Electrical Engineering ⇒ Topic : Inductive Coupling in Series

Gopal
 
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 L_{1} = inductance of first coil L_{2} = inductance of second coil M = mutual inductance between the two coils Seriesaiding: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 L_{1} and L_{2} plus the mutually induced e.m.f.s, i.e
FIGURE (A) ... in magnitude = (L_{1}+ L_{2} + 2M) di/dt If L_{T} is the total inductance of the circuit, then, L_{T} = L_{1}+ L_{2} + 2M ...fluxes additive (2) SERIES OPPOSING Figure(a) shows the seriesopposing 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 L_{1} and L_{2} 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}= L_{1}+ L_{2}  
 
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