Question

Resistivity of a conductor depends on

• A. its material and the dimensions of the conductor
• B. its material and temperature of the conductor
• C. the dimensions of the conductor only
• D. the temperature of the conductor only

Hint:

Distinguish clearly between Resistance (\(R\), in Ohms, \(\Omega\)) and Resistivity (\(\rho\), in Ohm-meters, \(\Omega\cdot\text{m}\)). Resistance is a property of an object (like a specific wire), while Resistivity is a property of a material (like copper in general).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question concerns the determinants of a conductor's electrical resistivity (\(\rho\)). It's crucial to differentiate between resistance (\(R\)) and resistivity (\(\rho\)).

Step 2: Detailed Explanation:
Resistivity (\(\rho\)):
Resistivity is an inherent material property quantifying its opposition to electric current flow.
- Material: Variations in atomic structure and free charge carrier density per unit volume lead to differing resistivities. Copper, for instance, exhibits lower resistivity than iron due to a higher free electron concentration. Thus, resistivity is material-dependent.
- Temperature: Elevated temperatures increase atomic/ionic vibrations, leading to more frequent electron-ion collisions. This impedes electron movement, thereby increasing resistivity. Hence, resistivity is temperature-dependent.
Resistance (\(R\)):
Resistance is an extrinsic property of an object, influenced by both material resistivity and physical dimensions (length \(L\) and cross-sectional area \(A\)). The governing equation is:\[ R = \rho \frac{L}{A} \]This formula indicates that resistance is dimension-dependent, whereas resistivity (\(\rho\)) is not.
Evaluating the options:
(A) Incorrect. Resistivity is independent of dimensions.
(B) Correct. Resistivity is influenced by material type and temperature.
(C) Incorrect. Resistivity is independent of dimensions.
(D) Incorrect. While temperature is a factor, the fundamental determinant is the material itself.

Step 3: Final Answer:
A conductor's resistivity is an intrinsic characteristic dependent on its material composition and temperature.