The correct option is A is true but R is false
Explanation
Resistivity ($\rho$) is an intrinsic physical property of a material that measures its ability to oppose the flow of electric current. Unlike resistance, which varies with the dimensions (length and cross-sectional area) of a specific object, resistivity is determined solely by the nature of the material and external physical conditions, primarily temperature.
Statement-wise Analysis
- Assertion (A): Correct. Resistivity is considered a characteristic property because it identifies the material itself. For instance, copper has a specific resistivity distinct from that of iron, regardless of the shape or size of the conductor. It depends on the number density of free electrons and the relaxation time specific to that material's atomic structure.
- Reason (R): Incorrect. The resistivity of a metal is not independent of temperature; rather, it is strongly dependent on it. As the temperature of a metal increases, the thermal agitation of the lattice ions increases, leading to more frequent collisions with free electrons. This reduces the average relaxation time between collisions. Since resistivity is inversely proportional to relaxation time, the resistivity of metals increases with a rise in temperature.
Key Takeaway: While resistivity is independent of a conductor's physical dimensions, it is strictly dependent on the material's nature and its temperature. For metals, resistivity increases as temperature rises.