Change set

Pick exam & year, then Go.

Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading…
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.

How others answered
Each bar shows the % of students who chose that option. Green bar = correct answer, blue outline = your choice.
Community Performance
Out of everyone who attempted this question.
71%
got it right
✓ Thank you! We'll review this.

SIMILAR QUESTIONS

CDS-I · 2018 · Q33 Relevance score: 5.08

Two metallic wires made from copper have the same length, but the radius of wire 1 is half that of wire 2. The resistance of wire 1 is R. If both the wires are joined together in series, the total resistance becomes:

  • (A) 2R
  • (B) 1.25R
  • (C) 0.5R
  • (D) 1.33R

CDS-I · 2017 · Q28 Relevance score: 3.39

A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will be:

A) R/5
B) 5R/4
C) R/2
D) 4R/5

CDS-II · 2017 · Q12 Relevance score: 3.00

Two wires are made having same length I and area of cross-section A. Wire 1 is made of copper and wire 2 is made of aluminium. It is given that the electrical conductivity of copper is more than that of aluminium. In this context, which one of the following statements is correct?

NDA-I · 2012 · Q79 Relevance score: 2.35

Two metallic wires A and B are of same material and have equal length. If the cross-sectional area of B is double that of A, then which one among the following is the electrical resistance of B?