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Q48 (CDS-II/2022) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of the same length but having double the diameter?

Result
Your answer: —  ·  Correct: B
Explanation

The resistance (R) of a metallic conductor is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A), expressed as R = ρ(l/A) [2]. For a wire with a circular cross-section, the area is calculated as A = π(d/2)² or A = πd²/4, where d is the diameter. This implies that resistance is inversely proportional to the square of the diameter (R ∝ 1/d²). When the diameter of the wire is doubled (2d) while keeping the length and material constant, the new cross-sectional area increases by a factor of four (2² = 4). Since resistance is inversely proportional to this area, the new resistance becomes one-fourth of the original value (R/4). Therefore, doubling the diameter reduces the opposition to electron flow by providing four times the space, resulting in a resistance of R/4.

Sources

  1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178
  2. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > What you have learnt > p. 192
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