Lecture Slides for the course Fundamentals of Electrical Engineering delivered by me to First Semester Diploma in Mechanical Engineering.

1. PEE-102A
Fundamentals of Electrical Engineering
Lecture-4
Instructor:
Mohd. Umar Rehman
EES, University Polytechnic, AMU
March 30, 2021
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2. Unit-II: Electromagnetic Induction & Alternating Current
Electromagnetic Induction—Faraday’s Laws & Lenz’s Law, Fleming’s Right Hand
Rule, Self & Mutual Induction/Inductance. Introduction to magnetic circuits with
simple numerical examples. Generation of AC, Important terms: Cycle, Time Pe-
riod, Frequency, Peak value, RMS value, Average value, pure R, L & C circuits on
AC—voltage, current & power, power factor, simple numerical problems. Introduc-
tion to Three phase systems, advantages. Y & ∆ connections, voltage, current &
power relations, applications.
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3. Electromagnetic Induction (EMI)
The phenomenon by which an emf is induced in a circuit (and hence current flows
when the circuit is closed) when magnetic flux linking with it changes is known as
electromagnetic induction.
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4. Electromagnetic Induction (EMI)
The phenomenon by which an emf is induced in a circuit (and hence current flows
when the circuit is closed) when magnetic flux linking with it changes is known as
electromagnetic induction.
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5. Demo of EMI
To demonstrate the phenomenon of electromagnetic induction, consider a coil
C of several turns connected to a galvanometer G as shown in above figure.
If a permanent magnet is moved towards the coil, it will be observed that the
galvanometer shows deflection in one direction. If the magnet is moved away
from the coil, the galvanometer again shows deflection but in the opposite di-
rection. In either case, the deflection will persist so long as the magnet is in
motion.
The production of EMF and hence current in the coil C is due to the fact that
when the magnet is in motion (towards or away from the coil), the amount of
flux linking the coil changes-the basic requirement for inducing EMF in the coil.
If the movement of the magnet is stopped, there is no change in flux and hence
no EMF is induced in the coil. Consequently, the deflection of the galvanometer
reduces to zero.
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6. Remarks
(i) The basic requirement for inducing EMF in a coil is not the magnetic flux linking
the coil but the change in flux linking the coil. No change in flux, no EMF is
induced in the coil.
(ii) The change in flux linking the coil can be brought about in two ways. Conductor
is moving and magnetic field is stationary (DC generators) OR conductor is
stationary and the magnetic field is moving (AC generators).
(iii) The product of number of turns (N) of the coil and the magnetic flux (φ) linking
the coil is called flux linkages i.e. λ = Nφ
Demo Video
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7. Faraday’s Laws of EM Induction
First Law: Whenever the magnetic flux linking a conductor or coil changes, an
EMF is induced in it.
Second Law: The magnitude of the EMF induced in a conductor or coil is
directly proportional to the rate of change of flux linkages i.e.
e ∝
change in λ
change in t
∝
Nφ2 −Nφ1
t2 −t1
= kN
∆φ
∆t
= N
∆φ
∆t
The constant of proportionality k is taken to be 1 in S. I. units.
An EMF of 1 V is said to be induced in a coil of 1 turn when the flux linking the
coil is changing at a rate of 1 Wb/s.
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8. Lenz’s Law
Faraday’s law only provides information about the magnitude of an induced EMF.
The direction of induced EMF is given by Lenz’s law, which states that: the direction
of induced current (or EMF) is such that it opposes the very cause that has produced
it. Lenz’s law is incorporated in the form of a negative sign that appears in the above
equation as follows:
e = −N
∆φ
∆t
Demo Video
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9. Fleming’s Right Hand Rule
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10. Fleming’s Right Hand Rule
It gives the direction of induced current in a conductor that is moving in a uniform
magnetic field.
Stretch out the forefinger, middle finger and thumb of your right hand so that they
are at right angles to one another. If the forefinger points in the direction of magnetic
field B, thuMb in the direction of Motion of the conductor, then the middle finger will
point in the direction of induced current I .
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11. Dynamically Induced EMF
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12. Dynamically Induced EMF
The EMF induced when conductor is moving and magnetic field is stationary is said
to be dynamically induced EMF.
B
θ v
C
Consider a single conductor C of length l metres moving at an angle θ to a uniform
magnetic field of B Wb/m2 with a velocity of v m/s. Then, dynamically induced EMF
is given by:
edyn = Blvsinθ
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13. Statically Induced EMF
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14. Statically Induced EMF
The EMF induced in a stationary conductor due to a moving magnetic field is called
statically induced EMF. It is further divided into two types:
(i) Self-Induced EMF
(ii) Mutually Induced EMF
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15. Self-Induced EMF
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16. Self-Induced EMF
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17. Self-Induced EMF...contd
The EMF induced in a coil due to the change of its own flux linked with it is
called self induced EMF.
When a coil is carrying current (See Fig.), a magnetic field is established
through the coil.
If current in the coil changes, then the flux linking the coil also changes. Hence
an EMF
= N
∆φ
∆t
is induced in the coil. This is known as self-induced EMF.
This phenomenon is known as Self Induction.
The direction of this EMF (by Lenz’s law) is such so as to oppose the cause
producing it, namely the change of current in the coil.
The self-induced EMF will persist so long as the current in the coil is changing.
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18. Remarks on Self-Induction
(i) When current in a coil changes, the self-induced EMF opposes the change of
current in the coil. This property of the coil is known as its self-inductance or
inductance.
(ii) The self-induced EMF (and hence inductance) does not prevent the current
from changing ; it serves only to delay the change. Thus after the switch is
closed , the current will rise from zero ampere to its final steady value in some
time (a fraction of a second). This delay is due to the self-induced EMF of the
coil.
(iii) Various expressions for self-inductance
L =
eself
∆i
∆t
=
Nφ
I
Unit of inductance is Henry (H).
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19. Mutually-Induced EMF
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20. Mutually-Induced EMF
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21. Mutually-Induced EMF...Contd
The EMF induced in a coil due to the changing current in the neighboring coil
is called mutually induced EMF.
Consider two coils A and B placed adjacent to each other as shown in the
figure.
A part of the magnetic flux produced by coil A passes through or links with coil
B. This flux which is common to both the coils A and B is called mutual flux φm
If current in coil A is varied, the mutual flux also varies and hence EMF is
induced in both the coils.
The EMF induced in coil A is called self-induced EMF as already discussed.
The EMF induced in coil B is known as mutually induced EMF, and the phe-
nomenon is known as mutual induction.
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22. Remarks on Mutual Induction
(i) The mutually induced EMF in coil B persists so long as the current in coil A is
changing. If current in coil A becomes steady, the mutual flux also becomes
steady and mutually induced EMF drops to zero.
(ii) The property of two neighbouring coils to induce voltage in one coil due to the
change of current in the other is called mutual inductance.
(iii) One expression for mutual inductance in terms of self-inductances is
M = k
√
L1L2
where, k is the coefficient of coupling between two coils. It is defined as the
fraction of magnetic flux produced by the current in one coil that links the other.
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23. Introduction to Magnetic Circuits
The closed path followed by magnetic flux is called a magnetic circuit just as
the closed path followed by current is called an electric circuit.
Many electrical devices (e.g. generator, motor, transformer etc.) depend upon
magnetism for their operation. Therefore, such devices have magnetic circuits
i.e. closed flux paths.
In order that these devices function efficiently, their magnetic circuits must be
properly designed to obtain the required magnetic conditions.
In the following discussion, we’ll focus on main quanitites pertaining to mag-
netic circuits.
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24. Magnetic Circuits...Contd
Consider a coil of N turns wound on an iron core as shown in Figure. When current
I is passed through the coil, magnetic flux φ is set up in the core. The flux follows
the closed path ABCDA and hence ABCDA is the magnetic circuit.
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25. Magnetic Circuits...Contd
The following points may be noted carefully :
(i) The amount of magnetic flux set up in the core depends upon current (I) and
number of turns (N). If we increase the current or number of turns, the amount
of magnetic flux also increases and vice-versa. The product NI is called the
magnetomotive force (MMF) and determines the amount of flux set up in the
magnetic circuit. It can be compared to electromotive force (EMF) which drives
current in an electric circuit. It is given by:
F or F = NI Amp-Turns
(ii) The opposition that the magnetic circuit offers to the magnetic flux is called
reluctance. It depends upon length of magnetic circuit (i.e. length ABCDA in
this case), area of X-section of the circuit and the nature of material that makes
up the magnetic circuit. It is given by the expression:
R or R =
l
µA
=
F
φ
AT/Wb
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26. Tutorial Problems
Try to solve simple problems based on the above discussion.
Problems are also posted with this lecture.
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