Two coupled coils are connected in series across an AC source of RMS voltage 12 V and angular frequency 100 rad/s . When the coils are connected such that their magnetic fluxes aid each other, the RMS current drawn from the source is 2 A . When the connections of one coil are reversed so that their fluxes oppose each other, the RMS current becomes 3 A . The mutual inductance between the coils is: (Assume the resistan

Step-by-step solution

Let the self-inductances of the 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 The inductive reactance is X_A = L_A = V I₁ 100(L₁ + L₂ + 2M) = 12 2 = 6 L₁ + L₂ + 2M = 0.06 H ... (i) The equivalent inductance in the series opposing configuration is: L_B = L₁ + L₂ - 2M The inductive reactance is X_B = L_B = V I₂ 100(L₁ + L₂ - 2M) = 12 3 = 4 L₁ + L₂ - 2M = 0.04 H ... (ii) Subtracting equation (ii) from (i): 4M = 0.02 H M = 0.0