L14 self and mutual inductance

ELE101/102 Dept of E&E,MIT Manipal 1
Self Induced emf & Self Inductance
The induced emf, e, in a coil is proportional to the rate
of the change of the magnetic flux passing through it
due to its own current. This emf is termed as Self
Induced EMF
The induced emf e is proportional to the rate of change
of current through coil and this proportionality constant
is called the self inductance, L.
The negative sign is used to indicate that EMF is
opposing the cause producing it
dt
di
Le1 −=

Mutually Induced emf & Mutual Inductance
If two coils of wire are placed near
each other, a change of current in
one coil will induce emfs e1 in the first
coil and e2 in the second coil.
The induced emf, e2, in coil 2 is
proportional to the rate of the change
of the magnetic flux passing through
it and hence proportional to rate of
change of current in first coil and is
termed as Mutually induced EMF.
e2
e1

The induced emf e2 is
proportional to the rate of change
of current through coil 1 and this
proportionality constant is called
the mutual inductance, M
The mutually induced emf is
expressed as
This induced emf can also be
expressed as
Self & Mutual Inductance…
M
N 1 N 2
L 1 L 2
φ 1 1 φ 1 2
φ 1 = φ 1 1 + φ 1 2
i 1
V 1 e 2
+
-
e 1
1
2
di
e M
dt
=
12
2 2
d
e N
dt
ϕ
=

Therefore
If is constant, is constant
and
Unit: Henry (H)
Mutual Inductance…
M
N 1 N 2
L 1 L 2
φ 1 1 φ 1 2
φ 1 = φ 1 1 + φ 1 2
i 1
V 1 e 2
+
-
e 1
1
12
2NM
di
dφ
=
rµ
1
12
di
dφ
1
12
2
I
Φ
NM =

Coupling Coefficient
1 2
1 1 2 2
1 2
1 2
2 12 1 21
1 2
12 1 21 2
2
1 2 2
1 2
Self Inductances and are
and
Mutual Inductance
where and
is thecoupling coeficie
L L
M
;
nt
or
N N
L L
I I
N N
M
I I
k k
k
M M
L L k
k L L
Φ Φ
= =
Φ Φ
= =
Φ = Φ Φ = Φ
= =

Example
Coil 1 of a pair of coupled coils has a continuous current
of 5A, and the corresponding fluxes φ1 and φ12 are
0.6mWb and 0.4 mWb respectively. If the turns are
N1=500 and N2=1500, find L1, L2, M and k.
Ans:
 k = Φ12/Φ1 = 0.667
 M = N2 Φ12/I1=0.12H
 L1 = N1 Φ1/I1= 0.06 H
 L2 = 0.539H

L14 self and mutual inductance

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L14 self and mutual inductance