Electrical Engineering ⇒ Topic : Inductive Coupling in Series

When two inductors are coupled in series and mutual inductance exists between them, the equivalent inductance of this series coupling can be calculated for series aiding and series opposing as follows:-

(1)SERIES AIDING

Consider two coils connected in series as shown in Figure.

Let L₁ = inductance of first coil

      L₂ = inductance of second coil

      M = mutual inductance between the two coils

Series-aiding:-This is the case when the coils are so arranged that their fluxes *aid each other i.e. in the same direction as shown in Figure (a). Suppose the current is changing at the rate di/dt. The total induced e.m.f. in the circuit will be equal to the sum of e.m.f.s induced in L₁ and L₂ plus the mutually induced e.m.f.s, i.e

                                                        FIGURE (A)

                           ... in magnitude

  = (L₁+ L₂ + 2M) di/dt

If L_T is the total inductance of the circuit, then,

L_T = L₁+ L₂ + 2M                                                               ...fluxes additive

(2) SERIES OPPOSING

Figure(a) shows the series-opposing connection i.e. the fluxes of the two coils oppose each other. Suppose the current is changing at the rate di/dt. The total induced e.m.f. in the circuit will be equal to sum of e.m.f.s induced in L₁ and L₂ minus the mutually induced e.m.f.s

        FIGURE  (A)

If L_T is the total inductance of the circuit, then,

Use + sign if fluxes are additive and ve sign if fluxes are subtractive

If the two coils are so positioned that *M = 0, then, L_T= L₁+ L₂