In the electrical lab, if the radius and length of a wire are made 4 times, its resistivity becomes

Resistivity vs Resistance

Resistivity (ρ) is a material property. It depends on the material (and temperature) only — not on size or shape.

When the radius and the length of the wire are both increased 4 times, the resistivity does not change. It remains the same because resistivity is intrinsic to the material.

Resistance R depends on resistivity and geometry via:

R = ρ · (L / A)

Here L = length and A = cross-sectional area. If radius r is changed, area A = πr2 changes too.

Step calculation:

Length L → 4L

Radius r → 4r, so area A = πr² → π(4r)² = 16·πr² = 16A

New resistance R' = ρ · (4L) / (16A) = (4/16) · ρ(L/A) = 1/4 · R

So: Resistance becomes one-fourth of the original, but resistivity ρ stays the same.

The resistivity remains unchanged; the resistance becomes R/4 when both radius and length are increased by 4×.