Resistivity of a wire depends on

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material

Explanation: Resistivity (also known as specific electrical resistance) is an intrinsic property of a material that quantifies how strongly a material opposes the flow of electric current. Unlike resistance, which depends on the physical dimensions of a conductor, resistivity is independent of length and cross-sectional area, depending solely on the material composition and temperature.

Working Principle: At the microscopic level, resistivity is defined by the relation $R = \rho \frac{l}{A}$. Here, $\rho$ (resistivity) is determined by the electron density, the mean free time between collisions of charge carriers (electrons) with the crystal lattice, and the charge of the carriers. Because these factors are determined by the atomic structure of the material, changing the dimensions of the wire does not alter the material's identity or its fundamental scattering characteristics.

Key Formulas: $R = \rho \frac{l}{A}$ — Resistance formula where $\rho$ is resistivity; $\rho = \frac{1}{\sigma}$ — Relationship between resistivity and conductivity ($\sigma$)

Key Points: Resistivity is an intrinsic property; it does not change with geometry.; The SI unit for resistivity is Ohm-meter ($\Omega \cdot m$).; Resistivity is temperature-dependent for metals, generally increasing with temperature.; Materials with low resistivity are classified as conductors, while those with high resistivity are insulators.

Advantages: Allows for standardized material comparison independent of geometry.; Essential for calculating the design parameters of electrical components.

Applications: Selection of wire materials for power transmission.; Designing heating elements using high-resistivity alloys like Nichrome.; Characterization of semiconductor doping levels.

Additional Info: For most metals, resistivity $\rho_T = \rho_0 [1 + \alpha(T - T_0)]$, where $\alpha$ is the temperature coefficient of resistance.. Option A and C are incorrect because length ($l$) and cross-sectional area ($A$) affect total resistance, not the material property resistivity.. Option D is incorrect because resistivity is fundamentally linked to the material's atomic structure.

Answer: B is correct — Resistivity is a material-specific property that does not change based on the physical dimensions of the conductor.

Exam Tip: Always distinguish between Resistance ($R$, measured in $\Omega$) and Resistivity ($\rho$, measured in $\Omega\cdot m$); resistance is a circuit parameter, whereas resistivity is a material constant.

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