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Question

Three solenoid coils of same dimension, same number of turns and same number of layers of winding are taken. Coil 1 with inductance L subscript 1 end subscript was wound using a Mn wire of resistance 11capital omega m to the power of negative 1 end exponent;Coil 2 with inductance L subscript 2 end subscript was wound using the similar wire but the direction of winding was reversed in each layer; Coil 3 with inductance L subscript 3 end subscriptwas wound using a superconducting wire. The self-inductance of the Coils L subscript 1 end subscript comma blank L subscript 2 end subscript comma blank L subscript 3 end subscript are

  1. L subscript 1 end subscript equals blank L subscript 2 end subscript equals blank L subscript 3 end subscript  
  2. L subscript 1 end subscript comma equals L subscript 2 end subscript semicolon blank L subscript 3 end subscript equals 0  
  3. L subscript 1 end subscript comma equals L subscript 3 end subscript semicolon blank L subscript 2 end subscript equals 0  
  4. L subscript 1 end subscript greater than L subscript 2 end subscript greater than L subscript 3 end subscript  

The correct answer is: L subscript 1 end subscript comma equals L subscript 3 end subscript semicolon blank L subscript 2 end subscript equals 0


    As inductance L subscript 2 end subscript was wound using the similar wire but the direction of winding is reversed, so flux through L subscript 2 end subscript is zero.
    therefore blank L subscript 2 end subscript proportional to ϕ equals 0
    Also, L subscript 1 end subscript equals L subscript 3 end subscript
    Therefore, L subscript 1 end subscript equals L subscript 3 end subscript comma blank L subscript 2 end subscript equals 0

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