Resistivity of a wire depends on

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material

Explanation: Resistivity ($\rho$) is an intrinsic property of a material, representing its innate ability to oppose the flow of electric current. It is independent of the physical dimensions (length or cross-sectional area) of the wire, depending solely on the material composition and its atomic structure.

Working Principle: The resistance of a conductor is determined by the formula $R = \rho \frac{L}{A}$, where $R$ is resistance, $L$ is length, and $A$ is cross-sectional area. Since $\rho = R \cdot \frac{A}{L}$, the units of $A$ and $L$ cancel out, demonstrating that $\rho$ remains constant for a specific material at a given temperature, regardless of the wire's geometry.

Key Formulas: $R = \rho \frac{L}{A}$ — Resistance formula relating geometry to material property; $\rho = R \frac{A}{L}$ — Defining resistivity as an intrinsic material constant

Key Points: Resistivity ($\rho$) depends only on the material and temperature.; Resistance ($R$) depends on resistivity, length, and cross-sectional area.; The SI unit of resistivity is Ohm-meter ($\Omega \cdot m$).; Metals have low resistivity, while insulators have very high resistivity.

Advantages: Used to identify materials based on electrical properties.; Essential for calculating power losses in transmission lines.

Applications: Selection of materials for wiring (Copper vs Aluminum).; Design of heating elements using high-resistivity materials like Nichrome.

Additional Info: Temperature significantly affects resistivity; for most metals, resistivity increases linearly with temperature.. Option A (length) and Option C (cross-section area) affect total resistance, not the material-specific resistivity.

Answer: B is correct — Resistivity is an intensive physical property of the material and does not depend on the physical dimensions of the conductor.

Exam Tip: Always distinguish between 'Resistance' (an extrinsic property that changes with shape) and 'Resistivity' (an intrinsic property of the material).

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