determine the equivalent inductancetwo coils of

Question

Determine the equivalent inductance:

Two coils of inductances 4H and 6H are connected in parallel. If their mutual inductance is 3 H, determine the equivalent inductance of the combination if (i) mutual inductance assists the self-inductance, and (ii) mutual inductance opposes the self-inductance.

Solution

L1 = 4 H           L2 = 6 H           M = 3 H

L (di/dt ) =   (L₁ L₂  - M² )/ (L₁ + L₂  + 2M) di/dt    =   4 × 6 - 3² /4 + 6 - 2 × 3= 3.75 H

L =   (L₁ L₂ - M²)/ (L₁ + L₂ +2M)  = 4 × 6 - 3² /4 + 6 + 2 × 3 = 0.9375 H