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NEETPhysicsCurrent Electricity

Match List-I with List-II regarding a uniform wire of initial resistance R₀ undergoing various modifications. The equivalent resistance in each case is R_ eq . List-I List-II (A) Stretched to twice its length, bent into a circle, measured across a diameter (I) R_ eq R₀ = 1 (B) Stretched to three times its length, bent into an equilateral triangle, measured across one side (II) R_ eq R₀ = 2 (C) Stretched to twice its

Options

  1. A(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
  2. B(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
  3. C(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
  4. D(A)-(III), (B)-(II), (C)-(I), (D)-(IV)

Correct answer

B. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Step-by-step solution

When a wire is stretched to n times its original length, its resistance becomes n^2 R₀ . (A) Stretched to 2l : R_ new = 4 R₀ . Bent into a circle, the two halves across a diameter are in parallel. Each half has resistance 2 R₀ . R_ eq = 2 R₀ 2 R₀ 2 R₀ + 2 R₀ = R₀ . Ratio = 1 . (A I) (B) Stretched to 3l : R_ new = 9 R₀ . Bent into an equilateral triangle, each side has resistance 3 R₀ . Across one side, one branch has 3 R₀ and the other has 6 R₀ (two sides in series). R_ eq = 3 R₀ 6 R₀ 3 R₀ + 6 R₀ = 2 R₀ . Ratio = 2

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