UPSC NDA II 2023 General Ability Solved Paper

Concept:Resistance and resistivity are related but distinct: resistance depends on the wire's geometry and material, while resistivity is an intrinsic material property.Explanation:Statement 1 is incorrect because resistivity does not depend on the cross-sectional area of the wire. Resistance $R$ is given by $R = \rho \frac{L}{A}$, where $\rho$ is resistivity, $L$ is length, and $A$ is area. So resistance depends inversely on area, but resistivity is independent of area.Statement 2 is correct. Both resistance and resistivity change with temperature. For most metals, resistance increases as temperature rises due to increased atomic vibrations; resistivity also follows the same trend (positive temperature coefficient).Statement 3 is correct. From the formula $R = \rho \frac{L}{A}$, for a fixed length and area, resistance is directly proportional to resistivity.Statement 4 is incorrect. Resistivity $\rho$ is a material constant; it does not depend on the length of the wire. Only resistance depends on length.Answer:Option C — statements 2 and 3 are correct.