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Q46 (NDA-I/2019) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

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 disspation P 1. Which one of the following is the correct relationship between P and P1?

Result
Your answer: —  ·  Correct: B
Explanation

The correct answer is Option 2: P = P1/2. This relationship is derived from the formula for electrical power dissipation, P = V²/R, and the formula for resistance, R = ρ(l/A), where A = πr².

For wire A, the resistance is R_A = ρl / πr². Therefore, the power dissipation is P = V² / (ρl / πr²) = (V²πr²) / ρl.

For wire B, the radius is 2r and the length is 2l. Its resistance is R_B = ρ(2l) / π(2r)² = ρ(2l) / 4πr² = ρl / 2πr². Comparing the two, we find R_B = R_A / 2.

Substituting R_B into the power formula for wire B: P1 = V² / R_B = V² / (R_A / 2) = 2(V² / R_A) = 2P. Rearranging this gives P = P1/2. Since wire B has half the resistance of wire A due to its larger cross-sectional area, it dissipates twice the power under the same voltage.

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