Resistivity of a conductor depends on

The correct option is: its material and temperature of the conductor.

To understand why this option is correct, let us analyze the nature of resistivity and distinguish it from electrical resistance.

1. Definition of Resistivity ($\rho$):
Resistivity (represented by the Greek letter rho, $\rho$) is an intrinsic property of a material that measures how strongly it opposes the flow of electric current. Unlike resistance ($R$), resistivity is independent of the size or shape (length and cross-sectional area) of the conductor.

2. Dependence on the Material:
Different materials have different densities of free electrons and unique atomic structures. In conductors, the ease with which electrons can move under the influence of an electric field depends directly on the nature of the material. For example, copper and silver have very low resistivities, whereas materials like nichrome or rubber have much higher resistivities.

3. Dependence on Temperature:
As the temperature of a metallic conductor increases, the thermal energy causes the atoms or ions in the lattice to vibrate more vigorously. This increase in vibration increases the frequency of collisions between the flowing free electrons and the lattice ions, obstructing the smooth flow of charge. Therefore, the resistivity of a conductor increases with an increase in temperature. The relationship is mathematically expressed as:
$\rho ={\rho }_0[1+\alpha (T-T_0\left)\right]$
where ${\rho }_0$ is the resistivity at a reference temperature $T_0$, and $\alpha$ is the temperature coefficient of resistivity.

4. Independence from Dimensions:
Although the overall resistance ($R$) of a conductor depends on its physical dimensions according to the formula:
$R=\rho \frac{l}{A}$
where $l$ is length and $A$ is the cross-sectional area, the resistivity ($\rho$) itself remains constant for a given material at a specific temperature, regardless of how long, short, thick, or thin the conductor is.

Thus, the resistivity of a conductor depends solely on the nature of its material and its temperature.