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Q28 (NDA-I/2008) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

A wire has a resistance of 32 Q . It is melted and drawn into a wire of half of its original length. What is the resistance of the new wire?

Result
Your answer: —  ·  Correct: C
Explanation

The resistance (R) of a conductor is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A), expressed as R = ρ(l/A) [c2][t7]. When a wire is melted and redrawn, its volume (V = A × l) remains constant. If the new length (l') is half the original length (l/2), the cross-sectional area must double (A' = 2A) to maintain the same volume [c1][t3]. Substituting these new values into the resistance formula, the new resistance R' = ρ(l/2) / (2A) = 1/4 × ρ(l/A) = R/4 [t6]. Given the original resistance is 32 Ω, the new resistance is 32 Ω / 4 = 8 Ω [t1]. This relationship demonstrates how geometric changes under constant volume conditions affect electrical properties [t10].

Sources

  1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Example 11.6 > p. 180
  2. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178
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