Question

The resistivity of a conductor depends upon :

• A. Area of cross-section of conductor
• B. Length of conductor
• C. 1 and 2 both
• D. None of the above

Hint:

Resistivity is an inherent property of the material itself and its temperature, indicating how well it resists current flow. It is independent of the conductor's length or cross-sectional area. These dimensions affect the overall resistance, but not the material's fundamental resistivity.

Answer 1

The Correct Option is D

Step 1: Define resistivity.
Resistivity ($\rho$) is an intrinsic property of a material that quantifies how strongly it resists electric current. It is a fundamental characteristic of the material itself, unlike resistance, which depends on the dimensions of the conductor. Step 2: Recall the formula for resistance and its relation to resistivity.
The resistance ($R$) of a conductor is given by the formula: $R = \rho \frac{L}{A}$ where:
$R$ is the resistance
$\rho$ (rho) is the resistivity of the material
$L$ is the length of the conductor
$A$ is the area of the cross-section of the conductor Step 3: Analyze the dependence of resistivity. Resistivity ($\rho$) depends only on:
Nature of the material: Different materials (e.g., copper, aluminum, silver) have different resistivities.
Temperature: The resistivity of most materials changes with temperature. For metals, resistivity generally increases with temperature. Resistivity does not depend on the geometric dimensions of the conductor, such as its length ($L$) or area of cross-section ($A$). These dimensions affect the resistance of the conductor, but not its intrinsic resistivity. Step 4: Evaluate the given options.
(1) Area of cross-section of conductor: Resistivity does not depend on the area of cross-section.
(2) Length of conductor: Resistivity does not depend on the length of the conductor.
(3) 1 and 2 both: Since neither (1) nor (2) affects resistivity, this option is incorrect.
(4) None of the above: This aligns with the understanding that resistivity is an inherent property of the material and its temperature, not its dimensions. $$(4) None of the above$$