Electrical Engineering ⇒ Topic : Parallel connection of coupled conductors

David
 
PARALLEL CONNECTION OF COUPLED COILS Consider two inductors with self inductances L_{1} and L_{2} connected parallel which are mutually coupled with mutual inductance Mas shown in Fig. 1 (a) and (b). \ figure (1) Let us consider Fig. 1 (a) where the self induced emf in each coil assists the mutually induced emf as shown by the dot convention. ............... (1) The voltage across the parallel branch is given by ........... (2) Substituting Eq. (1) in Eq. (2), we get
............. (3) If L_{eq} is the equivalent inductance of the parallel circuit in Fig. 1 (a) then is given by Substituting Eq. (4) in the above equation we get ........... (4) Equating Eq. (4) and Eq. (3), we get Rearranging and simplifying the above equation results in If the voltage induced due to mutual inductance oppose the self induced emf in each coil as shown by the dot convention in Fig. 4 (b), the equivalent inductance its given by  
 
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