Unit – I
DC Circuits
Definition of EMF
The Electrical force or pressure that causes the electrons to move in a particular
direction is called as the Electromotive force or EMF. The unit of EMF is volts and EMF
is also called as voltage or potential difference. It is denoted by V.
Current
Current is the movement of electrons inside a conducting material. It is denoted by
‘I’ & measured in ampere (A). The current is defined as the flow of charge per unit time
or the rate of change of charge with respect to time. Mathematically the charge-current
relation can be defined as
I
Q
t
Where I = Average current in amperes
Q = Total charge flowing
t = Time in seconds required for flow of charge
A current of 1 ampere is said to be flowing if a charge of one coulomb passes any
point in a conductor in one second. The charge on one electron is 1.6 x 10-19; one
coulomb corresponds to 6.25 x 1018 electrons. So when 6.25 x 1018 electrons [ass by a
point in a conductor in one second, a current of one ampere is said to be flowing through
the circuit.
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Resistance
The resistance of a material is defined as the property of material due to which it
opposes the flow of current. It is denoted by ‘R’ & measured in ohms (Ω). It also causes
the electrical energy to be converted into the heat energy.
The resistance of a circuit is said to be 1 ohm if a current of 1 ampere generates
the heat at the rate of 1 joule per second.
1 Joule = 0.24 calories
1 calorie = 4.186 Joule
The materials possessing large number of free electrons are offers less opposition
to the flow of current. Such elements are called as conductors of electricity. E.g.- copper,
silver, aluminum etc… While some materials have very less number of free electrons and
hence offers a large resistance to the flow of current. Such elements are termed to be
Insulators of Electricity. E.g. - glass, wood, rubber etc…
Factors Affecting Resistance: Following are the factors affecting the resistance of a material: -
 Length of material
The resistance of a material is directly proportional to the length of material. The
length of wire may be denoted by ’l’
 Cross sectional area
The resistance of a material is inversely proportional to the area of cross section
area of the material. More cross sectional area allows the passage of more number
of electrons, offering less resistance. The cross sectional area may be denoted by
‘a’.
 Type & nature of the material
Whether the material contains more number of free electrons or not, affects the
value of the resistance. So the conductors have less resistance while the insulators
have less resistance.
 Temperature
The temperature of the material affects the value of the resistance. Generally the
resistance of the material increases as its temperature increases. Also the effect of
small change in temperature is not taken into account as it is negligibly small.
Mathematically, the above factors can be relayed as:
| @ Temperature = constant
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
The effect of the nature of the material is considered through the constant of
proportionality denoted by ρ and is called as resistivity or specific resistance of the
material.
R  .
l
a
The resistivity or specific resistance of a material depends on the nature of the
material. It can be given as
a
l
  R.
Thus the resistivity of a material is the resistance of a material of unit length and
unit area of cross section. It is measured in Ω - M. It can be said that the material with
highest value of resistance is the best insulator and poorest value of resistivity is the best
conductor.
The following table gives resistivity values of popular materials.
Resistivity (Ω - M)
Material
Standard copper
172 x 10-8
Aluminium cast
2.6 x 10-8
Bronze
3.6 x 10-8
Wrought iron
10.7 x 10-8
Carbon graphite
4.6 x 10-8
Gold
2.36 x 10-8
Silver Annealed
158 x 10-8
Lead
22 x 10-8
Ohm’s Law: The voltage, current & resistance can be related by using Ohm’s law. It states that:
So long as the physical state (temperature, size, material) of a conductor remains
the same, the current flowing through the element is directly proportional to the potential
difference across it.
 I
V
R
Where ‘R’ is the resistance of the material
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Work: An Electrical work is the work done to transfer a charge from one point to another
point. It is denoted by W. The unit of electrical work done is Joules.
One joule of work is defined as the amount of work done to move a unit charge
(1colomb) through a potential difference of 1 Volt.
W  Q.V
Where Q – charge
V – Potential difference
Since, I 
Q
i.e. Q  I .t (t = time in seconds)
t
 W  V .I .t
Power: The Electrical power can be defined as the rate at which the Electrical work is
done in an Electric circuit. Its SI unit is joule per second or Watt (W).
Electrical Power 
P
Electrical Work
Time
W V .I .t

t
t
 P  V .I
Or P  I 2 R 
V2
R
The power consumed in electric circuit is 1 watt if the potential difference of 1V
applied across the circuit causes 1 ampere current t flow through it.
1 Watt = 1 Joule/second.
Energy: An Electrical energy is the amount of total work done in an electric circuit. The SI
unit of energy is joule or watt-second.
Electrical energy = Power X time
E  V .I .t
The electrical energy consumed by the circuit is said to be 1 joule when it utilizes
a power of 1 watt for 1 second.
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Resistance temperature coefficient
We know that, the temperature of the material affects the value of the resistance.
For different types of conductors the amount of change in resistance due to change in
temperature will have different values. For pure metals, the resistance increases linearly
with increase in temperature.
The above effect can be illustrated with atomic theory. Under the normal
temperature when the metal is subjected to a potential difference, ions i.e. immobile
charged particles get formed inside the metal. The electrons which are moving randomly
get aligned in a particular direction. At low temperature, the ions are almost stationary.
But as the temperature increases, the ions gain energy and start oscillating about their
mean position. Higher the temperature more is the vibration. Such vibrating ions cause
obstruction to the flowing electrons. Similarly, due to higher amplitude of the oscillating
ions chances of collision of electrons are more. Due to collision and obstruction due to
oscillation of ions, the resistance of material increases as temperature increases.
On the other hand the effect of rise in temperature on carbon & insulator is exactly
opposite to that of the metals. Resistance of carbon & insulators decreases as the
temperature increases. According to atomic theory, insulators do not have enough number
of free electrons and hence they are bad conductors of electricity. In carbon and insulators
due to increase in temperature the vibration of ion increases but due to high temperature
few electrons from atom gain extra energy and are made available as free electrons. So as
number of free electrons increases though vibration of ions increases overall difficulty to
the flow electrons reduces. This causes decrease in resistance.
The resistance of alloys increases as the temperature increases but the rate of
increase is not significant. Due to this property alloys are used in manufacturing of
resistance boxes.
Thus from above discussion we can conclude that the change in resistance is,

Directly proportional to the initial resistance

Directly proportional to the change in resistance

Depends on the nature of the material
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Let’s consider a conductor, the resistance of which increases with temperature
linearly,
R0 = Initial resistance at 00C
Let,
R1 = Resistance at T10C
R2 = Resistance at T20C
The graph below shows relationship of resistance VS temperature. (R0< R1< R2)
The slope of the graph is
Slope 
R2  R1
t 2  t1
This change in resistance with temperature can be related in accordance with the
factor called as resistance temperature coefficient (RTC). It is denoted by α. It is defined
as the ratio (at t0C) of change in resistance per degree centigrade to the resistance at t0C.
The unit of RTC is ‘per 0C’.
 = Change in resistance per 0C
Resistance at t10C
 = (R2 - R1)/ (t2 - t1)
Rt
RTC   t 
R. per 0 C
Rt
@ t 0C
The RTC can be used to calculate the resistance of material at some arbitrary
temperature t0C.
Let
o = RTC at 00C
R0 = Initial resistance at 00C
R1 = Resistance at T10C
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Then,
0 
R1  R0 / t1  0  R1  R0
R0
t1 R0
 R1  R0   0t1 R0
R1   0t1 R0  R0
R1  R0 1   0t1 
The above equation can be generalized for any temperature-‘t’ as
Rt  R0 1   0t 
Thus by knowing R0 and o at 00C, the resistance at any temperature at t0C can be
obtained.
Alternately, the above equation can be expressed as,
R1 = Initial resistance at t10C
Rt = Resistance at t0C
0 
Rt  R1 / t  t1 
R1
 0 R1 t  t1   Rt  R1
Rt  R1 1   0 t  t1 
Rt  R1 1   0 t 
Where, t  t  t1 
The above equation can be generalized for the temperature coefficient at any
temperature as,
R final  Rinitial 1   initial t 
Where, R final = the resistance at desired temperature t2
R initial = the resistance at initial temperature t1
α initial = temperature coefficient at initial temperature t1
∆t = difference
between final & initial temperature
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Series circuits: A series circuit is the circuit in which the circuit elements are connected such that
two or more components are connected end to end and the remaining two ends are
connected to the power supply. A simple series circuit consisting of three resistances is as
shown in the figure below: -
In the above circuit when voltage V is applied between points A & B, let the
current ‘I’ flows in the circuit. The current ‘I’ produces the voltages, VR1, VR2, & VR3
across the resistances R1, R2 & R3 respectively. Let ‘R” be the equivalent resistance of the
circuit. Hence we can write,
V  I .R
But,
V  VR1  VR 2  VR3
Where by Ohm’s law,
VR1  I .R1
VR 2  I .R2
&
VR 3  I .R3
Hence,
V  I .R1  I .R2  I .R3
 I .R  I .R1  I .R2  I .R3
 I .R  I .R1  R2  R3 
 R  R1  R2  R3
Thus in a series circuit it can be seen that the equivalent resistance of the circuit is
equal to the summation of the individual resistance. Also in series circuit the current
flowing through each circuit element is same but voltage across them is different.
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Parallel circuits: A parallel circuit is the one in which the circuit elements are connected such that,
the either ends of the components are connected together and a single terminal is formed
same is the workout for the second terminal. Thus two ends are formed for the
components. The figure below shows a simple parallel circuit.
In the above circuit when voltage ‘V’ is applied between points A & B, due to
which current ‘I’ is drawn from the battery. Let ‘R’ be the equivalent resistance the
circuit. Let I1, I2, & I3 be the currents flowing through resistances R1, R2 & R3
respectively. Thus by Ohm’s law, we can write,
V  I .R
Also,
V  I1.R1
V  I 2 .R2
&
V  I 3 .R3
In given parallel circuit, at point A, the current ‘I’ is divided into three branches
R1, R2 & R3 as I1, I2, & I3 respectively. Thus here,
I  I1  I 2  I 3

V V
V
V



R R1 R2 R3

1
1
1
1



R R1 R2 R3
Thus in parallel circuits, the reciprocal of the equivalent resistance is equal to the
summation of the reciprocals of the individual resistances. Also in parallel circuits, the
voltage applied across each circuit element is equal to the applied voltage.
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Division of current in two parallel branches: If two branches are connected in parallel then their current relations are to be
obtained in terms of total current (I). Let R1 & R2 be the two resistances connected in
parallel such that the currents flowing through them are I1 & I2. V is the applied electrical
potential.
Let R be the equivalent resistance of the circuit. Thus by Ohm’s law,
V  I .R
…………………… (1)
But we have to find I1 & I2 in terms of ‘I’. Since R1 & R2 are in parallel,
R
R1 .R2
R1  R2
V  I1 .R1
…………………… (2)
&
V  I 2 .R2
…………… (3)
Therefore from equations (1), (2) & (3) we get,
I1 .R1  I .R
 I 1 R1  I .
R1 .R2
R1  R2
 I1 
 I1  I .
I . R1 .R2
R1 R1  R2
R2
R1  R2
Similarly,
I2  I.
R1
R1  R2
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Kirchoff’s Laws: –
In 1847, a German Physicist, Kirchoff formulated two fundamental laws of
electricity. These laws are very important from network simplification point of view.
These laws are
1) Kirchoff’s current law: The Kirchoff’s current law states that,
The algebraic summation of currents at any junction point in the circuit is always
equal to zero. OR
The algebraic summation of currents flowing towards a junction point is equal to the
algebraic summation of currents flowing away from that junction point.
I  0
(At any junction point)
Sign conventions: Currents flowing towards the junction are assumed to be positive while the
currents flowing away from the junction point are assumed to be negative.
Consider a junction in a complex network as shown in figure.
By applying Kirchoff’s current law at point A gives,
I  0
i.e.  I
i.e.
I
1
1
 I2  I3  I4  I5  0
 I2  I3   I4  I5
2) Kirchoff’s voltage law: In any network, the algebraic summation of the voltage drop across the circuit
elements of any closed path (loop) is equal to the algebraic summation of the EMF in
that path.
OR
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
In any network, the algebraic summation of electrical energy supplied to a closed
circuit path is equal to the algebraic summation of the electrical energy consumed by the
circuit elements in that path.
Mathematically,
V   I .R
Sign conventions: 
Sign conventions for voltage: While tracing a circuit, the rise in voltage is assumed as positive and the
fall in voltage is assumed as negative. In other words, if the energy is supplied in
the same direction of tracing the circuit then that supply is assumed as positive &
if the energy supplied is in the opposite direction of tracing the circuit, then it
assumed to be negative.
When we go from negative terminal of the battery to the positive terminal
there is rise in potential & when we go from positive terminal to the negative
terminal of the battery, there is fall in potential. Also it is to be noted that the sign
of the battery is independent of the direction of the current through that branch.

Sign conventions for I.R: If the direction of the current flow through the resistance is in the same
direction as that of tracing the circuit, then the voltage drop I.R is assumed to be
negative. However if the direction of the current through the resistance is opposite
to that of the direction in which the circuit is traced then the voltage drop I.R is
assumed to be positive.
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Concept of magnetic circuit: What Is a Magnet? A magnet is as solid material that possesses the property of attracting the iron
pieces. When a magnet is rolled into iron pieces it will attract the iron pieces towards the
end points as shown below.
The points at which the iron pieces accumulate maximum are called poles of the
magnet while imaginary lines joining these poles called axis of the magnet. There are two
types of magnets

Natural magnet

Electromagnet
The natural magnets have the property of magnetism naturally present whereas
the electromagnets are formed by passing an electric current around a certain material.
The material then acts as magnet as long as the current is present. But it looses its
magnetic properties as soon as the current stops.
Properties of magnet: 1. A magnet attracts the iron pieces of iron.
2. A freely suspended magnet aligns itself in north-south direction.
3. Like poles of the magnet repel & unlike pole of the magnet attracts each other.
4. Magnetic induction.
5. Magnetic lines of force/ magnetic field/magnetic flux.
Magnetic Field: The magnetic field is defined as the region near a magnet within which the effect
or influence of the magnet is felt.
Magnetic Lines of Force: A line of force is defined as a line along which an isolated N-pole would travel if
it is allowed to move freely in a magnetic field.
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Properties of Magnetic Lines of Forces: 1. The magnetic lines of force always form a closed loop. They originate from Npole & terminate in S-pole.
2. The magnetic lines of force do not cross or intersect each other.
3. The magnetic lines of force which are parallel to each other & are acting in the
same direction tend to repel each other.
4. The magnetic lines of force behave like stretched elastic band & always try to
contract in length.
5. The magnetic lines of force always try to follow the minimum opposition
(reluctance) path.
Magnetic Circuit: A magnetic circuit is defined as the closed path followed by the magnetic lines of
force i.e. flux. This is very similar to an electric circuit which states that the electric
circuit is the closed path provided for the electric circuit. The quantities associated with
magnetic circuits are MMF, flux, reluctance permeability etc…
Magnetic Flux (): The magnetic flux is defined as the total number of magnetic lines of force in a
magnetic field. It is denoted by ‘’ & is measured in Webber (Wb). One Webber is
defined as the flux radiated out by a unit N-pole
1Wb = 108 lines of force
Magnetic Flux Density (B): The flux per unit area (A), measured in a plane perpendicular to the flux is defined
as the flux density. It is measured in tesla (T) or (Wb/m2).
B

A
Magnetic Field Strength or Magnetic Field Intensity (H): The magnetic field strength at a point in the magnetic field is defined as the force
experienced by a unit North Pole placed at that point in the magnetic field. It is measured
in Newton per Weber (N/Wb).
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Magneto Motive Force (MMF): The Magneto Motive Force is defined as the force responsible for the generation
of the flux. It is nothing but the work done on a unit magnetic pole to take it around a
closed magnetic circuit.
The MMF is the driving force behind the magnetic circuit. It is given by the
product of the number of turns of the magnetizing coil & the current passing through the
coil. Mathematically,
MMF= N.I
Where, N = number of turns of the magnetizing coil
I = current passing through the coil
The SI unit of the MMF is Ampere-turn (AT)
Reluctance (S): The reluctance of a material is the opposition offered by that material for passage
of magnetic lines of force (magnetic flux) through it. It is denoted by ‘S’. The reluctance
of a material is directly proportional to the length of the magnetic circuit & inversely
proportional to the area of cross section.

S
l
a
S 
K .l
a
Where K = constant of proportionality
= reciprocal of the absolute permeability
=

S 
l

l
 .a
It is measured in Webber/ ampere (Wb/A)
Also the reluctance of a material is defined as the ratio of magneto motive force to
the magnetic flux produced.
S 
MMF
S 
N .I


(AT/Wb) or (A/Wb)
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Comparison between Electrical and Magnetic Circuits: -
Sr. No.
Electric Circuit
Magnetic Circuit
Similarities
1
It is the combination of paths through It is the combination of paths through
which the electric current can pass
which the magnetic flux can pass
2
EMF is the driving force
MMF is the driving force
3
Resistance is the opposing factor
Reluctance is the opposing factor
4
I
5
DC battery gives constant EMF
6
V
R
Current

passes
from
MMF
S
Permanent magnet gives constant MMF
positive
to Flux passes from N-pole to S-pole
negative polarity
Differences
7
8
9
Electrical
energy
is
continuously Magnetic energy is required only to
required to produce & maintain current
setup flux. & not required to maintain it.
The charges actually flows to form the Flux is not actually flowing, it is simply
current
set up.
Resistance is a temperature dependant Reluctance is temperature independent
phenomenon.
phenomenon
10
It may be open or closed circuit
Magnetic circuits are always closed
11
Electrical insulation can be provided
No magnetic insulation exists
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Magnetic leakage and fringing: -
If the current is passed through an exciting coil wound on a magnetic core having
an air gap as shown in figure, the flux is produced in the core due to the coil current.
Ideally it is expected that the flux produced by the magnetizing coil should complete its
path only through the core & air gap. In that case all the produced flux will be available at
the air gap as the useful flux. But practically this doesn’t happen. That means all the
produced flux does not complete its path through air gap or in general the surrounding the
core.
The flux which completes its path through the air gap or the medium surrounding
the magnetic circuit instead of completing it through the core & air gap is known as the
leakage flux & the phenomenon is known as magnetic leakage.
The flux passing through the core is the useful flux. The magnetic lines of force
inside the core are running parallel to each other & are in the same direction. Also the
magnetic lines of force that are acting in same direction exert the force of repulsion on
each other. This repulsive force causes the magnetic flux to spread out or bulge out at the
edges of the air gap as shown in figure. This tendency of the magnetic flux to spread out
at the edges of the air gap is called as Magnetic Fringing.
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Due to the magnetic fringing the effective cross sectional area of the air gap is
increased & thus the flux density is reduced.
The only way to reduce the above phenomenon is use of high quality magnet &
making the air gap size as small as possible.
The concept of air gap flux finds the following applications: 1. Construction of DC Machines (motors & generators)
2. In solenoid valves
3. Electromagnets
4. Magnetic levitation
Magnetic Hysteresis
The lag or delay of a magnetic material known commonly as Magnetic Hysteresis, relates
to the magnetization properties of a material by which it firstly becomes magnetized and
then de-magnetized. We know that the magnetic flux generated by an electromagnetic
coil is the amount of magnetic field or lines of force produced within a given area and
that it is more commonly called "Flux Density". Given the symbol B with the unit of flux
density being the Tesla, T.
We also know from the previous tutorials that the magnetic strength of an electromagnet
depends upon the number of turns of the coil, the current flowing through the coil or the
type of core material being used, and if we increase either the current or the number of
turns we can increase the magnetic field strength, symbol H.
Previously, the relative permeability, symbol μr was defined as the product of the
absolute permeability μ and the permeability of free space μo (a vacuum) and this was
given as a constant. However, the relationship between the flux density, B and the
magnetic field strength, H can be defined by the fact that the relative permeability, μr is
not a constant but a function of the magnetic field intensity thereby giving magnetic flux
density as: B = μ H. Then the magnetic flux density in the material will be increased by a
larger factor as a result of its relative permeability for the material compared to the
magnetic flux density in vacuum, μoH and for an air-cored coil this relationship is given
as:
𝐵=
∅
𝐵
𝑎𝑛𝑑 𝜇𝑜 =
𝐴
𝐻
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
So for ferromagnetic materials the ratio of flux density to field strength (B/H) is not
constant but varies with flux density. However, for air cored coils or any non-magnetic
medium core such as woods or plastics, this ratio can be considered as a constant and this
constant is known as μo, the permeability of free space, ( μo = 4.π.10-7 H/m ).
By plotting values of flux density, ( B ) against the field strength, ( H ) we can produce a
set of curves called Magnetization Curves, Magnetic Hysteresis Curves or more
commonly B-H Curves for each type of core material used as shown below.
The set of magnetization curves, M above represents an example of the relationship
between B and H for soft-iron and steel cores but every type of core material will have its
own set of magnetic hysteresis curves. You may notice that the flux density increases in
proportion to the field strength until it reaches a certain value were it can not increase any
more becoming almost level and constant as the field strength continues to increase.
This is because there is a limit to the amount of flux density that can be generated by the
core as all the domains in the iron are perfectly aligned. Any further increase will have no
effect on the value of M, and the point on the graph where the flux density reaches its
limit is called Magnetic Saturation also known as Saturation of the Core and in our simple
example above the saturation point of the steel curve begins at about 3000 ampere-turns
per meter.
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
Saturation occurs because as we remember from the previous Magnetism tutorial which
included Weber's theory, the random haphazard arrangement of the molecule structure
within the core material changes as the tiny molecular magnets within the material
become "lined-up". As the magnetic field strength, ( H ) increases these molecular
magnets become more and more aligned until they reach perfect alignment producing
maximum flux density and any increase in the magnetic field strength due to an increase
in the electrical current flowing through the coil will have little or no effect.
Retentivity
Let’s assume that we have an electromagnetic coil with a high field strength due to the
current flowing through it, and that the ferromagnetic core material has reached its
saturation point, maximum flux density. If we now open a switch and remove the
magnetizing current flowing through the coil we would expect the magnetic field around
the coil to disappear as the magnetic flux reduced to zero.
However, the magnetic flux does not completely disappear as the electromagnetic core
material still retains some of its magnetism even when the current has stopped flowing in
the coil. This ability to retain some magnetism in the core after magnetization has stopped
is called Retentivity or Remanence while the amount of flux density still present in the
core is called Residual Magnetism, BR .
The reason for this that some of the tiny molecular magnets do not return to a completely
random pattern and still point in the direction of the original magnetizing field giving
them a sort of "memory". Some ferromagnetic materials have a high Retentivity
(magnetically hard) making them excellent for producing permanent magnets.
While other ferromagnetic materials have low Retentivity (magnetically soft) making
them ideal for use in electromagnets, solenoids or relays. One way to reduce this residual
flux density to zero is by reversing the direction of the current flowing through the coil,
thereby making the value of H, the magnetic field strength negative. This effect is called a
Coercive Force, HC .
If this reverse current is increased further the flux density will also increase in the reverse
direction until the ferromagnetic core reaches saturation again but in the reverse direction
from before. Reducing the magnetising current, i once again to zero will produce a similar
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
amount of residual magnetism but in the reverse direction. Then by constantly changing
the direction of the magnetising current through the coil from a positive direction to a
negative direction, as would be the case in an AC supply, a Magnetic Hysteresis loop of
the ferromagnetic core can be produced.
Magnetic Hysteresis Loop
The Magnetic Hysteresis loop above, shows the behavior of a ferromagnetic core
graphically as the relationship between B and H is non-linear. Starting with an
unmagnetised core both B and H will be at zero, point 0 on the magnetization curve.
If the magnetization current, i is increased in a positive direction to some value the
magnetic field strength H increases linearly with i and the flux density B will also
increase as shown by the curve from point 0 to point a as it heads towards saturation.
Now if the magnetizing current in the coil is reduced to zero the magnetic field around the
core reduces to zero but the magnetic flux does not reach zero due to the residual
magnetism present within the core and this is shown on the curve from point a to point b.
To reduce the flux density at point b to zero we need to reverse the current flowing
through the coil. The magnetizing force which must be applied to null the residual flux
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Anup Chandrashekhar Joshi
Unit – I
DC Circuits
density is called a "Coercive Force". This coercive force reverses the magnetic field rearranging the molecular magnets until the core becomes un magnetized at point c. An
increase in the reverse current causes the core to be magnetized in the opposite direction
and increasing this magnetization current will cause the core to reach saturation but in the
opposite direction, point d on the cure which is symmetrical to point b. If the magnetizing
current is reduced again to zero the residual magnetism present in the core will be equal
to the previous value but in reverse at point e.
Again reversing the magnetizing current flowing through the coil this time into a positive
direction will cause the magnetic flux to reach zero, point f on the curve and as before
increasing the magnetization current further in a positive direction will cause the core to
reach saturation at point a. Then the B-H curve follows the path of a-b-c-d-e-f-a as the
magnetizing current flowing through the coil alternates between a positive and negative
value such as the cycle of an AC voltage. This path is called a Magnetic Hysteresis Loop.
The effect of magnetic hysteresis shows that the magnetization process of a ferromagnetic
core and therefore the flux density depends on which part of the curve the ferromagnetic
core is magnetized on as this depends upon the circuits past history giving the core a form
of "memory". Then ferromagnetic materials have memory because they remain
magnetized after the external magnetic field has been removed. However, soft
ferromagnetic materials such as iron or silicon steel have very narrow magnetic hysteresis
loops resulting in very small amounts of residual magnetism making them ideal for use in
relays, solenoids and transformers as they can be easily magnetized and demagnetized.
Since a coercive force must be applied to overcome this residual magnetism, work must
be done in closing the hysteresis loop with the energy being used being dissipated as heat
in the magnetic material. This heat is known as hysteresis loss, the amount of loss
depends on the material's value of coercive force. By adding additive’s to the iron metal
such as silicon, materials with a very small coercive force can be made that have a very
narrow hysteresis loop. Materials with narrow hysteresis loops are easily magnetized and
demagnetized and known as soft magnetic materials.
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Anup Chandrashekhar Joshi