ELECTRICAL CIRCUITS
EEE
MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY
V
=
L
1
𝒅𝑰
𝟏
𝒅𝒕
+ M
𝒅𝑰
𝟐
𝒅𝒕
V
=
L
2
𝒅𝑰
𝟐
𝒅𝒕
+ M
𝒅𝑰
𝟏
𝒅𝒕
From the above figure,
i=i
1
+i
2
Therefore total inductance is given by,
ELECTRICAL CIRCUITS
EEE
MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY
PARALLEL OPPOSING:
Suppose two coils are in parallel with opposite place dot.
When 2 dots are at the opposite place of both inductors(while one at entering place and
other at leaving place)as shown in below figure i.e. the total
mutual inductance gets
differed
V
=
L
1
𝒅𝑰
𝟏
𝒅𝒕
− M
𝒅𝑰
𝟐
𝒅𝒕
V
=
L
2
𝒅𝑰
𝟐
𝒅𝒕
− M
𝒅𝑰
𝟏
𝒅𝒕
From the above figure,
i=i
1
+i
2
Therefore total inductance is given by,
ELECTRICAL CIRCUITS
EEE
MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY
COEFFICIENT OF COUPLING
:
The fraction of magnetic flux produced by the current in one coil that links with the other coil is
called
coefficient of coupling
between the two coils. It is denoted by (k).
Two coils are taken coil A and coil B, when current flows through one coil it produces flux; the
whole flux may not link
with the other coil coupled, and this is because of leakage flux by a
fraction (k) known as
Coefficient of Coupling.
k=1 when the flux produced by one coil completely links with the other coil and is called
magnetically tightly coupled.
k=0 when the flux produced by one coil does not link at all with the other coil and thus the coils
are said to be magnetically isolated.
DERIVATION:
Consider two magnetic coils A and B.
When current I
1
flows through coil A.
Considering coil B in which current I
2
flows
Multiplying equation (1) and (2)
ELECTRICAL CIRCUITS
EEE
MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY
The above equation (A) shows the relationship between mutual inductance and self inductance
between two the coils
SERIES MAGNETIC CIRCUIT:
A series magnetic circuit is analogous to a series electric circuit.
A magnetic circuit is said
to be series, if the same flux is flowing through all the elements connected in a magnetic
circuit. Consider a circular ring having a magnetic path of ‘l’ meters, area of cross section
‘a’ m
2
with a mean radius of ‘R’ meters having a coil of ‘N’ turns carrying a current of ‘I’
amperes wound uniformly as shown in below fig
The flux produced by the circuit is given by
Magnetic flux=
𝑀𝑀𝐹
𝑅𝐸𝐿𝑈𝐶𝑇𝐴𝑁𝐶𝐸
=
𝑁𝐼
𝑆
=
𝑁𝐼
𝑙/𝜇𝑎
In the above equation NI is the MMF of
the magnetic circuit, which is analogous to EMF in the
electrical circuit.
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