1) The document discusses self-induction and back emf in circuits containing coils or inductors. When the current through a coil changes, it produces a back emf opposing the change due to Lenz's law. 2) It also describes how transformers work using mutual induction between two coils. The primary coil is connected to a changing current that induces a current in the secondary coil. 3) Transformers can be used to change voltages by adjusting the turn ratios of the coils. They allow efficient long-distance power transmission by stepping voltages up for transmission and down for usage.

1. Prepared by
Md. Amirul Islam
Lecturer
Department of Applied Physics & Electronics
Bangabandhu Sheikh Mujibur Rahman Science &
Technology University, Gopalganj – 8100

3. Self Induction and Back emf:
Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.1, Page – 1015
Consider the circuit consisting of a
switch, a resistor, and a source of
emf, as shown in figure. When the
switch is thrown to its closed
position, the source current does
not immediately jump from zero to
its maximum value Ԑ/R. Faraday’s
law of electromagnetic induction
can be used to describe this effect
as follows: As the source current
increases with time, the magnetic flux through the circuit loop due to this
current also increases with time. This increasing flux creates an induced
emf in the circuit. The direction of the induced emf is such that it would
cause an induced current in the loop, which would establish a magnetic
field that would oppose the change in the source magnetic field.

4. Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.1, Page – 1015
Thus, the direction of the induced
emf is opposite the direction of the
source emf; this results in a gradual
rather than instantaneous increase
in the source current to its final
equilibrium value. This effect is
called self-induction because the
changing flux through the circuit
and the resultant induced emf arise from the circuit itself. The emf ԐL
set up in this case is called a self-induced emf. It is also often called a
back emf.

6. Inductor or Solenoid:
Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.1, Page – 1015
Consider a coil wound on a cylindrical iron core as shown in figure.
(a) A current in the coil produces a magnetic field directed to the left (Screw
rule) (b) If the current increases, the increasing magnetic flux creates an
induced emf having the polarity shown by the dashed battery (Lenz’s Law) (c)
The polarity of the induced emf reverses if the current decreases.

7. Quantitative Analysis:
Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.1, Page – 1015
From Faraday’s law we know that the induced emf ԐL is equal to the
negative time rate of change of the magnetic flux (– dФB/dt).
Again, a self-induced emf ԐL is always proportional to the time rate
of change of the source current (dI/dt).
Thus, we can write,
where L is a proportionality constant — called the inductance of the
coil — that depends on the geometry of the circuit and other
physical characteristics. From this expression, we see that the
inductance of a coil containing N turns is,

8. Unit of Inductance:
Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.1, Page – 1015
From the equation of induced emf, we can write that,
Thus the SI unit of inductance is Henry and can be written as,

10. Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.3, Page – 1021
Because the emf induced in an inductor prevents a battery from
establishing an instantaneous current, the battery must do work
against the inductor to create a current. Part of the energy supplied
by the battery appears as internal energy in the resistor, while the
remaining energy is stored in the magnetic field of the inductor.
Applying KVL, we get,
IԐ is the energy supplied from the source, I2R is the energy
delivered to the resistor and thus, LI(dI/dt) is the energy stored in
the inductor.

11. Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.3, Page – 1021
If we let U denote the energy stored in the inductor at any time,
then we can write the rate dU/dt at which energy is stored as,
To find the total energy stored in the inductor, we can rewrite this
expression as dU = LIdI and integrate over the limit 0 to I:
This is the equation of energy stored in an inductor.

13. Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.3, Page – 1021
Very often, the magnetic flux through the area enclosed by a circuit
varies with time because of time-varying currents in nearby circuits.
This condition induces an emf through a process known as mutual
induction, so called because it depends on the interaction of two
circuits.
Consider the two closely wound
coils of wire in cross-sectional view
in figure. The current I1 in coil 1,
which has N1 turns, creates
magnetic field lines, some of which
pass through coil 2, which has N2
turns. The magnetic flux caused by
the current in coil 1 and passing
through coil 2 is represented by
Ф12.

14. Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.3, Page – 1021
In analogy to equation L = NФ/I,
we define the mutual inductance
M12 of coil 2 with respect to coil 1:
Induced emf in coil 2 is,

15. Reference: Physics II by Robert Resnick and David Halliday, Topic – 32.3, Page – 1021
In the preceding discussion, we assumed that the source current is in
coil 1. We can also imagine a source current I2 in coil 2. The
preceding discussion can be repeated to show that there is a mutual
inductance M21 . If the current I2 varies with time, the emf induced
by coil 2 in coil 1 is,
It can be experimentally shown that,
M12 = M21 = M and thus,
The unit of mutual inductance is also Henry.

17. Reference: Physics II by Robert Resnick and David Halliday, Topic – 33.8, Page – 1060
When electric power is transmitted over great distances, it is
economical to use a high voltage and a low current to minimize the
I2R loss in the transmission lines. Consequently, 33,000V lines are
common. At the receiving end of such lines, the consumer requires
power at a low voltage. Therefore, a device is required that can
change the alternating voltage and current without causing
appreciable changes in the power delivered. The ac transformer is
that device.
Construction:
The ac transformer consists of two
coils of wire wound around a core of
iron, as illustrated in figure. The coil
on the left, which is connected to the
input alternating voltage source and
has N1 turns, is called the primary
winding (or the primary).

18. Reference: Physics II by Robert Resnick and David Halliday, Topic – 33.8, Page – 1060
The coil on the right, consisting of N2 turns and connected to a load
resistor R, is called the secondary winding (or the secondary). The
purpose of the iron core is to increase the magnetic flux through the
coil and to provide a medium in which nearly all the flux through
one coil passes through the other coil. Eddy current losses are
reduced by using a laminated core. Iron is used as the core material
because it is a soft ferromagnetic substance and hence reduces
hysteresis losses. Although practical transformer have some power
loss due to the resistance of the coil wire, as we assumed an ideal
transformer, so energy losses in the windings and core are zero.
Working Principle:
According to Faraday’s law the voltage
∆V1 across the primary is,

19. Reference: Physics II by Robert Resnick and David Halliday, Topic – 33.8, Page – 1060
where ФB is the magnetic flux through each turn. If we assume that
all magnetic field lines remain within the iron core, the flux through
each turn of the primary equals the flux through each turn of the
secondary. Hence, the voltage across the secondary is:
Dividing and then rearranging
these two equations, we get,
When, N2 > N1, then ∆V2 > ∆V1. This setup is referred to as a step-up
transformer. When N2 < N1 , the output voltage is less than the input
voltage, and we have a step-down transformer.

20. Reference: Physics II by Robert Resnick and David Halliday, Topic – 33.8, Page – 1060
For an ideal transformer, there is no power loss on primary or
secondary winding. Thus,
When a resistive load RL is
connected to the secondary, then
current I2 on the secondary will be,
Furthermore, the current in the primary is,
Where,

21. Reference: Physics II by Robert Resnick and David Halliday, Topic – 33.8, Page – 1060
The above equation relates to the input resistance to the output
resistance. Req is the equivalent resistance of the load resistance
when viewed from the primary side. From this analysis we see that a
transformer may be used to match resistances (impedance matching)
between the primary circuit and the load. In this manner, maximum
power transfer can be achieved between a given power source and
the load resistance.