1. BASIC ELECTRICAL ENGINEERING
D. C. KULSHRESHTHA,
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2. Chapter 7 Self and Mutual Inductances
D.C. Kulshreshtha
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3. Man often becomes what he believes himself to be. Thought of the DAY
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Ch. 8 DC Transients
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4. Topics to be Discussed Self Inductance. Mutual Inductance.
Magnetic Coupling.
Coefficient of Coupling (k).
Sign of Mutual Voltage.
Dot Convention.
Coupled Coils in Series.
Coupled Coils in Parallel.
Measurement of M.
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5. Self Inductance
It is the property of a coil, due to which an emf is induced in itself whenever there is a change in the current flowing through it.
The self-induced emf is directly proportional to the rate of change of current,
The constant L is called the coefficient of self inductance or simply inductance.
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6. The SI unit of inductance is henry (H).
For a linear inductor, the magnitude of inductance is independent of the magnitude of current.
An air-cored inductor is linear.
When iron is used as core, the inductor becomes nonlinear.
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7. Energy stored in an Inductor :
Inductance from Geometrical Viewpoint :
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8. Example 1
A coil of 150 turns is linked with a flux of 0.01 Wb when carrying a current of 10 A.
Calculate the inductance of the coil.
If this current is uniformly reversed in 0.01 s, calculate the emf induced
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Solution :
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9. Example 2
An air-cored solenoid with length 30 cm and internal diameter 1.5 cm has a coil of 900 turns wound on it.
Estimate its inductance.
Also, calculate the amount of energy stored in it when the current through the coil rises from 0 to 5 A.
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10. Solution : Cross-sectional area of the solenoid, The energy stored,
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The energy stored,
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11. Example 3
The resistance and inductance of a coil are 3 Ω and 0.1 mH, respectively.
What potential difference exists across the terminals of this coil at the instant when the current is 1 A, but increasing at the rate of A per second ?
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12. Solution :
The potential difference across the coil will be due to the drop across its resistance as well as the emf induced in the inductance. Thus,
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13. MUTUAL INDUCTANCE
When interchange of energy takes place between two circuits, we say that the two circuits are mutually coupled.
Conductively coupled circuits.
Electrostatically coupled circuits.
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14. Magnetically Coupled Circuits
A part of magnetic flux produced by a coil in one circuit interlinks with the coil in other circuit.
Energy may be transferred from one circuit to the other through the medium of magnetic flux that is common to both circuits.
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15. When current in one coil changes, there occurs a change in the flux linking with the other. As a result, there is an induced emf in the other coil,
The constant of proportionality M is called coefficient of mutual inductance, or simply mutual inductance.
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16. A circuit element called “mutual inductor” does not exist.
It is defined with reference to two pairs of terminals.
The physical device whose operation is based inherently on mutual inductance is called transformer.
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17. Magnetic Coupling
Current i1 flowing in coil  establishes a total magnetic flux Φ1.
Only a part of this flux, Φ12, links with the coil.
The remaining flux Φ11 is confined to coil  itself.
Thus, Φ1 = Φ11 + Φ12.
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18. The emf induced in coil  due to the current i1 is given as
Also,
Similarly, the expression for mutual inductance from coil to coil  is
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19. from Geometrical Viewpoint :
Mutual Inductance
from Geometrical Viewpoint :
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20. Coefficient of Coupling (k)
It is a measure of how close is the coupling between two coils.
It gives an idea of what portion of the flux produced by one coil links with the other coil.
The flux that links with the coil  is only a part of Φ1.
That is,
where 0  k  1.
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21. If k = 1, the coils are tightly coupled.
The entire flux produced in one coil links with the other
If k = 0, the coils are magnetically isolated.
It can be shown that
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22. Example 4
A solenoid consists of 2000 turns of wire wound on a length of 70 cm.
A search coil of 500 turns having a mean area of 30 cm2 is placed centrally inside the solenoid.
Assuming k = 1, calculate
(a) the mutual inductance, and
(b) the emf induced in the search coil if the current in the solenoid uniformly changes at a rate of 260 A/s.
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23. Solution : Click Click Next Sunday, November 18, 2018
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24. Example 5
The numbers of turns in two coupled coils are 600 and 1700, respectively.
When a current of 6 A flows in the second coil, the total magnetic flux produced in this coil is 0.8 mWb, and the flux that links with the first coil is only 0.5 mWb.
Calculate L1, L2, k and M.
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25. Solution :
Click
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Since the self-inductance of a coil is proportional to the square of number of turns,
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26. DOT CONVENTION
Note that the voltage due to mutual inductance is present independently of and in addition to any voltage due to self-induction.
In other words, the voltage across the terminals of coil  is composed of two terms,
Similarly,
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27. Sign of Mutual Voltage
The sign depends not only on the current directions, but also on the way the two coils are wound.
“Dot convention” is a convenient way of determining the sign of mutual voltage, without going into the physical construction of the two coils.
The existence of mutual coupling between two coils is indicated by a double-headed arrow.
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28. DOT CONVENTION
A current entering the dotted terminal of one coil produces an open-circuit voltage which is positively sensed at the dotted terminal of the second coil.
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29. (a) (b)
(c) (d)
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30. Fig. (a) is equivalent to Fig. (d), and
Fig. (b) is equivalent to Fig. (c)
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31. COUPLED COILS IN SERIES
There are two ways of connecting two coupled coils in series.
Current flowing in the series combination may produce the two fluxes
either in the same direction (series aiding),
or in the opposite direction (series opposing)
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32. COUPLED COILS IN PARALLEL
Parallel aiding combination,
Parallel opposing combination,
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33. Measurement of M
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34. Review Self Inductance. Mutual Inductance. Magnetic Coupling.
Coefficient of Coupling (k).
Sign of Mutual Voltage.
Dot Convention.
Coupled Coils in Series.
Coupled Coils in Parallel.
Measurement of M.
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