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JEE MainPhysicsElectromagnetic Induction

Two coils are connected in series. When their magnetic fluxes aid each other, the equivalent inductance of the combination is 26 mH . When their fluxes oppose each other, the equivalent inductance is 14 mH . If the self-inductance of one of the coils is 2 mH , the coefficient of coupling between the coils is:

Options

  1. A1
  2. B3 2 19
  3. C0.5
  4. D3 19

Correct answer

C. 0.5

Step-by-step solution

Let the self-inductances of the two coils be L₁ and L₂ , and their mutual inductance be M . The equivalent inductance in the series aiding configuration is: L_A = L₁ + L₂ + 2M = 26 mH ... (i) The equivalent inductance in the series opposing configuration is: L_B = L₁ + L₂ - 2M = 14 mH ... (ii) Adding equations (i) and (ii): 2(L₁ + L₂) = 40 mH L₁ + L₂ = 20 mH Given L₁ = 2 mH , we have: 2 + L₂ = 20 L₂ = 18 mH Subtracting equation (ii) from (i): 4M = 12 mH M = 3 mH The coefficient of coupling k is given by: k = M L₁ L

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