**Parallel Connection of Coupled Coils:**

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 M as shown in Fig. 10.20.

Let us consider Fig. 10.20(a) where the self induced emf n each coil assists the mutually induced emf as shown by the dot convention.

The voltage across the parallel branch is given by

also

Substituting Eq. 10.4 in Eq. 10.3, we get

If L_{eq} is the equivalent inductance of the Parallel Connection of Coupled Coils in Fig 10.20 (a) then υ is given by

Substituting Eq. 10.4 in the above equation we get

Equating Eq. 10.6 and Eq. 10.5, 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. 10.20(b), the equivalent inductance is given by