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There are two solenoids of same length and inductance L but their diameters differ to the extent that one can just fit into the other. They are connected in three different ways in series. (1) They are connected in series but separated by large distance, (2) they are connected in series with one inside the other and senses of the turns coinciding, (3) both are connected in series with one inside the other with senses

Options

  1. A0 , 4 L 0 , 2 L 0
  2. B4 L 0 , 2 L 0 , 0
  3. C2 L 0 , 0 , 4 L 0
  4. D2 L 0 , 4 L 0 , 0

Correct answer

D. 2 L 0 , 4 L 0 , 0

Step-by-step solution

When two solenoids of inductance L 0 are connected in series at large distance and current i is passed through them, the total flux linkage ϕ t o t a l is the sum of the flux linkages L 0 i and L 0 i , i e , ϕ t o t a l = L 0 i + L 0 i If L be the equivalent inductance of the system, then ϕ t o t a l = L i ∴ L i = L 0 i + L 0 i or L = 2 L 0 When solenoids are connected in series with one inside the other and senses of the turns coinciding, then there will be mutual inductance L between them. In this case the result

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