A uniform wire of resistance R is uniformly compressed along its length, until its radius becomes n times the original radius. Now resistance of the wire becomes
Correct answer: A. R/n4
- A. R/n4
- B. R/n2
- C. R/n
- D. Nr
Explanation
Correct. Let's derive the new resistance.Original Resistance:R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area (πr²).New Dimensions:New radius = nrNew area (A') = π(nr)² = n²πr² = n²AVolume Conservation:The volume of the wire remains constant.Original volume (V) = ALNew volume (V') = A'L'AL = A'L'AL = n²AL'L' = L/n²New Resistance (R'):R' = ρL'/A'R' = ρ(L/n²) / (n²A)R' = ρL / (n⁴A)R' = (1/n⁴) (ρL/A)R' = R/n⁴
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