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Q43 (NDA-II/2015) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

The resistance of a wire of length / and area of cross-section a is x ohm. If the wire is stretched to double its length, its resistance would become:

Result
Your answer: —  ·  Correct: C
Explanation

The resistance (R) of a wire is determined by the formula R = ρ(l/A), where ρ is resistivity, l is length, and A is the cross-sectional area [1]. When a wire is stretched to double its length (l' = 2l), its volume (V = l × A) must remain constant [1]. Consequently, if the length doubles, the cross-sectional area must decrease to half its original value (A' = A/2) to maintain the same volume [1]. Substituting these new dimensions into the resistance formula, the new resistance R' becomes ρ(2l / (A/2)), which simplifies to 4 × ρ(l/A) [1]. Therefore, the new resistance is four times the original resistance (4x ohm) [1]. This quadrupling effect occurs because resistance is directly proportional to length and inversely proportional to the area of cross-section [1].

Sources

  1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178
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