
We can see the resistance is directly proportional to the length or the conductor ($l$) and inversely proportional to area of cross section ($A$).

i.e. $R\propto \dfrac{l}{A}$
$R=\rho \dfrac{l}{A}$
Where, $\rho$ is the proportionality constant known as resistivity of a conductor. The S.I. unit of resistivity is $\Omega m$. We can obtain the expression for resistivity as,
$\rho =\dfrac{RA}{l}$

From this, we can define resistivity as the resistance of a wire of a particular material of unit length and unit area of cross section. Resistivity only depends on the material. So if different materials have the same dimensions, their resistivity will not be the same.
The only factor that resistivity of a material depends upon is temperature. So, the correct answer is “Option D”.

Note:
We mustn’t get confused between the words resistivity and specific resistance. They are the same. If we take the reciprocal of resistivity we will get conductivity. Always keep in mind that resistivity of a conductor from a specific material is a constant and it will not vary with change in length or area of cross section.