1. Coupled Circuits

2. ELE101/102 Dept of E&E,MIT Manipal 2
Coils in Series – Aiding
L1 + L2 + 2M
2M)L(LL
dt
di
2M)L(Leee
dt
di
M
dt
di
Le
dt
di
M
dt
di
Le
21eq
2121
22
11
++=
++=+=
+=
+=
Equivalent circuit
 
M
L1 L2

3. ELE101/102 Dept of E&E,MIT Manipal 3
Coils in Series – Opposing
L1 + L2 - 2M
1 1
2 2
1 2
1 2
1 2
( 2
and
)
2
eq
eq
di di
e L M
dt dt
di di
e L M
dt dt
e e e
di di
L L M L
dt dt
L L L M
= −
= −
= +
= + −
+∴
=
= −
Equivalent circuit
 
M
L1 L2

4. ELE 101/102 Basic Electrical
Technology
L12.4
Dot Rule
To determine the sign of mutual induced emf
Sign of M terms same as sign of L terms Sign of M terms opposite to sign of L terms

5. ELE101/102 Dept of E&E,MIT Manipal 5
Coils in Parallel
Aiding:
MLL
MLL
Leq
221
2
21
−+
−
=
Opposing:
MLL
MLL
Leq
221
2
21
++
−
=

6. ELE101/102 Dept of E&E,MIT Manipal 6
Two coils with inductances in the ratio 1:4 have a
coupling coefficient k=0.6. When these coils are
connected in series aiding the equivalent inductance is
44.4mH. Find L1, L2, and M
Ans:
L1 =6mH
L2 =24mH
M =7.2mH
Example

7. ELE101/102 Dept of E&E,MIT Manipal 7
Problems
Obtain the dotted equivalent for the coupled circuit shown in the figure
Vs
+
-
R
M
L1
L2
C

8. ELE101/102 Dept of E&E,MIT Manipal 8
Problems
0.8H
K=0.7
0.3H
Obtain the equivalent inductance of the parallel connected coils
shown in figure

