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Match List-I with List-II. List-I (Infinite L-section ladder) List-II (Equivalent resistance) (A) Series 1 , Shunt 2 (I) 2 (B) Series 2 , Shunt 4 (II) 4 (C) Series 3 , Shunt 18 (III) 9 (D) Series 4 , Shunt 12 (IV) 8 Choose the correct answer from the options given below:

Options

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

Correct answer

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

Step-by-step solution

For an infinite L-section ladder with series resistance R_s and shunt resistance R_ sh , the equivalent resistance R is given by: R = R_s + R_ sh R R_ sh + R R(R_ sh + R) = R_s(R_ sh + R) + R_ sh R R^2 - R_s R - R_s R_ sh = 0 For (A): R_s = 1 , R_ sh = 2 R^2 - R - 2 = 0 (R - 2)(R + 1) = 0 R = 2 . So, (A) matches with (I). For (B): R_s = 2 , R_ sh = 4 R^2 - 2R - 8 = 0 (R - 4)(R + 2) = 0 R = 4 . So, (B) matches with (II). For (C): R_s = 3 , R_ sh = 18 R^2 - 3R - 54 = 0 (R - 9)(R + 6) = 0 R = 9 . So, (C) matches with

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