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

Explanation:

The resistance of a conductor depends on three factors: \[ R = \rho \frac{L}{A} \] where
R = resistance
ρ (rho) = resistivity of the material
L = length of the conductor
A = area of cross-section

Why Resistance Changes:
From the formula: – Resistance is directly proportional to length (R ∝ L).
– Resistance is inversely proportional to area of cross-section (R ∝ 1/A). Therefore: – If the length increases, resistance increases.
– If the area increases, resistance decreases. So, when length or area changes, the value of resistance changes.

Why Resistivity Does Not Change:
Resistivity (ρ) is a property of the material itself. It depends only on: – Nature of the material
– Temperature It does NOT depend on: – Length of the conductor
– Area of cross-section Therefore, even if the conductor is stretched (changing length and area), the material remains the same. Hence, resistivity remains unchanged (provided temperature is constant).

Conclusion:
Resistance changes because it depends on length and area of the conductor. Resistivity does not change because it is an intrinsic property of the material and depends only on the nature of the material and temperature.