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?
P = 2P₁
P = P₁/2
P = 4P₁
P = P₁
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2019
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.