Question

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

Answer 1

Hint: Resistivity is the property of material. Resistance and resistivity are completely different phenomena. Resistance depends on area, length, and nature of material. While resistivity is just proportionality constant in resistance.

Complete step by step solution:
Resistivity is also known as specific resistance. At a given particular temperature, the electric resistance of conductor is depend on
Length of the conductor
Area of cross section of the conductor
Nature of martial of the conductor
It is observed that resistance (R) of conductor is directly proportional to its length (l), and inversely proportional; to its area of cross section (A).
$R\alpha l$
$\begin{align}
  & R\alpha \dfrac{1}{A} \\
 & R\alpha \dfrac{l}{A} \\
 & R=\rho \dfrac{l}{A} \\
 & \\
\end{align}$
Where, $\rho $ is the proportionality constant and it is also called specific resistance or resistivity of conductor. So resistivity is denoted by $\rho $. SI unit of resistivity is ohm meter.
It states that the resistivity of material is the resistance of wire of unit length and unit area of cross section.
Thus, the resistance of different materials having the same dimensions should be different. Hence resistivity is a characteristic of the material.
Reciprocal of resistivity is conductivity. Denoted by $\sigma $. SI unit of conductivity is Siemens/metre.
Resistivity also depends on temperature. We can define material on the basis of resistivity.

Conductor: those materials whose resistivity is very less are called conductors.
Insulator: those materials whose resistivity is very high are called insulators.
Semiconductor: those materials whose resistivity lies between that of conductor and insulator are called semiconductor.

Thus resistivity is dependent on conductor material of conductor.

Note: Do not get confused between specific resistance and resistivity. Both the terms have the same meaning. As we can see in the formula no term of area of cross section and length is involved. Therefore resistivity does not depend on length or area of the section of material or conductor. Reciprocal of resistivity is conductivity. Unit of resistivity is ohm meter.