Coupling
 When two coils ( or more than two coils ) are connected by common magnetic flux, they are called as coupled with each other.
Mutual
coupling
 The circuit element used to represent magnetic coupling is known as Mutual coupling.
 It is donated by symbol M and its unit is Henry.
 The induced emf in the second coil due to current flows through one coil is related by
e_{2} = M di_{1} / dt
 The dot sign indicates direction of current in the coil.
 If the current flows through both coil A and coil B, the induced emf in the two coils A and coil B is
e1 = L1 ( di_{1}
/ dt ) + M ( di_{2} / dt )
e2 = L2 ( di_{2}
/ dt ) + M ( di_{1} / dt )
Inductances are in series : Series
aiding

Figure A shows
two coils are connected in series such that the current enter the dot end of
the coil A whereas it leaves dot end of the other coil B.

This type of coil
connection is called as series aiding connection of coil.

The total
induced emf in coil A and coil B due to self inductance and emf induced due to
other coil is given by
e1 = L1 ( di /
dt ) + M ( di / dt )
= [ L1 + M ] ( di / dt ) ……..( 1 )
e2 = L2 ( di /
dt ) + M ( di / dt )
= [ L2 + M ] ( di / dt )…….( 2 )
From equation (
1 ) and ( 2 )
Now total
induced emf e = e1 + e2
= [ L1 + L2 + M ] ( di / dt )………..( 3 )
Now e = L ( di / dt )……………….( 4 )
From equation ( 3
) and ( 4 )
L ( di / dt ) =
[ L1 + L2 + M ] ( di / dt )
L = [ L1 + L2 + 2M
]
Figure A shows
two coils are connected in series such that the current enter the dot end of
the coil A whereas it leaves dot end of the other coil B.
This type of coil
connection is called as series aiding connection of coil.
The total
induced emf in coil A and coil B due to self inductance and emf induced due to
other coil is given by