Question

A wire having length l and radius r is redrawn without change in volume so that its radius is half. Compare the new resistance and original resistance.

Answer 1

$\bold{\boxed{Hoi!}}$

Let the original
Length of wire = L
radius = R
resistivity= k

therefore, Resistance = kL/πR²

now, if radius is half, i.e. r = R/2

=> new resistance = kL/π(R/2)² = k4L/πR²

comparing both we get,

(4kL/πR²)÷(kL/πR²)= 4/1

therefore ratio of new resistance to old one = 4:1

$\bold{\underline{Thanks!}}$☺️