Question

Specific resistance of a wire depends on the
A. Length of the wire
B. Area of cross section of the wire
C. Resistance of the wire
D. Material of the wire

Answer 1

Hint: First of all, we should keep in mind that specific resistance is defined as the resistance of a wire of unit length and unit cross sectional area. Hence, it has nothing to do with the length and cross sectional area of the wire, since they are made equal to unity in the definition. We just need to show that specific resistance doesn't depend on resistance as well.

Complete step-by-step answer:
Origin of the idea of specific resistance $\rho$-
The resistance of conducting wire was known from long ago. It was considered to be a problem since greater resistance always means more power dissipation. And people have always been trying to find a way to reduce the resistance of a wire. A lot of experiments were performed in order to get low resistance wire for better efficiency. At this time it was found that resistance not only depends on the size and dimensions of a wire but on something more.
The resistance (R) of a wire was experimentally found to be proportional to its length (l). Also it was inversely proportional to its cross sectional area (A).
Hence, R is proportional to $\dfrac{l}{A}$
Or, we may say, $$ R=\dfrac{\rho l}{A}$$
Where $\rho$ is introduced as a constant of proportionality. Hence $\rho$ doesn’t depend on resistance as well. So, it depends on the material of the wire.
So, option D is the correct answer.

Additional information: The reciprocal of specific resistance is called conductance of the wire which also is the property of the material of the wire.

Note: From the free electron theory of metals, it can be shown that,
$$\rho=\dfrac{\sqrt{12m_ekT}}{ne^2\lambda}$$
Where n is the number density of electrons and $\lambda$ is the mean free path of the free electrons, both of which depend on the material of the wire. (Other symbols have usual meanings)