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 asks about the factors that determine the electrical resistivity (\(\rho\)) of a conducting material. It is important to distinguish between resistance (\(R\)) and resistivity (\(\rho\)).

Step 2: Detailed Explanation:
Resistivity (\(\rho\)):
Resistivity is an intrinsic property of a material. It quantifies how strongly a given material opposes the flow of electric current.
- Material: Different materials have different atomic structures and numbers of free charge carriers per unit volume. For example, copper has a lower resistivity than iron because it has more free electrons available for conduction. Therefore, resistivity depends on the material.
- Temperature: When the temperature of a conductor increases, the atoms/ions in the material vibrate with greater amplitude. This increases the frequency of collisions between the free electrons and the ions, which impedes the flow of electrons and thus increases the resistivity. Therefore, resistivity depends on temperature.
Resistance (\(R\)):
Resistance is an extrinsic property of an object. It depends not only on the material's resistivity but also on the object's physical dimensions (length \(L\) and cross-sectional area \(A\)). The relationship is given by: \[ R = \rho \frac{L}{A} \] From this formula, we can see that resistance depends on dimensions, but resistivity (\(\rho\)) does not.
Evaluating the options:
(A) Incorrect. Resistivity does not depend on the dimensions.
(B) Correct. Resistivity depends on the nature of the material and its temperature.
(C) Incorrect. Resistivity does not depend on dimensions.
(D) Incorrect. While it depends on temperature, it also fundamentally depends on the material itself.

Step 3: Final Answer:
The resistivity of a conductor is an intrinsic property that depends on the nature of the material and its temperature.