220V is applied to two different conductors made of the same material. One conductor is twice as long and twice as thick as the second. What is the ratio of the power transformed in the first relative to the second?

For calculating resistance of a conductor, the formula is

R = ρ l / A, ρ is specific resistance, l is length and A is cross sectional area of wire.

For first wire length is l₁, area is A₁ resistance is R₁, for second resistance is R₂, length is l₂ and area is A₂

Given, l₁ = 2l₂, A₁ = 4A₂, area is proportional to square of thickness.

R₁ / R₂ = I₁A₂ / I₂A₁

= 2l₂ x A₁ / 4 I₂A₁

= 1 / 2

2R₁ = R₂

Power = V² / R

Ratio of power = (V² / R₁) x (R₂ / V²)

= R₂ / R₁

= 2.