Question

two wires a and b both with equal resistance are made of same material. if radius of wire b is doubled than that of a determine the ratio of their length

Answer 1

Let radius of a and b be x and 2x respectively.

Given,
There densities are same as there material are same.
Resistance of a = Resistance of b = R(say)

Now,

R = ρ 1/A₁

Or A₁ = ρ/R

Or x² = ρ/R

Or x = √(ρ/R)

Also,

R = ρ 1/A₂

Or A₂ = ρ/R

Or 4x² = ρ/R

Or x² = ρ/4R

Or x = √(ρ/4R)

Now,

Ratio of lengths = √(ρ/R) / √(ρ/4R)

= √(ρ/R) / 1/2 √(ρ/R)

= 2

Thus ratio is 2:1