A cylindrical rod has a resistivity of P. If we triple its length and diameter, what is its resistivity in terms of P?

The resistivity (ρ) of a material is a fundamental property that depends only on the nature of the material and temperature, not on its dimensions.

Given:

Initial resistivity = P

Length is tripled

Diameter is tripled

Key Concept:

Resistivity is independent of:

Length

Area (or diameter)

It only depends on:

Material type

तापमान (temperature)

So, even after changing dimensions:

New resistivity = P

Important Clarification:

Although resistivity remains unchanged, the resistance (R) will change because:

R = ρ × L / A

Length ↑ → Resistance increases

Area ↑ (since diameter ↑) → Resistance decreases

But resistivity stays constant.

Key Takeaway:

Even after tripling both length and diameter, the resistivity remains P, because it is a material property, not a dimensional property.