Module No. 29

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Module # 29
Dielectric, Induction & EMF
Dielectric
The insulating material between the metal plates of a capacitor is
called dielectric and is of great importance in the design and
construction of capacitors. Different dielectrics create different
values of capacitance.
Dielectric Strength
For every dielectric there is a potential that if applied across the
dielectric, the bonds within the dielectric will be broken and
current will flow. It is the voltage per unit length (electric field
intensity) which establishes conduction in a dielectric.
When potential difference applied across opposite sides of a
sheet of insulating material is gradually increased, a point is
reached when there is a spark discharge and the insulation
breaks down. This is the breakdown voltage and the potential
gradient necessary to cause breakdown is called dielectric
strength.
Permittivity
Permittivity is the ability of an insulating material to concentrate
electric flux. It is the ratio of electric flux density to electric field

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strength. If flux density is D and electric field strength E, then
D/E = Є
Permittivity of Free Space
In equation, Fe = K q1q2 /r2 if we take Fe=1N, q1=q2=1C & r =1m,
the value of constant K turns out to be, K=8.98742×109
N-m2
C-2
≈
9×109
N-m2
C-2
. The constant K is generally expressed in terms of
another quantity known as permittivity of the free space εο such
that K = 1/ 4πεο = 9×109 N-m2C-2 .
Dielectric Constant or Relative Permittivity
The relative permittivity or dielectric constant of a medium is equal
to the ratio of the capacitance of a given capacitor with the
medium as dielectric to the capacitance of the capacitor with a
vacuum as the dielectric.
OR
The dielectric constant or relative permittivity is also defined as
the ratio of the capacitance of a capacitor with an insulating
material as dielectric to the capacitance of the same capacitor
with air as dielectric.
The dielectric constant of vacuum is defined as 1, and that of air
is very close to 1. These values are used as a reference and all
other materials have values of εr specified with respect to that of

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vacuum or air.
Relative permittivity or dielectric constant is a dimensionless
number, represented by Єr. Its value is unity in vacuum. The
product of electric space constant and relative permittivity is
called absolute permittivity.
Є = ЄοЄr Farad/ meter
The Є is the Greek letter, epsilon. The Єr is the relative
permittivity and depends upon the material used as dielectric.
The value of absolute permittivity εo is 8.85 x 10-12 F/m (farads per
meter).
Permeability
Permeability of a material is a measure of the ease with which
magnetic flux is established in the material. The permeability of
iron is greater than that of air.
The cores of different materials with the same physical
dimensions are magnetized differently. The magnetic strength
varies in accordance with core material. This variation in strength
is due to the greater or lesser number of flux lines passing
through the core. Materials in which flux lines can easily be set
up are said to have high permeability.
The permeability of free space or magnetic space constant is the

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constant value of permeability for a magnetic circuit consisting of
vacuum or air or non-magnetic medium. It is denoted by the
symbol μο. It is a measure of the flux density established in space
by one ampere-turn per unit length or by unit magnetizing force,
that is,
μο = B / H
The ratio between flux density (B) and the field intensity (H) is
called the permeability of the core. In any ferromagnetic
substance, permeability is not a constant quantity but one that
depends upon the intensity of the field.
Relative Permeability
The ratio of the permeability of a material to that of free space is
called its relative permeability, denoted by the symbol μr, that is
μr = μ / μο
In general, for ferromagnetic material, μ ≥ 100, and for non-
magnetic materials μr = 1.
Absolute Permeability
For any material, the ratio of the flux density (B) to the
magnetizing force (H) is known as the absolute permeability, that
is

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μ = B / H or B= μH= μο μr H
Permeance
It is the reciprocal of reluctance and resembles electrical
conductance. Its unit is henry.
Reluctance
The reluctance of a magnetic circuit is directly proportional to the
length of the flux path and inversely proportional to the cross-
section and permeability of the material.
The ratio of the magneto motive force required to establish a
given flux to the amount of flux is called reluctance of magnetic
circuit. It is denoted by the symbol S and its units are ampere -
turns per Weber. The reluctance is analogous to the resistance in
electrical circuits.
If a magnetic circuit consists of several parts in series, then total
reluctance is
S = S1+S2+S3 +.............
Reluctance is the opposition offered by a substance to the
magnetic flux. Thus, resistance to magnetic lines of force is called
Reluctance.

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Air (& vacuum) has very high reluctance and low permeability
while ferrous materials (such as iron and steel) have very low
reluctance and very high permeability.
Reluctivity
It is specific reluctance and corresponds to electrical resistivity
which is 'specific resistance'.
Induction
A material is magnetized through induction.
Induced Magnetism
If we place a piece of un-magnetized magnetic material in the
magnetic field of a magnet, the attraction between the external
magnet and the molecules of the magnetic substance causes the
molecules to line up in a direction. Thus, the material is
magnetized. Magnetism produced in this way is called induced
magnetism.
Magnetic Induction
The magnetic Induction is equal to the force exerted on a wire of
length one meter carrying one Ampere current placed at right
angle to the field. The SI unit of magnetic induction is
Newton/Ampere-Meter. It is also called Tesla (T). When the
magnetic fields are small, a smaller unit called Gauss (G) is also

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used. The two units are related as below:
1T = 10,000 G
Electromagnetic Induction
One of the most important applications of electromagnetic
induction is in the form of a transformer.
It was discovered by Oersted in 1820 that an electric current
flowing through a conductor can create a magnetic field. Can a
magnetic field create an electric current in a conductor? In 1831,
Michael Faraday, the famous English scientist, discovered that an
electric current can be produced by means of a magnetic field.
The process is named as electromagnetic induction.
Thus, the phenomenon of inducing the current or emf by changing
the magnetic flux is called electromagnetic induction.
Mutual Induction
In an electrical circuit, a change of current is always accompanied
by a change in the magnetic field surrounding the circuit. If the
current is increasing the field is said to be expanding. If the
current is decreasing the field is said to be collapsing or
decreasing in intensity. When a conductor is placed within a
magnetic field in which the expanding or collapsing lines of force
cut the conductor, a voltage will be induced in it.

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Inductance
Self-induction or inductance is the property of a circuit by virtue of
which an emf is established when the current changes. In a pure
inductance applied voltage leads the current by 90 degrees.
The unit of inductance is henry (H). In a pure inductance no net
power is taken from the supply over the cycle.
Mutual Inductance
When two coils are so located that a change of current in one coil
will cause a change of flux linkage in a second coil, they are said
to have mutual inductance. The coil in which the current is
changing is called the primary coil whereas the second coil in
which the flux linkage is changed and emf is induced is known as
the secondary coil.
Mutual inductance (M) is measured in henry. Two coils have a
mutual inductance of 1 henry if a change in current at the rate of 1
ampere per second in one coil results in a voltage of 1 volt being
induced in the other coil.
Self-Inductance
The phenomenon in which an electric circuit opposes any change
of current in itself is known as self-inductance. In other words, it is

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the ability of a conductor to induce voltage in itself when the
current changes itself.
We know that an emf is induced in a coil whenever the magnetic
flux linked with the coil changes no matter what causes this
change of flux. The change of flux may be due to change of
current in the coil.
Units of Self-Inductance
The unit of self-inductance is henry. The self-inductance of a coil
is one henry if current changes at the rate of one ampere per
second through it which causes an induced emf of one volt in
itself.
Effect of Iron Core in a Coil
When an iron core is inserted into a coil, a much greater amount
of flux is produced with the same magneto motive force. This is
because of much greater permeability of iron as compared to air.
When a coil is placed around an iron core, very powerful magnets
called electromagnets may be made.
Soft iron is the material usually used for the core of an
electromagnet because of its high permeability. The strength of
an electromagnet with a given number of turns on the exciting coil
may be varied by varying the amount of current through the coil.

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This is the method of varying the amount of flux, and hence the
amount of generated emf, in a generator.
Electromagnets are largely used in electrical machinery. One
important application is in the generator. Electromagnets are also
used as lifting magnets. They are used in relays, circuit breakers,
motor brakes, etc.
Tesla & Gauss
The magnetic induction is said to be one tesla, if a charge of one
coulomb moving at right angle to the magnetic field with a velocity
of one meter per second experiences a force of one Newton.
The magnetic induction is equal to the force exerted on a wire of
length one meter carrying one ampere current placed at right
angle to the field. The SI unit of magnetic induction is
newton/ampere-meter. It is also called tesla T. When the
magnetic fields are small, a smaller unit called gauss (G) is also
used. The two units are related as below:
1T = 104
G
Quality Factor (Q)
In the resonant circuits, the quality factor has a great importance.
It is the ratio of the reactive power of the inductance or the
capacitance to the power of the resistance, at resonance.

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Thus,
Q = reactive power / resistive power
Rule for the Polarity of a Coil Carrying a Current
When viewing one end of the coil, it will be of N polarity if the
current is flowing in an anticlockwise direction and of S polarity if
the current is flowing in a clockwise direction.
Field Due to Current in Solenoid
A solenoid is constructed by winding wire in a helix around a
cylindrical surface. The turns of the winding are ordinarily closely
spaced and may consist of one or more layers. A solenoid is a
coil whose axial length is greater than its diameter. A wire can be
moved into a coil to concentrate the magnetic field into a small
package. Such a coil is called solenoid.
A toroid is a solenoid that has been bent into a circle.
Henry
Mutual inductance is measured in the same units as self-
inductance. Thus, when a rate of change of one ampere per
second in the primary coil will produce one volt in the secondary
coil, the two coils are said to have mutual inductance of one
henry. However small units milli-henry (10-3
henry) and micro-
henry (10-6
henry) are commonly used.

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Electromotive Force
The electromotive force of a cell is regarded as being equal to the
potential difference across its terminals when it is not producing
current in a circuit.
The electric power used in our homes and industries generated at
the power station is produced on the principle of emf induced due
to changing flux of a magnetic field.
When a source of electrical energy, say a cell, is connected to an
electric circuit, a current flows through the circuit and itself. The
energy required to drive the charge around the circuit is called
electromotive force and is defined as the potential energy applied
per unit charge. Its unit is volt.
Potential energy supplied
e.m.f. = -------------------------------------
Charge
The devices which can maintain a potential difference between
two points to which they are attached are known as sources of
electromotive force.
A source of emf must be able to do work on charge carriers that
enter it.

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Clearly the unit of emf is joule / coulomb which is volt. Thus, we
can say that a battery has an emf of 1 volt if work done in
transporting one coulomb charge through the source from
negative to positive terminal is one joule.
In all kinds of sources of emf, some kind of energy is transformed
into electrical energy. A few examples are given below:
(1) Batteries or cells convert chemical energy into electrical
energy.
(2) Electrical generators convert mechanical energy into
electrical energy.
(3) Thermocouples convert heat energy into electrical energy.
(4) Photo voltaic cell converts light energy into electrical energy.
Dynamically Induced EMF
Dynamically induced emf is the emf produced when a conductor
and a magnetic field are relatively moved. Thus, when a
conductor and a magnetic field have relative motion between
them, an emf is induced in the conductor. The emf induced in this
way is called dynamically induced emf. The magnitude of emf
induced may be determined by equating the electrical power
generated in the conductor to the mechanical power expended in
moving it.

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Statistically Induced emf
Statistically induced emf is the emf produced when the flux
changes due to change in current. Thus, when current in a
conductor is changed, keeping the conductor stationary, the flux
linked with it is changed. When current increases, the flux also
increases and a decrease in current results in a decrease in flux.
The emf induced due to this change of flux is called statically
induced emf. When the magnetic flux linking a coil is changed, an
emf is induced in the coil whose direction is given by the Lenz’s
law. Such an emf is called the emf of self-induction. If there are
two coils linking the varying flux produced by current flowing in
one of them, an emf induced in the second coil is known as emf of
mutual induction. The principle of mutual induction is the basis for
transformers.
Sinusoidal EMF
We know that a coil which rotates in a magnetic field gives rise to
a sinusoidal emf. This is the type of voltage and current that is
commercially supplied. All sinusoidal currents and voltages have
an average value of zero over one or more complete cycles.

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Difference between Potential Difference and E.M.F
A source of emf in a circuit does work on the moving charges
whereas the potential difference is the work done by the charges
in passing through the circuit.
Electromotive Force of a Cell
The e.m.f. of a cell in volts is defined as the total work done in
joules per coulomb of electricity conveyed in a circuit in which the
cell is connected.
Resistance Vs Reactance
Resistance and reactance together determine the magnitude and
phase of the impedance through the following relations:
Resistance
Resistance R is the real part of impedance; a device with a purely
resistive impedance exhibits no phase shift between the voltage
and current.

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Reactance
Reactance X is the imaginary part of the impedance; a
component with a finite reactance induces a phase shift θ
between the voltage across it and the current through it.
Reactance X is a measure of the opposition of capacitance and
inductance to current. Reactance varies with the frequency of the
electrical signal. Reactance is measured in ohms, symbol Ω.
There are two types of reactance: capacitive reactance (Xc) and
inductive reactance (XL).
The total reactance (X) is the difference between the two:
X = XL – XC
Capacitive Reactance, Xc
Xc = 1/2 fC
Where Xc = reactance in ohms (Ω)
f = frequency in hertz (Hz)
C = capacitance in farads (F)
Xc is large at low frequencies and small at high frequencies
(inversely proportional).

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For steady DC which is zero frequency, Xc is infinite (total
opposition), hence the rule that capacitors pass AC but block DC.
Inductive Reactance, XL
Inductive reactance is the opposition offered by the inductance to
current.
The unit of inductive reactance is ohm (Ώ).
XL = 2 fL
Where XL = reactance in ohms (Ω)
f = frequency in hertz (Hz)
L = inductance in henrys (H)
XL is small at low frequencies and large at high frequencies.
For steady DC (frequency zero), XL is zero (no opposition),
hence the rule that inductors pass DC but block high frequency
AC.
Inductive Susceptance, Conductance and Admittance
As conductance is the reciprocal of resistance, susceptance is the
reciprocal of reactance and admittance is the reciprocal of
impedance.
For RL parallel circuits, conductance, inductive susceptance and
admittance are expressed as

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G =1/R
BL =1/XL
Y =1/Z
Where G, BL and Y are the conductance, inductive susceptance
and admittance respectively. The units for G, BL and Y are the
siemen (s), which is the reciprocal of the ohm.
Conductance
The units of conductance and susceptance are Siemens(S).
It is reciprocal of resistance and may be defined as being that
property of a circuit or of a material which tends to permit the flow
of current (electricity), or it may be defined as:
Conductance is a measure of the ability of an electric circuit to
pass current. The letter symbol for conductance is G. The SI unit
of conductance is the siemens. (In the English system of
measurement, the unit of conductance was the mho). The unit
symbol for Siemens is S.
A good conductor offers a low resistance and a poor conductor
offers a high resistance. The term conductance is, therefore, used
as the opposite resistance and it follows that as resistance goes
down, conductance goes up.

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Admittance
The admittance is the reciprocal of impedance. It is the ease with
which an alternating current can flow in a circuit. When a voltage
V is applied to a circuit, a current I flows in the circuit given by
I = V/Z
where Z is the impedance of the circuit.
The reciprocal of impedance, that is, 1/Z is denoted by letter Y
and is called admittance.
The equation I = V/Z can be written as I = VY
In SI the unit of admittance, conductance and susceptance is
Siemens (S).
Impedance
The impedance is the opposition to sinusoidal current in a circuit,
as resistance is the opposition to direct current. So we can write
Ohm’s Law for RL circuit as,
Z = V/I
The current in an ac circuit is directly proportional to the voltage
across the circuit and inversely proportional to the impedance of
the circuit.
The resistance and inductive reactance must be combined at right

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angles to each other to obtain the impedance.
The resistance and the capacitive reactance must be combined at
right angles to each other to obtain the impedance. The right
triangle obtained in this way is called the impedance triangle.
The angle by which the current leads the applied voltage is the
phase angle ф.
In an alternating current circuit impedance opposes the current.
The unit of impedance is ohm (Ώ).

Module No. 29

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Module No. 29