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Q100 (IAS/2001) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

Two wires have their lengths, diameters and resistivities, all in the ratio of 1 : 2. If the resistance of the thinner wire is 10 ohms, the resistance of the thicker wire is

Result
Your answer: —  ·  Correct: A
Explanation

Resistance R of a wire is given by R = ρL/A, so R is directly proportional to resistivity and length and inversely proportional to cross-sectional area [1]. For cylindrical wires area A ∝ d^2, so if diameters are in ratio 1:2, the area ratio is 1:4 . Given the thinner wire (wire 1) to thicker wire (wire 2) ratios: ρ2/ρ1 = 2, L2/L1 = 2, and A2/A1 = 4. Thus R2/R1 = (ρ2 L2 / A2) / (ρ1 L1 / A1) = (2 × 2) / 4 = 1. Hence R2 = R1 = 10 Ω, so the correct choice is option 1.

Sources

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