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: Specific Resistance also called Resistivity of a material is the resistance offered by the wire of the material having unit length and unit cross-section. In order to find the factors affecting resistivity we can use the formula $\rho=\dfrac{m}{ne^2\tau}$, where m is the molecular mass of the material, n is the number of electrons per unit volume in the conductor, e is the charge of electrons and $\tau$ is the average relaxation time.

Complete step-by-step answer:
We know that the resistivity or specific resistance is generally denoted by $\rho$ and is given by the formula $\rho=\dfrac{m}{ne^2\tau}$, where m is the molecular mass of the material, n is the number of electrons per unit volume in the conductor, e is the charge of electrons and $\tau$ is the average relaxation time.
From the formula, we can understand that the resistivity of the material of a conductor depends on the following factors:
1. It is inversely proportional to n, that is the number of free electrons per unit volume of the conductor which in turn depends upon the nature of material.
2. It is also inversely proportional to the average relaxation time $(\tau)$ of the free electrons in the conducting material which in turn depends upon the temperature.
So, from the above to inferences, we can say that the specific resistance depends on the material and temperature.
Hence option d is the right answer.

Additional information:
Relaxation time is the gap in the time difference between the successive collisions of electrons in a conductor. It depends on the drift velocity and is heavily affected by temperature. As the temperature of a conducting material increases, the increase in thermal energy increases the drift velocity and thus the collision starts to occur more frequently and ultimately decreases the average relaxation time.

Note: It can happen that we get confused with the resistance formula $R=\rho\dfrac{L}{A}$, from which we can derive $\rho=\dfrac{RA}{L}$. But we should keep in mind that here $\rho$ is being used as a constant.