ELECTRICAL FUNDAMENTALS DGCA

Course - B1
3.11 – Inductance / Inductor Module-3

M.03 - ELECTRICAL
FUNDAMENTALS
Sub-Topic 3.11 –
Inductance/Indicator
Hours Allotted – 06 Hrs.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INTRODUCTION

o Inductor is a coil of wire with or without iron

core.
o It opposes rate of change of current.
o It stores energy in magnetic field.

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 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTOR SYMBOL

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 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FARADAY’S LAW OF ELECTROMAGNETIC

INDUCTION

o Faraday’s First Law

o Whenever a conductor cuts magnetic

flux, an e.m.f is induced in that
conductor. or, Whenever the magnetic
flux linked with a circuit changes an
e.m.f is always induced in it.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FARADAY’S LAW OF ELECTROMAGNETIC

INDUCTION

o Faraday’s Second Law

o The magnitude of the induced e.m.f is

equal to the rate of change of flux-
linkages. (When 1x108 lines of force are
cut per second, an e.m.f of 1volt will be
induced).

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FARADAY’S LAW OF ELECTROMAGNETIC

INDUCTION

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FARADAY’S LAW OF ELECTROMAGNETIC

INDUCTION

Where N is number of turn (-ve sign is to

show opposing direction
dΦ/dt is rate of change of flux OR

Change of flux/time
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FARADAY’S LAW OF ELECTROMAGNETIC

INDUCTION

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FARADAY’S LAW OF ELECTROMAGNETIC

INDUCTION

o The greater the number of magnetic field

lines cutting across the conductor, the
greater the induced voltage.

o The faster the field lines cut across the a

conductor or the conductor cuts across
the field lines, the greater the induced
voltage.
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

LENZ’S LAW

o This law states, in effect, that

electromagnetically induced current
always flows in such direction that the
action of the magnetic field set up by it
tends to oppose the very cause which
produces it.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

LENZ’S LAW

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

LENZ’S LAW

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTORS AFFECTING INDUCED EMF

o By experiment, the following factors may
be noted:

o The faster the magnet (or coil) is moved,

the greater is the deflection obtained on
the meter. This shows that the
magnitude of the emf is proportional to
the rate of relative movement.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTORS AFFECTING INDUCED EMF

o Repeating the experiment using a

stronger magnet results in greater meter
deflection for the same rates of
movement.

o Hence the magnitude of the emf is

proportional to the flux density.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTORS AFFECTING INDUCED EMF

o Reversal of the direction of motion

produces meter deflecting in the
opposite sense. The direction of the
induced emf therefore depends on the
direction of motion.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTORS AFFECTING INDUCED EMF

o Using the south pole of the magnet

instead of the north results in meter
deflections in the opposite sense,
showing that the direction of the induced
emf depends upon the direction of the
magnetic field.
o If more turns are used on the coil, meter
deflection is greater and is proportional
to the number of turns (N).
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTORS AFFECTING INDUCED EMF

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTORS AFFECTING INDUCED EMF

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTORS AFFECTING INDUCED EMF

o The induced emf can be either

o a. Dynamically induced emf

o The field is stationary and conductors

cut across it e.g. d.c. generators.
o E =Blv

o B= flux density, l =length of conductor,

v= velocity of conductor cutting flux
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTORS AFFECTING INDUCED EMF

o b. Statically induced emf

o The conductor or the coil remains

stationary and the flux linked with it is
changed by increasing or decreasing the
current producing this flux e.g.
transformers.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

STATICALLY INDUCED EMF

o (i) mutually induced e.m.f

o An e.m.f induced in one coil by the
influence of the other coil is called
mutually induced e.m.f.
o (ii) self-induced e.m.f.
o The counter e.m.f induced in a coil,
whenever there a change in the current
through it is called the self-induced
e.m.f.
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

SELF INDUCTANCE

o When current through a coil changes,

the changing flux induces an emf that
opposes the current flow.
o This emf is the result of self inductance
and is called ‘back emf’.
o The term ‘self inductance’ is often
replaced merely by inductance.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

SELF INDUCTANCE

o The value of back emf is given by:

o Back emf = - L(dI/dt)

o L = Inductance in henry
o dI/dt = rate of change of current

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTANCE

o If current changing at a rate of 1 amp a

second induces an emf of 1 volt then the
inductance is 1 henry.

o L = 1v/1amps per second

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTANCE

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTANCE

o All circuits have inductance even a

straight conductor, but if a straight piece
of wire is formed into a coil the number
of flux linkages increases and so does
the inductance.
o A further increase in inductance is
achieved by increasing the flux density.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTANCE

o This depends on the area, the length of

the coil and the permeability of material
in which flux is established,
L = µ0 µr N2A/l
µ0 - Absolute Permeability,
µr - Relative permeability of core
N - No. of turns,
A - Cross section area of coil
l - Length of coil.
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

PARAMETERS AFFECTING INDUCTANCE

o The number of turns.

o The cross-sectional area of the coil.

o The length of a coil.

o The core material around which the coil

is formed.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

MUTUAL INDUCTANCE

o If the changing flux in a coil links with

the turns of a second coil, the two coils
are said to be mutually coupled and
mutual inductance exists between them.

o The unit of mutual inductance is Henry

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

MUTUAL INDUCTANCE

o If the primary current, changing at a rate

of 1 amp per second, induces a
secondary voltage of 1v, then the mutual
inductance is 1 henry.

o Thus: Es = M × (dIP/dt)

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

MUTUAL INDUCTANCE

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

MUTUAL INDUCTANCE

M = µ0µrN1N2A/l
N1 =no of turns in primary
N2 = no of turns in secondary
A = area cross-section of coil
l = length of coil

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

COUPLING FACTOR

o If all the flux of a primary coil links with

all the turns of a secondary then 100%
coupling exists.
o Maximum Coupling (100%) is
represented by a k value of 1.
o Thus if flux linkage is 97% the coupling
factor is 0.97.
o M = K (L1L2 )

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

COUPLING FACTOR

o Where L1 and L2 are individual

inductance’s of the mutually coupled
coils.
o The value of k depends on:
o Purpose of coils involved
o Relative positions of the coils
o Frequency or rate of change of current
o and can be as high as 0.98 or as low as
0.0001.
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTOR AFFECTING MUTUAL INDUCTANCE

o number of turns in coil

o physical size of coil

o permeability of coil

o position of coils with respect to each

other

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

FACTOR AFFECTING MUTUAL INDUCTANCE

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

ENERGY STORED IN MAGNETIC FIELD

o If we consider the theoretical case of a

circuit with inductance only, all of the
energy used in the circuit must go into
the magnetic field.
o It can be shown that the energy stored
in the magnetic field is given by
equation:
o Energy stored = ½ L I2 joules

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

ENERGY STORED IN MAGNETIC FIELD

o As the current increases through an

inductor, flux builds up and energy is
stored in the magnetic field.
o On short circuiting an inductor, the
magnetic field collapses and the energy
is returned to the circuit in the form of an
emf that tries to maintain the current
flow.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

ENERGY STORED IN MAGNETIC FIELD

o If the circuit is open-circuited rather than

short-circuited by a resistor, as in the
case of the circuit studied (moving the
switch to B), then the collapsing flux will
produce a large back-emf that may
cause sparking across the switch
contacts as they are opened.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

ENERGY STORED IN MAGNETIC FIELD

o The sparks damage the contacts,

produce heat, could ignite fuel vapour
and transmit electromagnetic radiation
which interferes with communication and
navigation equipment.
o The large emf’s can also cause electric
shocks on what are considered safe, low
voltage d.c. circuits.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTORS IN DC CIRCUIT

o An inductance opposes any change in

current by producing a back emf.
o The back emf tries to prevent current
flow when the circuit is switched ‘ON’
and tries to maintain current flow when
the circuit is switched ‘OFF’.
o Current can therefore not rise instantly to
a maximum, or fall instantly to zero

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTORS IN DC CIRCUIT

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTORS IN DC CIRCUIT

By Kirchhoff’s voltage law

E - Eb = VR (Eb = back
emf)
but Eb = -L (dI/dt)
and VR = IR

hence E = L (dI/dt) - IR volts

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTORS IN DC CIRCUIT

o In the above equation, E, L and R are

constant, therefore as I increases,
dI/dt (the slope of the graph at any point)
must decrease.
o The current therefore follows a curve
whose gradient is continually decreasing
and which is called an ‘exponential
curve’.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

THE RL TIME CONSTANT

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 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

THE RL TIME CONSTANT

τ = L/R
Where:
τ = seconds
L = inductance (H)
R = Resistance (Ω)

A certain time is required for the current to

make a change from one value to another.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

THE RL TIME CONSTANT

o The time taken for a current to reach its

maximum value if the initial rate of
increase were maintained.

o The time taken for the current to reach

0.632 of its maximum value (or 63.2%).

o Maximum Current flows after 5L/R i.e.

After 5 time constant.
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

THE RL TIME CONSTANT

NOTE…..!!!!!!!

o When the current reaches its maximum

value it is no longer producing a
changing flux and therefore not
producing a back-emf.

o At this time, the whole supply voltage is

dropped across the resistor.
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTOR IN SERIES

o The same current flows through both

inductors and, therefore, both will be
subject to the same rate of change of
current.

o When inductors are connected in series,

the total inductance LT, is the sum of the
individual inductors.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTOR IN SERIES

LT = L₁ + L₂ + L₃ + … LN

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTOR IN SERIES

o If the coils are positioned so that the

mutual induced emf’s in each coil aid the
self induced emf’s then the coils are said
to be series aiding, and
o LT = L1 + L2 + 2M

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTOR IN SERIES

o If the coils are positioned so that

mutually induced emf’s in each coil
oppose the self induced emf’s, the coils
are said to be in series opposing, and
o LT = L1 + L2 - 2M

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTOR IN PARALLEL

o When inductors are connected in

parallel, the total inductance is less than
the smallest inductance.

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 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTOR IN PARALLEL

1/LT = 1/L1 + 1/L2.......1/LN

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 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

TYPES OF INDUCTOR

o Inductors are classified by the type of

core and the method of winding them.

o Most common core materials : Air,

solid ferrite, powdered ferrite, steel,
toroid and ferrite toroid.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

TYPES OF INDUCTOR

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

o Inductive reactance is a measure of how

much the countering EMF in the circuit
will oppose current variations.

o The inductive reactance of a component

is directly proportional to the inductance
of the component and the applied
frequency to the circuit.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

XL = 2πfL

Where:
XL = inductive reactance in ohms
L = inductance in henry
f = frequency in cycles per second
π = 3.141 6

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 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

o When the current is a.c. and constantly

changing in value, the result is that it
always lags behind the supply voltage.
For a pure inductance the angle of lag is
90º.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

Back-emf = - L × Rate of Change of

Current
Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy
 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

o The rate of change of current in the

circuit is dependent on frequency of AC
supply.
o As frequency increases, XL will
increase and so current flow will
decrease.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

o The rate of change of current in the

circuit is dependent on frequency of AC
supply.
o As frequency increases, XL will
increase and so current flow will
decrease.

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy

 ELECTRICAL FUNDAMENTALS DGCA
Course - B1
3.11 – Inductance / Inductor Module-3

INDUCTIVE REACTANCE

XL = V/I

Issue Date : 29-07-20 Revision : 1 Prepared by : Suajy