Download DETERMINATION OF SELF, Mutual inductnces

DETERMINATION OF SELF, MUTUAL INDUCTNCES AND
COEFFICIENT OF COUPLING
AIM
To determine the self-inductance, mutual inductance and coefficient of coupling
of the given 1- transformer.
APPARATUS:S. No
Name of the apparatus
Range
Type
Quantity
1
Single phase transformer
230V / 115V, 3KVA
-
01No
2
1- auto transformer
230V / 0-270V,10A,
Induction
01No
3
Ammeter
(0-2) A
MI
01 No
4
Voltmeter
(0-600) / (0-300) V
MI
01No
5
Ammeter
(0-2) A
MC
01No
6
Connecting wires
-
-
Required number
7
Voltmeter
0-1V
MC
01No
PRECAUTIONS:
1. Ensure the minimum position of autotransformer during power on and off.
2. Set the ammeter pointer at zero position.
3. Take the readings without parallax error.
4. Avoid loose connections.
Circuit for finding ‘ M’ Value:-
Circuit for self inductance (L1):-
Circuit for self inductance (L2):-
Theory:A voltage is induced in a coil when there is a time rate of charge of current
through it. The inductance parameter L, is defined in terms of the voltage across it and
the time rate of change of current through it V(t) =
Where V(t) is the voltage across
the coil.
I(t) is the current through the coil,L is the inductance of the coil,Strictly speaking, this
definition is of self-inductance and this is considered as a circuit element with a pair of
terminals. Where as circuit element “mutual inductor” does not exist mutual inductance
is a property associated with two or more coils or inductors which are in close proximity
and the presence of common magnetic flux which links the coils. A transformer is such a
device whose operation is based on mutual inductance. The two coils, or circuits are said
to be inductively coupled, because of this property they are called “
coupled elements “ , are coupled circuits and the induced voltage or emf is called voltage
(or) emf of mutual induction and is given by V2(t) =
volts.
Where V2 is the voltage induced in coil L2
And M1 is the co-efficient of proportionality and is called the co-efficient of mutual
inductance or simple mutual inductance.
The amount of coupling b/wn the inductively coupled coils is expressed in terms
of the co-efficient of coupling which is defined as
K=
where M= mutual inductance b/wn the coils,
L1 = self inductance of first coil,
L2 = self inductance of second coil.
Co-efficient of coupling is always less than unity, and has a maximum value of
1(or100%).
This case, for which K=1 is called perfect coupling when the entire flux of one
coil links the other. The greater the co-efficient of coupling b/wn the two coils, the
greater the mutual inductance between them, and vice-versa. It can be expressed as the
fraction of the magnetic flux produced by the current in one coil that links the other coil.
The co-efficient of coupling k is a non magnetic number and is independent of the
reference directions of the currents in the coils. If the two coils are a great distance apart
in space, and K is also very small. For iron core coupled circuits, the value of K may be
as high as 0.999, for air-core coupled ckts, K varied between 0.4 to 0.8.
Circuit for RDC1:
Circuit for RDC2:-
Procedure:To find Z1: Apply rated voltage (V1) i.e 115 to primary winding and note down
corresponding ammeter reading. Then find out Z given
. We use auto
transformer to vary voltage.
To find Z2: Apply rated voltage i.e 230 to primary winding and note down corresponding
ammeter reading. Then find out Z2 using the formula
.
To find Rdc1: Apply low voltage to primary winding i.e 115 V and note down corresponding
ammeter readings. Then find Rdc given by
and from this Rac1 = 1.0 Rdc.
To find Rdc2 : Apply a low voltage to primary i.e 230V winding and note down corresponding
ammeter readings. Then find Rdc2 given by
and from this Rac2 = 1.6 Rdc2.
To find M : Apply voltage of primary winding till the voltmeter in secondary reads 115V and
note down corresponding ammeter reading in primary.
To find Z1:-
S.No
V1
(Volts)
I1
(amp)
Z1 
V1
Ω
I1
V2
(Volts)
I2
(amp)
Z2 
V2
Ω
I2
V
(Volts)
I
(amp)
V1
(Volts)
I1
(amp)
R1 
V1
Ω
I1
V2
(Volts)
I2
(amp)
R2 
V2
Ω
I2
1
To find Z2:-
S.No
1
To find M :S.No
M=V/I
1
To find Rdc1:S.No
1
To find Rdc2 :-
S.No
1
Calculations:XL1 =
=
XL2 =
=
XL1 = 2 fL1
L1 =
XL2 = 2 fL2
L2 =
Co-efficient of coupling K=
Where M =
=
=
Result:-
Review Questions:1. Derive an expression for Mutual coupling coefficient.
2. Explain series aiding & series opposing in coupled circuit.
3. Explain parallel aiding& parallel opposing in a coupled
Circuit
4. Two coupled coils with self-inductance L1 and L2 have 500 turns And 1000 turns
respectively. The coefficient of coupling between Them is 0.8.The portion of flux that
links both the coils when a current Of 5A flows through coil is 0.9 wb.Find the values of
L1 and L2.
CONCLUSION:
The coefficient of coupling, K of the given 1- iron cored transformer is less than unity.