Question

Due to change in length and area of cross-section of a conductor, resistance of conductor changes while resistivity does not change. Why ?

Hint:

Think of resistivity like "density" (constant for a substance) and resistance like "mass" (changes with size).

Answer 1

Step 1: Understanding the Concept:
Resistance (\( R \)) depends on the dimensions of the conductor, while resistivity (\( \rho \)) is a fundamental characteristic of the material itself.
Step 2: Detailed Explanation:
1. Resistance (\( R \)): Defined as \( R = \rho \frac{l}{A} \). It is directly proportional to length and inversely proportional to area. Thus, changing \( l \) or \( A \) physically alters the opposition to current.
2. Resistivity (\( \rho \)): It is the resistance of a unit cube of the material. It only depends on the nature of the substance (electronic structure) and the temperature.
Even if you stretch or cut the wire, the material remains the same, so its intrinsic resistivity remains constant.
Step 3: Final Answer:
Resistivity is independent of the shape and size of the conductor; it only depends on the nature of material and temperature.