Two metallic wires A and B are made using copper. The radius of wire A is r while its length is l. A dc voltage V is applied across the wire A, causing power dissipation, P. The radius of wire B is 2r and its length is 2l and the same dc voltage V is applied across it causing power dissipation, P₁. Which one of the following is the correct relationship between P and P₁?

The resistance of a wire is given by R = ρ (l / A), where ρ is resistivity, l is length, and A is the cross-sectional area (A = πr²). Power dissipated is P = V²/R. For wire A: R_A = ρ (l / (πr²)). Power P = V² / R_A = V² / [ρ (l / (πr²))] = (V²πr²) / (ρl). For wire B: radius is 2r, length is 2l. R_B = ρ (2l / (π(2r)²)) = ρ (2l / (4πr²)) = ρ (l / (2πr²)). Power P₁ = V² / R_B = V² / [ρ (l / (2πr²))] = (2V²πr²) / (ρl). Comparing P and P₁: P₁ = 2 [(V²πr²) / (ρl)]. Since P = (V²πr²) / (ρl), we have P₁ = 2P. This relationship can be rewritten as P = P₁/2.