Electrical Engineering ⇒ Topic : Parallel connection of coupled conductors
PARALLEL CONNECTION OF COUPLED COILS
Consider two inductors with self inductances L1 and L2 connected parallel which are mutually coupled with mutual inductance Mas shown in Fig. 1 (a) and (b).
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.
The voltage across the parallel branch is given by
Substituting Eq. (1) in Eq. (2), we get
If Leq 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
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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