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NEETPhysicsElectromagnetic Induction

Match List-I with List-II regarding the change in self-inductance of an ideal air-cored solenoid when its parameters are modified. List-I List-II (A) Doubling total turns and doubling length, keeping area constant (I) Inductance becomes 4 times (B) Doubling turns per unit length and doubling length, keeping area constant (II) Inductance becomes 2 times (C) Halving total turns, keeping length and area constant (III) I

Options

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

Correct answer

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

Step-by-step solution

The self-inductance of a solenoid in terms of total turns N is L = ₀ N^2 A l . In terms of turns per unit length n ( n = N l ), it is L = ₀ n^2 A l . (A) Doubling N and doubling l : L' = ₀ (2N)^2 A 2l = 2 ( ₀ N^2 A l ) = 2L . (Matches II) (B) Doubling n and doubling l : L' = ₀ (2n)^2 A (2l) = 8 ( ₀ n^2 A l) = 8L . (Matches IV) (C) Halving N only: L' = ₀ (N/2)^2 A l = 1 4 L . (Matches III) (D) Inserting a core of _r = 4 : L' = ₀ _r n^2 A l = 4L . (Matches I) Therefore, the correct matching is (A) - (II), (B) - (IV),

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