Notesale: Turn your study into money

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Electrical Engineering
Chapter – 1
...
Capacitor Circuit






Capacitor Circuit
Types of capacitors
Electrostatc thoery
Energy stored in a capacitor
Capacitor in serieal and parallel

Chapter – 3
...
A C Circuit







A C Thoery
Resistance, Reactance and impedance
Pharors
Reactive Circuit
Resonant circuit
Power Factor

Chapter – 5
...
DC Genrator



Working Principle
Saprate, shunt and Compound

Chapter – 7
...
Phase Thoery






Single Phase
Three Phase motor
Balanced Load
Star and Delta
Synchronous motor

Chapter – 9
...
Transformer





Transformer Principle
Core Loss
Losses in a Transformer
Efficiency

Chapter – 11
...
Registers
Registers types and color codes

A register is a very small amount of very fast memory that is built into the CPU (central
processing unit) in order to speed up its operations by providing quick access to commonly
used values
...
e
...
e
...

Registers are the top of the memory hierarchy and are the fastest way for the system to
manipulate data
...

Registers are used to store data temporarily during the execution of a program
...
Data and instructions must be
put into the system
...

The basic computer registers with their names, size and functions are listed below
Register
Symbol
AC
DR
TR

Register Name

Number
Bits
16
16
16

AR
PC

Accumulator
Data Register
Temporary
Register
Instruction
16
Register
Address Register 12
Program Counter 12

INPR
OUTR

Input Register
Output Register

IR

8
8

of

Description
Processor Register
Hold memory data
Holds temporary Data
Holds Instruction Code
Holds memory address
Holds address of next
instruction
Holds Input data
Holds Output data

Components and wires are coded are with colors to identify their value and function
...
All 5-band resistors use a colored tolerance band
...


Example
...

Example
...
2 Ω with a tolerance of +/- 10%
...
3

A resistor colored White-Violet-Black would be 97 Ω with a tolerance of +/- 20%
...

Example
...
3 kΩ with a tolerance of
+/- 0
...

Example
...
58 Ω with a tolerance of +/2%
...
6

A resistor colored Blue-Brown-Green-Silver-Blue would be 6
...
25%
...
A student of Physics has written such formulas down
so many times that they have memorized it without trying to
...
In the
field of Modern Physics, there is E = m • c2
...
In the field of Wave Mechanics, there is v = f • λ
...

The predominant equation which pervades the study of electric circuits is the equation
ΔV = I • R
In words, the electric potential difference between two points on a circuit (ΔV) is
equivalent to the product of the current between those two points (I) and the total
resistance of all electrical devices present between those two points (R)
...
Often referred to as the Ohm's lawequation, this equation is a powerful
predictor of the relationship between potential difference, current and resistance
...
Yet while this equation serves as
a powerful recipe for problem solving, it is much more than that
...
The current in a circuit is
directly proportional to the electric potential difference impressed across its ends and
inversely proportional to the total resistance offered by the external circuit
...
e
...
And the greater
the resistance, the less the current
...
In fact, a twofold increase in the
battery voltage would lead to a twofold increase in the current (if all other factors are kept
equal)
...


Electric Power

Electric Power
Electric power is the rate of energy consumption in an electrical circuit
...

 Electric power definition
 Electric power calculation
 Power of AC circuits
 Power factor
 Power calculator
Electric power definition
The electric power P is equal to the energy consumption E divided by the consumption time
t:

P is the electric power in watt (W)
...

t is the time in seconds (s)
...

Solution:
E = 120J
t = 20s
P = E / t = 120J / 20s = 6W
Electric power calculation
P=V·I
or
P=I2·R
or
P=V2/R
P is the electric power in watt (W)
...

I is the current in amps (A)
...

Power of AC circuits
The formulas are for single phase AC power
...
73)
...


Real power
Real or true power is the power that is used to do the work on the load
...

Reactive power
Reactive power is the power that is wasted and not used to do work on the load
...

Apparent power
The apparent power is the power that is supplied to the circuit
...

However, sometimes in complex circuits such as bridge or T networks, we can not simply
use Ohm’s Law alone to find the voltages or currents circulating within the circuit
...

In 1845, a German physicist, Gustav Kirchoff developed a pair or set of rules or laws
which deal with the conservation of current and energy within electrical circuits
...

Kirchoffs First Law – The Current Law, (KCL)
Kirchoffs Current Law or KCL, states that the “total current or charge entering a junction
or node is exactly equal to the charge leaving the node as it has no other place to go except
to leave, as no charge is lost within the node“
...

This idea by Kirchoff is commonly known as the Conservation of Charge
...
Then this means we can also
rewrite the equation as;
I1 + I2 + I3 – I4 – I5 = 0
The term Node in an electrical circuit generally refers to a connection or junction of two
or more current carrying paths or elements such as cables and components
...
We can use Kirchoff’s
current law when analysing parallel circuits
...
In other words the algebraic sum of all voltages within the loop must be
equal to zero
...

Kirchoffs Voltage Law

Starting at any point in the loop continue in the same direction noting the direction of all
the voltage drops, either positive or negative, and returning back to the same starting
point
...
We can use Kirchoff’s voltage law when
analysing series circuits
...
These terms are used frequently in
circuit analysis so it is important to understand them
...

Path – a single line of connecting elements or sources
...
A node is indicated by a dot
...

Loop – a loop is a simple closed path in a circuit in which no circuit element or node
is encountered more than once
...
There are no
components inside a mesh
...

Components are said to be connected in Parallel if the same voltage is applied across
them
...

Using Kirchoffs Current Law, KCL the equations are given as;
At node A : I1 + I2 = I3
At node B : I3 = I1 + I2
Using Kirchoffs Voltage
Loop 1 is given as :
Loop 2 is given as :
Loop 3 is given as :

Law, KVL the equations are given as;
10 = R1 x I1 + R3 x I3 = 10I1 + 40I3
20 = R2 x I2 + R3 x I3 = 20I2 + 40I3
10 – 20 = 10I1 – 20I2

As I3 is the sum of I1 + I2 we can rewrite the equations as;
Eq
...
No 2 : 20 = 20I2 + 40(I1 + I2) = 40I1 + 60I2

We now have two “Simultaneous Equations” that can be reduced to give us the values
of I1 and I2
Substitution of I1 in terms of I2 gives us the value of I1 as -0
...
429 Amps
As : I3 = I1 + I2
The current flowing in resistor R3 is given
as : -0
...
429 = 0
...
286 x 40 = 11
...
In fact, the 20v battery is charging the 10v battery
...
Assume all voltages and resistances are given
...
)
2
...
( I1, I2, I3 etc
...
Find Kirchoff’s first law equations for each node
...
Find Kirchoff’s second law equations for each of the independent loops of the circuit
...
Use Linear simultaneous equations as required to find the unknown currents
...
In the next tutorial about DC circuits, we will look at Mesh Current
Analysis to do just that
...
The current is the same through each resistor
...


A series circuit is shown in the diagram above
...
If the values of the three resistors are:

With a 10 V battery, by V = I R the total current in the circuit is:
I = V / R = 10 / 20 = 0
...
The current through each resistor would be 0
...


Registers in Parallel

For resistors placed in parallel, the arithmetic is a little more complicated because the
reciprocal of the total resistance is equal to the sum of the reciprocals of the constituent
resistors:

Resistors in parallel
As the voltage across all the resistors is the same and the current is shared
according to the resistance of the individual resistors, the formula for calculating the overall
resistance of the resistors in parallel is more complicated than the series resistor case and
becomes:

A parallel circuit is a circuit in which the resistors are arranged with their heads
connected together, and their tails connected together
...
The voltage across each resistor in parallel is the same
...


A parallel circuit is shown in the diagram above
...
If
the values of the three resistors are:

With a 10 V battery, by V = I R the total current in the circuit is: I = V / R = 10 / 2 = 5 A
...
The voltage across each resistor is
10 V, so:
I1 = 10 / 8 = 1
...
25 A
I3=10 / 4 = 2
...

A parallel resistor short-cut
If the resistors in parallel are identical, it can be very easy to work out the equivalent
resistance
...
So, two 40-ohm resistors in parallel are
equivalent to one 20-ohm resistor; five 50-ohm resistors in parallel are equivalent to one
10-ohm resistor, etc
...

Here's a way to check your answer
...
The equivalent resistance will always be between the
smallest resistance divided by the number of resistors, and the smallest resistance
...

You have three resistors in parallel, with values 6 ohms, 9 ohms, and 18 ohms
...

Doing the calculation gives 1/6 + 1/12 + 1/18 = 6/18
...


Internal Resistance

The electromotive force (e) or e
...
f
...
It is equal to the potential
difference across the terminals of the cell when no current is flowing
...
When electricity flows round a circuit the internal resistance of the cell itself resists the
flow of current and so thermal (heat) energy is wasted in the cell itself
...
This is the potential difference across the terminals of the cell when current is flowing in
the circuit, it is always less than the e
...
f
...


Diode

Diode resistance is the resistance which a diode offers in a circuit
...

Unlike resistors, though, diodes are not linear devices
...
It changes parabolically
...
It does not vary
when either voltage or current is changed in a circuit
...

The resistance can be calculated by the formula,R=V/I
...
Diodes are not linear devices; they are
nonlinear
...
Their resistance changes based on the voltage and current that
falls across them
...

And diode resistance does not change in a linear sense, but in a parabolic sense
...

The diode has 2 key resistance change periods, at the breakdown voltage and at the
threshold voltage
...
The threshold voltage is the voltage where the diode has enough voltage
to conduct a large amount of current through it
...
The threshold voltage is normally 0
...
3V for germanium diodes
...
Resistance does not change much until the diode reaches
the breakdown voltage
...
The breakdown voltage is the voltage which the diode has
received the maximum reverse voltage that a diode can withstand
...

Diodes are meant to only pass current when forward biased
...

Diode Resistance Formula
The resistance of diodes is equal to the below formula:

Diode resistance is equal to the thermal voltage, VT, divided by the current, Id, passing
through the diode
...

The precise formula to calculate thermal voltage is:

VT= kT/q
Where k is the Boltzmann constant, T is the absolute temperature of the pn junction,
and q is the magnitude of the electron charge
...

The current passing through the diode can be calculated according to the formula:

This formula can be used to calculate diode current
...
Connect the probes in series with the circuit and then
read the amount of current
...


Chapter – 2
...
This
component consists of two conductors which are separated by a dielectric medium
...
The circuit symbol of a capacitor is shown below:

The capacitance or the potential storage by the capacitor is measured in Farads which is
symbolized as ‘F’
...

The charge stored in a capacitor is given by
Q = CV
Where Q - charge stored by the capacitor
C - Capacitance value of the capacitor
V - Voltage applied across the capacitor
Note the other formula of current,
I = dQ/dt
Taking the derivative with respect to time,
dQ/dt = d(CV)/dt
From the above statement, we can express the equation as
I = C (dV/dt)
As you turn on the power supply, the current begins to flow through the capacitor
inducing the positive and negative potentials across its plates
...
Once the capacitor is fully charged at the end of this phase,
it gets open circuited for DC
...
The charging and discharging of the capacitor is given by a time constant
...


The conductors offer a series resistance and if the capacitor is constructed using tubular
structure then some inductance is also induced
...


Types of capacitors

1
...
They are available in almost any value and voltages as high as 1500
volts
...
01%
...
There are two types of film capacitors, radial lead
type and axial lead type
...
The film capacitor is shown in figure below:

Film Capacitors are sometimes called plastic capacitors because which use
polystyrene, polycarbonate or Teflon as their dielectrics
...
The film capacitors are
physically larger and more expensive, they are not polarized, so they can be used in AC
voltage applications, and they have much more stable electrical parameters
...

2
...
This gives the many properties including a low loss factor, and a
reasonable level of stability, but this depends upon the exact type of ceramic used
...
1 µF
...
This type of
ceramic capacitor is extensively for applications like decoupling and coupling applications
...
The more commonly seen types include:
COG: Normally used for low values of capacitance
...

X7R: Used for higher capacitance levels as it has a much higher dielectric constant than
COG, but a lower stability
...

3
...
Here instead of using a very thin metallic film layer for one of the electrodes, a
semi-liquid electrolyte solution in the form of a jelly or paste is used which serves as the
second electrode (usually the cathode)
...
This insulating layer is
so thin that it is possible to make capacitors with a large value of capacitance for a small
physical size as the distance between the plates, d is very small
...
e
...

All polarised electrolytic capacitors have their polarity clearly marked with a negative
sign to indicate the negative terminal and this polarity must be followed
...
One main disadvantage of electrolytic capacitors is their relatively
low voltage rating and due to the polarisation of electrolytic capacitors, it follows then that
they must not be used on AC supplies
...


a
...
The thickness of the aluminium oxide film and high breakdown
voltage give these capacitors very high capacitance values for their size
...
This anodizing
process sets up the polarity of the plate material and determines which side of the plate is
positive and which side is negative
...
This gives a smaller sized capacitor than a plain foil type of equivalent value
but has the disadvantage of not being able to withstand high DC currents compared to the
plain type
...
Typical values of
capacitance for an aluminium electrolytic capacitor range from 1uF up to 47,000uF
...
But
aluminium electrolytic’s are “polarised” devices so reversing the applied voltage on the leads
will cause the insulating layer within the capacitor to become destroyed along with the
capacitor
...

Since the electrolyte has the properties to self-heal a damaged plate, it also has the
ability to re-anodize the foil plate
...
Since the electrolyte has the ability to conduct
electricity, if the aluminium oxide layer was removed or destroyed, the capacitor would
allow current to pass from one plate to the other destroying the capacitor, “so be aware”
...
Tantalum Electrolytic Capacitors
Tantalum Electrolytic Capacitors and Tantalum Beads, are available in both wet (foil)
and dry (solid) electrolytic types with the dry or solid tantalum being the most common
...


The dielectric properties of tantalum oxide is also much better than those of
aluminium oxide giving a lower leakage currents and better capacitance stability which
makes them suitable for use in blocking, by-passing, decoupling, filtering and timing
applications
...
Solid tantalum capacitors are usually used in circuits where the AC
voltage is small compared to the DC voltage
...
Generally, the positive lead is identified on the capacitor body by
a polarity mark, with the body of a tantalum bead capacitor being an oval geometrical
shape
...

Aluminium & Tantalum Electrolytic Capacitor

4
...
This type of capacitors utilized to set frequency of resonance in LC
circuits, for instance, to adjust the radio for impedance matching in antenna tuner devices
...
A
branch of electromagnetism, which deals with the interaction of electric charges when all
the charges are stationary is called as electrostatics
...
This charge can be positive or negative and
unlike charges attract each other, whereas like charges repel each other
...
In all
substances, the charges are building blocks of an atom
...
The charge on the electron is negative, which revolves around the
nucleus
...
e
...
So the nucleus contains the positively charged proton and neutrons, which are
electrically neutral as shown in below figure
...
This neutral condition of
some of the atoms of a body is disturbed when the body is charged either by subtracting or
adding one or more electrons
...
Two particles with charges of same
polarities repel each other and with same polarity attract each other
...
He determined a direct
relationship between the two point charges which are separated by a small distance
...
This interaction is a non-contact force acts over some distance of separation
...

Coulomb’s law states that the magnitude of the electrostatic force that exist between
the two point charges is directly proportional to the scalar product of the magnitudes of
point charges and inversely proportional to the square of the distance between the point
charges
...
This force is repulsive, if the two point charges are of the same sign and the
force is attractive if they are of opposite sign
...


If the Q1 and Q1 are the two point electric charges at rest and are separated by a
distance r then the force exerted on each other given as
F = K (Q1 × Q2)/r2
Where

F = force in newtons

Q = charge in coulombs
r = distance in meters and
K is the constant which has the value
K = 1/ 4 π єo
єo is the permittivity of free space and its measured value is
єo = 8
...
987 × 109 Nm2 C-2
But for most numerical applications, this value is considered as 9 × 109 Nm2 C-2
The above force equation only gives the magnitude of the force between the two
points, but does not give any indication of direction
...
The above figure shows the two point charges separated by the
unit vectors
...


Energy stored in a capacitor

The energy stored on a capacitor can be expressed in terms of the work done by the
battery
...
The voltage V is proportional to the amount of charge which is already on the
capacitor
...


Capacitor in series and parallel

When capacitors are connected in series, the total capacitance is less than any one of
the series capacitors? individual capacitance's
...
As we've just seen, an increase in plate
spacing, with all other factors unchanged, results in decreased capacitance
...
The formula for calculating the series total capacitance is
the same form as for calculating parallel resistances:

When capacitors are connected in parallel, the total capacitance is the sum of the
individual capacitors capacitance's
...
As we've just seen, an increase in plate area, with all
other factors unchanged, results in increased capacitance
...
The formula for calculating the parallel total capacitance is the same form
as for calculating series resistances:

As you will no doubt notice, this is exactly opposite of the phenomenon exhibited by
resistors
...
With capacitors, its the reverse: parallel
connections result in additive values while series connections result in diminished values
...
Electromagnet Magnetism

Magnetic Circuit

Magnetic circuit, closed path to which a magnetic field, represented as lines of
magnetic flux, is confined
...

In a ring-shaped electromagnet with a small air gap, the magnetic field or flux is
almost entirely confined to the metal core and the air gap, which together form the
magnetic circuit
...
Each magnetic field line makes a complete unbroken loop
...
If the flux is divided, so that part of it is confined to a portion of the
device and part to another, the magnetic circuit is called parallel
...


In analogy to an electric circuit in which the current, the electromotive force
(voltage), and the resistance are related by Ohm’s law (current equals electromotive force
divided by resistance), a similar relation has been developed to describe a magnetic circuit
...
The magnetomotive force,
mmf, is analogous to the electromotive force and may be considered the factor that sets up
the flux
...
If either the current through a coil (as in an electromagnet) or
the number of turns of wire in the coil is increased, the mmf is greater; and if the rest of the
magnetic circuit remains the same, the magnetic flux increases proportionally
...
Reluctance depends on the geometrical and material properties of the circuit that
offer opposition to the presence of magnetic flux
...
Iron, for example, has an
extremely high permeability as compared to air so that it has a comparatively small
reluctance, or it offers relatively little opposition to the presence of magnetic flux
...
In a magnetic circuit, in summary, the magnetic
flux is quantitatively equal to the magnetomotive force divided by the reluctance
...
Unlike a permanent magnet, the
strength of an electromagnet can easily be changed by changing the amount of electric
current that flows through it
...

An electromagnet works because an electric current produces a magnetic field
...
The magnetic field can be strengthened even more by
wrapping
the
wire
around
a
core
...
Normally, the atoms in something
like a lump of iron point in random directions and the individual magnetic fields tend to
cancel each other out
...
All of their
little magnetic fields add together, creating a stronger magnetic field
...
At least, up to a point
...
At this point, the magnet is said to be
saturated and increasing the electric current flowing around the core no longer affects the
magnetization of the core itself
...
A definition of B requires a consideration of the forces
produced by electromagnetic fields
...
A very
good demonstration is the so-called catapult field experiment in which a wire carrying a d
...

current can be made to move in the field of two flat magnets
...
Notice that the wire moves away from the area of highest field intensity (where the
magnetic field lines are closest) to a region lower intensity
...
The force is given by the equation:

Force on current in magnetic field:
F = BIL sin θ
The units for B are tesla (T)
...
This
gives the greatest force on the wire
...

Fleming's left- hand rule gives the direction of motion for the case when field and
current are at right angles (see diagrams below)
...

For a large permanent magnet of the type used in schools the flux density between the
poles is about 1 T, magnadur magnets have a flux density of some 0
...

Having defined B we can express the magnetic flux passing through a surface as BA
where A is the area of the surface at right angles to the field
...

Magnetic flux (φ) = Magnetic flux density (B) x Area (A

Genrator Principle

An Electrical Generator is a device that produces an Electromotive Force (e
...
f
...
Figure 1 is one type of Generators
...


Operation principle of a Generator is based on Electromagnetic Induction, which is
defined by Faraday?s Law, which states:

The Electromotive Force, Eemf, induced in a Coil is proportional to the number of turns,
N, in the Coil and the Rate of Change, dΦ / dt, of the number of Magnetic Flux Lines, Φ,
passing through the surface (A) enclosed by the Coil
...

In the Generator, the Coil is under a Stationary Magnetic Field
...
As the Loop rotates at different angles, there is a change in Aeff which is shown in
Figure 2
...
The Induced E emf output by the Generator
is an AC Voltage and its Waveform is shown in Figure 4
...
These are
also called asAsynchronous Motors, because an induction motor always runs at a speed
lower than synchronous speed
...

There basically 2 types of induction motor depending upon the type of input supply - (i)
Single phase induction motor and (ii) Three phase induction motor
...
But in aninduction motor only the stator winding is fed with an AC supply
...

This alternating flux revolves with synchronous speed
...

The relative speed between stator RMF and rotor conductors causes an induced emf in
the rotor conductors, according to the Faraday's law of electromagnetic induction
...
That is why such motors are called as induction motors
...
)
Now, induced current in rotor will also produce alternating flux around it
...
The direction of induced rotor current, according
to Lenz's law, is such that it will tend to oppose the cause of its production
...
Thus the
rotor rotates in the same direction as that of stator flux to minimize the relative
velocity
...

This is the basic working principle of induction motor of either type, single phase of 3
phase
...


where, f = frequency of the spply
P = number of poles
Slip:
Rotor tries to catch up the synchronous speed of the stator field, and hence it rotates
...
If rotor catches up the stator speed,
there wont be any relative speed between the stator flux and the rotor, hence no induced
rotor current and no torque production to maintain the rotation
...
That is why the rotor rotates at speed which is always less the
synchronous speed
...


Transformer Principle

One of the main reasons that we use alternating AC voltages and currents in our homes
and workplace’s is that AC supplies can be easily generated at a convenient voltage,
transformed (hence the name transformer) into much higher voltages and then distributed
around the country using a national grid of pylons and cables over very long distances
...
These higher AC transmission voltages and currents can then be
reduced to a much lower, safer and usable voltage level where it can be used to supply
electrical equipment in our homes and workplaces, and all this is possible thanks to the
basic Voltage Transformer
...
A transformer basically is very simple static (or stationary) electromagnetic passive electrical device that works on the principle of Faraday’s law of induction
by converting electrical energy from one value to another
...
A
transformer operates on the principals of ‘electromagnetic induction’, in the form of Mutual
Induction
...
Then we can say that transformers work in
the ‘magnetic domain’, and transformers get their name from the fact that they ‘transform’
one voltage or current level into another
...

A single phase voltage transformer basically consists of two electrical coils of wire, one
called the ‘Primary Winding’ and another called the ‘Secondary Winding’
...
In a single-phase voltage
transformer the primary is usually the side with the higher voltage
...
This soft iron core is
not solid but made up of individual laminations connected together to help reduce the core’s
losses
...
When an electric current passed through the primary winding, a magnetic field is
developed which induces a voltage into the secondary winding as shown
...
Generally, the
primary winding of a transformer is connected to the input voltage supply and converts or
transforms the electrical power into a magnetic field
...

Transformer Construction (single-phase)








Where:
VP - is the Primary Voltage
VS - is the Secondary Voltage
NP - is the Number of Primary Windings
NS - is the Number of Secondary Windings
Φ (phi) - is the Flux Linkage
Notice that the two coil windings are not electrically connected but are only linked
magnetically
...
When a transformer is used to increase the voltage

on its secondary winding with respect to the primary, it is called a Step-up transformer
...

However, a third condition exists in which a transformer produces the same voltage on
its secondary as is applied to its primary winding
...
This type of transformer is called an
Impedance Transformer and is mainly used for impedance matching or the isolation of
adjoining electrical circuits
...

As the transformer is basically a linear device, a ratio now exists between the number of
turns of the primary coil divided by the number of turns of the secondary coil
...
This turns ratio value dictates the operation of the transformer and the
corresponding voltage available on the secondary winding
...
The turns ratio, which has no units, compares the two
windings in order and is written with a colon, such as 3:1 (3-to-1)
...
Then we can see that if the ratio between the number
of turns changes the resulting voltages must also change by the same ratio, and this is true
...
The ratio of the primary to the secondary, the ratio of
the input to the output, and the turns ratio of any given transformer will be the same as its
voltage ratio
...
The actual
number of turns of wire on any winding is generally not important, just the turns ratio and
this relationship is given as:
A Transformers Turns Ratio

Assuming an ideal transformer and the phase angles: ΦP ≡ ΦS
Note that the order of the numbers when expressing a transformers turns ratio value is
very important as the turns ratio 3:1 expresses a very different transformer relationship and
output voltage than one in which the turns ratio is given as: 1:3
...
What will be the turns ratio (TR) of the transformer
...
As the ratio moves from a larger number on the left to a smaller
number on the right, the primary voltage is therefore stepped down in value as shown
...


Again confirming that the transformer is a ?step-down transformer as the primary
voltage is 240 volts and the corresponding secondary voltage is lower at 80 volts
...
If the secondary output voltage is to be the same value as the
input voltage on the primary winding, then the same number of coil turns must be wound
onto the secondary core as there are on the primary core giving an even turns ratio
of 1:1 (1-to-1)
...

If the output secondary voltage is to be greater or higher than the input voltage, (stepup transformer) then there must be more turns on the secondary giving a turns ratio
of 1:N (1-to-N), where N represents the turns ratio number
...

Transformer Action
We have seen that the number of coil turns on the secondary winding compared to the
primary winding, the turns ratio, affects the amount of voltage available from the secondary
coil
...
When an alternating voltage ( VP ) is applied to the primary coil,
current flows through the coil which in turn sets up a magnetic field around itself,
called mutual inductance, by this current flow according to Faraday’s Law of electromagnetic
induction
...


As the magnetic lines of force setup by this electromagnet expand outward from the coil
the soft iron core forms a path for and concentrates the magnetic flux
...

However, the strength of the magnetic field induced into the soft iron core depends upon
the amount of current and the number of turns in the winding
...

When the magnetic lines of flux flow around the core, they pass through the turns of the
secondary winding, causing a voltage to be induced into the secondary coil
...
dΦ/dt (Faraday’s Law), where N is the number of
coil turns
...

Then we can see that the same voltage is induced in each coil turn of both windings
because the same magnetic flux links the turns of both the windings together
...
However, the peak amplitude of the output voltage available on the secondary
winding will be reduced if the magnetic losses of the core are high
...
The
product of amperes times turns is called the ampere-turns, which determines the
magnetizing force of the coil
...
If one volt is applied to the one turn of the primary coil, assuming no
losses, enough current must flow and enough magnetic flux generated to induce one volt in
the single turn of the secondary
...

As the magnetic flux varies sinusoidally, Φ = Φmax sinωt, then the basic relationship
between induced emf, ( E ) in a coil winding of N turns is given by:
emf = turns x rate of change






Where:
? - is the flux frequency in Hertz, = ω/2π
Ν - is the number of coil windings
...
For the primary winding emf, N will be
the number of primary turns, ( NP ) and for the secondary winding emf, N will be the
number of secondary turns, ( NS )
...
In other words,Transformers DO NOT Operate on DC Voltages, ONLY AC
...
Thus
the winding will draw a very high current from the DC supply causing it to overheat and
eventually burn out, because as we know I = V/R
...
The maximum value of the magnetic flux density is 1
...
Calculate:
a)
...


b)
...


c)
...


Electrical Power in a Transformer
Another one of the transformer basics parameters is its power rating
...
In an ideal
transformer (ignoring any losses), the power available in the secondary winding will be the
same as the power in the primary winding, they are constant wattage devices and do not
change the power only the voltage to current ratio
...

That is the electric power at one voltage/current level on the primary is ?transformed?
into electric power, at the same frequency, to the same voltage/current level on the
secondary side
...
Thus, when a transformer steps-up a voltage, it steps-down the current and
vice-versa, so that the output power is always at the same value as the input power
...


Power in a Transformer

Where: ΦP is the primary phase angle and ΦS is the secondary phase angle
...
If the voltage was increased by a factor of 10,
the current would decrease by the same factor reducing overall losses by factor of 100
...
This means that
there are no friction or windage losses associated with other electrical machines
...

Copper losses, also known as I2R loss is the electrical power which is lost in heat as a
result of circulating the currents around the transformers copper windings, hence the name
...
The actual
watts of power lost can be determined (in each winding) by squaring the amperes and
multiplying by the resistance in ohms of the winding (I2R)
...
This lagging (or out-of-phase) condition
is due to the fact that it requires power to reverse magnetic molecules; they do not reverse
until the flux has attained sufficient force to reverse them
...
Hysteresis within the transformer can be reduced by making the core from
special steel alloys
...
The efficiency of a
transformer is reflected in power (wattage) loss between the primary (input) and secondary
(output) windings
...

An ideal transformer is 100% efficient because it delivers all the energy it receives
...
For a transformer operating with a
constant voltage and frequency with a very high capacity, the efficiency may be as high as
98%
...

Generally when dealing with transformers, the primary watts are called ?voltamps?, VA to differentiate them from the secondary watts
...
Here the three quantities of VA, W and η have been
superimposed into a triangle giving power in watts at the top with volt-amps and efficiency
at the bottom
...


Magnetic Flux

Magnetic Flux
Magnetic flux is the number of magnetic field lines passing through a surface placed in a
magnetic field
...
We find it with following formula;
Ф=B
...
cosӨ
Where Ф is the magnetic flux and unit of Ф is Weber (Wb)
B is the magnetic field and unit of B is Tesla
A is the area of the surface and unit of A is m2
In the first one, magnetic field lines are perpendicular to the surface, thus, since angle
between normal of the surface and magnetic field lines 0 and cos0=1equation of magnetic
flux becomes;
Ф=B
...
A
...
A
...
In this unit we learn magnetic permeability that is the quantity of ability to conduct
magnetic flux
...
Magnetic permeability is the distinguishing property of the
matter, every matter has specific µ
...


Magnetic permeability of the vacuum is denoted by;µo and has value;
µo=4π
...
/Amps
...

µr=µ/µo
Diamagnetic matters: If the relative permeability f the matter is a little bit lower than 1
then we say these matters are diamagnetic
...

Ferromagnetic matters: If the relative permeability of the matter is higher than 1 with
respect to paramagnetic matters then we say these matters are ferromagnetic matters
...
A C Circuit

A C Thoery

Most students of electricity begin their study with what is known as direct
current (DC), which is electricity flowing in a constant direction, and/or possessing a
voltage with constant polarity
...

As useful and as easy to understand as DC is, it is not the only ‘kind’ of electricity in use
...
Either as
a voltage switching polarity or as a current switching direction back and forth, this ’kind’ of
electricity is known as Alternating Current (AC): Figure below

Direct vs alternating current
Whereas the familiar battery symbol is used as a generic symbol for any DC voltage
source, the circle with the wavy line inside is the generic symbol for any AC voltage
source
...
It is true that in
some cases AC holds no practical advantage over DC
...
However, with AC it is possible to build electric
generators, motors and power distribution systems that are far more efficient than DC,
and so we find AC used predominately across the world in high power applications
...

If a machine is constructed to rotate a magnetic field around a set of stationary wire
coils with the turning of a shaft, AC voltage will be produced across the wire coils as that
shaft is rotated, in accordance with Faraday’s Law of electromagnetic induction
...
Connected to a load, this reversing voltage polarity
will create a reversing current direction in the circuit
...

While DC generators work on the same general principle of electromagnetic induction,
their construction is not as simple as their AC counterparts
...
All this is necessary to switch the coil’s changing output polarity
to the external circuit so the external circuit sees a constant polarity:
Figure below

DC generator operation
The generator shown above will produce two pulses of voltage per revolution of the
shaft, both pulses in the same direction (polarity)
...
The diagram
shown above is a bit more simplified than what you would see in real life
...
If the atmosphere surrounding the machine contains flammable or
explosive vapors, the practical problems of spark-producing brush contacts are even
greater
...

The benefits of AC over DC with regard to generator design is also reflected in electric
motors
...
In fact, AC and DC motor designs are very similar
to their generator counterparts (identical for the sake of this tutorial), the AC motor being
dependent upon the reversing magnetic field produced by alternating current through its
stationary coils of wire to rotate the rotating magnet around on its shaft, and the DC
motor being dependent on the brush contacts making and breaking connections to
reverse current through the rotating coil every 1/2 rotation (180 degrees)
...
This relative simplicity translates into greater reliability and lower cost of
manufacture
...
There is an effect of electromagnetism known as mutual induction, whereby two or
more coils of wire placed so that the changing magnetic field created by one induces a
voltage in the other
...
When used as such, this device is known
as a transformer: Figure below

Transformer transforms AC voltage and current
...
The AC voltage induced in the unpowered coil
is equal to the AC voltage across the powered (primary) coil multiplied by the ratio of
secondary coil turns to primary coil turns
...
This relationship has a very close mechanical
analogy, using torque and speed to represent voltage and current, respectively:
Figure below

Speed multiplication gear train steps torque down and speed up
...

If the winding ratio is reversed so that the primary coil has less turns than the secondary
coil, the transformer steps up the voltage from the source level to a higher level at the load:
Figure below

Speed reduction gear train steps torque up and speed down
...

The transformer’s ability to step AC voltage up or down with ease gives AC an
advantage unmatched by DC in the realm of power distribution in figure below
...


Transformers enable efficient long distance high voltage transmission of electric energy
...

Without the ability to efficiently step voltage up and down, it would be cost-prohibitive to
construct power systems for anything but close-range (within a few miles at most) use
...
Because the
phenomenon of mutual inductance relies onchanging magnetic fields, and direct current
(DC) can only produce steady magnetic fields, transformers simply will not work with
direct current
...
Perhaps more than any other
reason, this is why AC finds such widespread application in power systems
...

Resistance is essentially friction against the motion of electrons
...
When
alternating current goes through a resistance, a voltage drop is produced that is in-phase
with the current
...

Reactance is essentially inertia against the motion of electrons
...
When alternating current goes
through a pure reactance, a voltage drop is produced that is 90o out of phase with the
current
...

Impedance is a comprehensive expression of any and all forms of opposition to
electron flow, including both resistance and reactance
...
When alternating current goes through an impedance, a voltage drop is
produced that is somewhere between 0o and 90o out of phase with the current
...

Perfect resistors (Figure below) possess resistance, but not reactance
...
All components possess impedance, and because of this universal quality, it
makes sense to translate all component values (resistance, inductance, capacitance) into
common terms of impedance as the first step in analyzing an AC circuit
...

The impedance phase angle for any component is the phase shift between voltage
across that component and current through that component
...
For an perfect inductor, voltage drop always leads
current by 90o, and so an inductor’s impedance phase angle is said to be +90o
...


Impedances in AC behave analogously to resistances in DC circuits: they add in series,
and they diminish in parallel
...

While this qualified equivalence may be arithmetically challenging, it is conceptually
simple and elegant
...
Because reactance doesn’t dissipate power as resistance does, the
concept of power in AC circuits is radically different from that of DC circuits
...
Also the terms lead and lag as well as in-phase and out-of-phase
were used to indicate the relationship of one waveform to the other with the generalized
sinusoidal expression given as: A(t) = Am sin(ωt Φ) representing the sinusoid in the
time-domain form
...
One way to
overcome this problem is to represent the sinusoids graphically within the spacial or phasordomain form by using Phasor Diagrams, and this is achieved by the rotating vector method
...

A phasor is a vector that has an arrow head at one end which signifies partly the
maximum value of the vector quantity ( V or I ) and partly the end of the vector that
rotates
...
This
anti-clockwise rotation of the vector is considered to be a positive rotation
...

Although the both the terms vectors and phasors are used to describe a rotating line
that itself has both magnitude and direction, the main difference between the two is that a
vectors magnitude is the peak value of the sinusoid while a phasors magnitude is the rms
value of the sinusoid
...

The phase of an alternating quantity at any instant in time can be represented by a
phasor diagram, so phasor diagrams can be thought of as ‘functions of time
...
Then a Phasor is a quantity that has both
Magnitude and Direction
...
Consider the phasor diagram below
...
If the length of its
moving tip is transferred at different angular intervals in time to a graph as shown above, a
sinusoidal waveform would be drawn starting at the left with zero time
...
When the
vector is horizontal the tip of the vector represents the angles at 0o, 180o and at 360o
...
Then the time
axis of the waveform represents the angle either in degrees or radians through which the
phasor has moved
...

Sometimes when we are analysing alternating waveforms we may need to know the
position of the phasor, representing the Alternating Quantity at some particular instant in
time especially when we want to compare two different waveforms on the same axis
...
We have assumed in the waveform above that the waveform
starts at time t = 0 with a corresponding phase angle in either degrees or radians
...
Consider the diagram
below from the previousPhase Difference tutorial
...
So the difference between the two phasors representing the two sinusoidal
quantities is angle Φ and the resulting phasor diagram will be
...
The lengths of the phasors are proportional to the values of the voltage, ( V ) and the
current, ( I ) at the instant in time that the phasor diagram is drawn
...


If however, the waveforms are frozen at time t = 30o, the corresponding phasor
diagram would look like the one shown on the right
...

However, as the current waveform is now crossing the horizontal zero axis line at this
instant in time we can use the current phasor as our new reference and correctly say that
the voltage phasor is ‘leading’ the current phasor by angle, Φ
...

Phasor Addition
Sometimes it is necessary when studying sinusoids to add together two alternating
waveforms, for example in an AC series circuit, that are not in-phase with each other
...
For example, if two
voltages of say 50 volts and 25 volts respectively are together in-phase, they will add or
sum together to form one voltage of 75 volts
...

Consider two AC voltages, V1 having a peak voltage of 20 volts, and V2 having a peak
voltage of 30 volts where V1 leads V2 by 60o
...


Phasor Addition of two Phasors

By drawing out the two phasors to scale onto graph paper, their phasor
sum V1 + V2 can be easily found by measuring the length of the diagonal line, known as
the resultant r-vector, from the zero point to the intersection of the construction lines 0-A
...
Also, while this graphical method gives an answer which is accurate
enough for most purposes, it may produce an error if not drawn accurately or correctly to
scale
...

Mathematically we can add the two voltages together by firstly finding their vertical
and horizontal directions, and from this we can then calculate both the vertical and
‘horizontal’ components for the resultant r vector, VT
...

In the rectangular form, the phasor is divided up into a real part, x and an imaginary
part, y forming the generalised expression Z = x ’ jy
...
This then gives us a mathematical expression that represents both the
magnitude and the phase of the sinusoidal voltage as:
Definition of a Complex Sinusoid

So the addition of two vectors, A and B using the previous generalised expression is as
follows:

Reactive Circuit

Consider a circuit for a single-phase AC power system, where a 120 volt, 60 Hz AC
voltage source is delivering power to a resistive load: (Figure below)

Ac source drives a purely resistive load
...
The power dissipated
at the load would be 240 watts
...
If we were to plot the voltage, current, and power waveforms for this circuit, it
would look like Figure below
...

Note that the waveform for power is always positive, never negative for this resistive
circuit
...
If the source were a mechanical
generator, it would take 240 watts worth of mechanical energy (about 1/3 horsepower) to
turn the shaft
...

This different frequency prohibits our expression of power in an AC circuit using the same
complex (rectangular or polar) notation as used for voltage, current, and impedance,

because this form of mathematical symbolism implies unchanging phase relationships
...

As strange as it may seem, the best way to proceed with AC power calculations is to
use scalar notation, and to handle any relevant phase relationships with trigonometry
...


AC circuit with a purely reactive (inductive) load
...
Though it is alternately absorbed from
and returned to the source
...

(Figure above) This means that power is being alternately absorbed from and returned to
the source
...
The
generator shaft would be easy to spin, and the inductor would not become warm as a
resistor would
...


AC circuit with both reactance and resistance
...
319 Ω of
inductive reactance
...
319 Ω, or 85
...
152o
...
078 Ω)
...
410 amps
...

We already know that reactive components dissipate zero power, as they equally
absorb power from, and return power to, the rest of the circuit
...
The only thing left to dissipate
power here is the resistive portion of the load impedance
...


A combined resistive/reactive circuit dissipates more power than it returns to the source
...

As with any reactive circuit, the power alternates between positive and negative
instantaneous values over time
...
However, in circuits with mixed resistance and reactance like this one, the power
waveform will still alternate between positive and negative, but the amount of positive
power will exceed the amount of negative power
...

Looking at the waveform plot for power, it should be evident that the wave spends
more time on the positive side of the center line than on the negative, indicating that
there is more power absorbed by the load than there is returned to the circuit
...
If the source were a mechanical generator, the amount of
mechanical energy needed to turn the shaft would be the amount of power averaged
between the positive and negative power cycles
...
Furthermore, the phase angle for
power means something quite different from the phase angle for either voltage or
current
...
Because of this way in which AC power differs from AC
voltage or current, it is actually easier to arrive at figures for power by calculating
with scalar quantities of voltage, current, resistance, and reactance than it is to try to
derive it from vector, or complex quantities of voltage, current, and impedance that we’ve
worked with so far
...
Because inductive reactance
increases with increasing frequency and capacitive reactance decreases with increasing
frequency, there will only be one frequency where these two reactances will be equal
...

In the above circuit, we have a 10 ?F capacitor and a 100 mH inductor
...
Plugging in
the values of L and C in our example circuit, we arrive at a resonant frequency of 159
...

What happens at resonance is quite interesting
...
Now, we use the parallel
impedance formula to see what happens to total Z:

We can't divide any number by zero and arrive at a meaningful result, but we can
say that the result approaches a value ofinfinity as the two parallel impedances get closer
to each other
...
We can plot the
consequences of this over a wide power supply frequency range with a short SPICE
simulation:

Power Factor

The power factor is equal to the real or true power P in watts (W) divided by the
apparent power |S| in volt-ampere (VA):
PF = P(W) / |S(VA)|
PF - power factor
...

|S| - apparent power - the magnitude of the complex power in volt?amps (VA)
...

φ is the apprent power phase angle
...
Circuit Analysis

Circuit Analysis

Solving a set of equations that represents a circuit is straightforward, if not always
easy
...
The two commonly taught
methods for forming a set of equations are the node voltage (or nodal) method and the
loop-current (or mesh) method
...
I will end with a discussion of a third method, Modified Nodal
Analysis, that has some unique benefits
...
If
you are only interested in using that program you may go directly to the page describing
SyCiSi
...
Dependent sources can be added in a straightforward way, but are not
considered here
...

Selective a reference node (usually ground)
...

Apply Kirchoff's current law to each node not connected to a voltage source
...

Example 1
Consider the circuit shown below

Steps 1 and 2 have already been applied
...
Plugging in numbers and solving the circuit
we get

The node-voltage method is generally straightforward to apply, but becomes a bit more
difficult if one or more of the voltage sources is not grounded
...


Clearly this circuit is the same as
R1 interchanged
...
Instead we have

Note that the last line is the same as that from the previous circuit, but to solve the
circuit we had to first solve for va
...
Another way to handle this
problem is to use the concept of a supernode, which complicates the rules for setting up the
equations
...

The examples chosen here were simple but illustrated the basic techniques of nodal
analysis
...
The technique of modified nodal analysis, introduced later,
also has no difficulties when presented with floating voltage sources
...

To apply the loop current method to a circuit with n loops (and with m current
sources), perform the following steps
...
This is easiest with a consistent method, e
...
all unknown
currents are clockwise, all know currents follow direction on current source
...

Solve the system of n-m unknown voltages
...


We can apply KVL to both loops

Since there are two equations and two unknowns we can solve by substitution or by matrix
methods
...
General Comments
The choice between the node voltage method and the loop current method is often made
on the basis of the circuit at hand
...
Therefore the node voltage method would be
expected to be easier
...


For this circuit you would draw three loops, but two of them go through known current
sources - so you would only need one equation
...


Thevenin's Theorem

Thevenin's Theorem states that Any linear circuit containing several voltages and
resistances can be replaced by just one single voltage in series with a single resistance
connected across the load?
...

Thevenin's Theorem is especially useful in the Circuit Analysis of power or battery
systems and other interconnected resistive circuits where it will have an effect on the
adjoining part of the circuit
...


As far as the load resistor RL is concerned, any complex one-port network consisting of
multiple resistive circuit elements and energy sources can be replaced by one single
equivalent resistanceRs and one single equivalent voltage Vs
...

For example, consider the circuit from the previous section
...
This is done by shorting out all the voltage sources connected to the circuit, that
is v = 0, or open circuit any connected current sources making i = 0
...

The value of the equivalent resistance, Rs is found by calculating the total resistance
looking back from the terminals A and B with all the voltage sources shorted
...


Find the Equivalent Resistance (Rs)

The voltage Vs is defined as the total voltage across the terminals A and B when there is
an open circuit between them
...

Find the Equivalent Voltage (Vs)

We now need to reconnect the two voltages back into the circuit, and as VS = VAB the
current flowing around the loop is calculated as:

This current of 0
...
33amps) =

or
VAB = 10 + (10Ω x 0
...
33 volts
...
33 volts, the same
...
67Ωs and
a voltage source of 13
...
With the 40Ω resistor connected back into the circuit we get:

and from this the current flowing around the circuit is given as:

which again, is the same value of 0
...

Thevenin's theorem can be used as another type of Circuit Analysis method and is
particularly useful in the analysis of complicated circuits consisting of one or more voltage or
current source and resistors that are arranged in the usual parallel and series connections
...
However, Thevenin’s equivalent circuits of Transistors, Voltage
Sources such as batteries etc, are very useful in circuit design
...
When looking back from
terminals A and B, this single circuit behaves in exactly the same way electrically as the
complex circuit it replaces
...

The basic procedure for solving a circuit using Thevenin’s Theorem is as follows:


1
...




2
...




3
...




4
...


Norton Thoerm

This theorem is just alternative of Thevenin theorem
...
In this theorem,
the circuit network is reduced into a single constant current source in which, the equivalent
internal resistance is connected in parallel with it
...
Suppose, in complex network we have to find out the
current through a particular branch
...
As in the said branch current comes from the
network, it can be considered that the network itself is a current source
...

The looking back resistance of a network is the equivalent electrical resistance of the
network when someone looks back into the network from the terminals where said branch is
connected
...
Actually in Norton theorem, the branch of the
network through which we have to find out the current, is removed from the network
...

Then we calculate the short circuit current that flows between the terminals
...
The equivalent resistance between
the said terminals with all sources removed leaving their internal resistances in the circuit is
calculated and said it is RN
...
For getting clearer concept of this theorem, we have
explained it by the following example, In the example two resistors R1 and R2 are
connected in series and this series combination is connected across one voltage source of
emf E with internal resistance Ri as shown
...
Now we have
to find out the current through RL by applying Norton theorem
...
Second, we have to calculate the short circuit
current or Norton equivalent current IN through the points A and B
...
Now the equivalent resistance as viewed from open
terminals A and B is RN,
Norton Equivalent Circuit

Maximum Power transfer Thoerm

Often we would like to transfer the most power from a source to a load placed across the
terminals as possible
...
The
source resistance is Rs and the open circuit voltage of the source is vs:

The current in this circuit is found using Ohm's Law:

The voltage across the load resistor, vL, is found using the voltage divider rule:

We can now find the power dissipated in the load, PL as follows:

We can now rewrite this to get rid of the RL on the top:

Assuming the source resistance is not changeable, then we obtain maximum power by
minimising the bracketed part of the denominator in the above equation
...
In this case, it is equal to 2
...
DC Genrator

Working Principle

A dc generator is an electrical machine which converts mechanical energy into direct
current electricity
...
This article outlines basic construction and working of a DC
generator
...
Thus, a DC generator or a DC motor can be broadly termed as
a DC machine
...
Hence, let's
call this point as construction of a DC machine instead of 'construction of a dc generator'
...
A DC
machine consists two basic parts; stator and rotor
...

1
...


3
...
It is made up of cast iron or
steel
...

Poles and pole shoes: Poles are joined to the yoke with the help of bolts or welding
...
Pole shoes serve two
purposes; (i) they support field coils and (ii) spread out the flux in air gap uniformly
...
Field coils are former wound and
placed on each pole and are connected in series
...


Armature core (rotor)
4
...


6
...
It is cylindrical in shape
with slots to carry armature winding
...
It may be provided with air ducts for the
axial air flow for cooling purposes
...

Armature winding: It is usually a former wound copper coil which rests in armature
slots
...
Armature winding can be wound by one of the two methods; lap
winding or wave winding
...
A
double layer winding means that each armature slot will carry two different coils
...
The function of a commutator, in a dc
generator, is to collect the current generated in armature conductors
...
A
commutator consists of a set of copper segments which are insulated from each other
...
Each segment is
connected to an armature coil and the commutator is keyed to the shaft
...
They rest on commutator segments and slide
on the segments when the commutator rotates keeping the physical contact to collect
or supply the current
...
The magnitude of induced emf can be
calculated from the emf equation of dc generator
...
In a DC generator, field coils
produce an electromagnetic field and the armature conductors are rotated into the field
...
The
direction of induced current is given by Fleming?s right hand rule
...
Let?s consider an armature
rotating clockwise and a conductor at the left is moving upward
...
Hence, the direction of current in every armature conductor will be
alternating
...
But with a split ring commutator,
connections of the armature conductors also gets reversed when the current reversal
occurs
...

Types Of A DC Generator:
DC generators can be classified in two main categories, viz; (i) Separately excited and
(ii) Self-excited
...

(ii) Selfexcited: In this type, field coils are energized from the current produced by the
generator itself
...
The
generated emf causes a part of current to flow in the field coils, thus strengthening the field
flux and thereby increasing emf generation
...
It consists of an armature and one or
several permanent magnets situated around the armature
...
So, they are rarely found in industrial applications
...

Separately Excited DC Generator

These are the generators whose field magnets are energized by some external dc source
such as battery
...

Ia = Armature current IL = Load current V = Terminal voltage Eg = Generated emf

Voltage drop in the armature = Ia ? Ra (R/sub>a is the armature resistance) Let, Ia = IL
= I (say) Then, voltage across the load, V = IRa Power generated, Pg = Eg?I Power
delivered to the external load, PL = V?I
...
In these type of machines field coils are internally connected with the
armature
...
When the
armature is rotated some emf is induced
...
This
small current flows through the field coil as well as the load and thereby strengthening the
pole flux
...
This increased field current further raises
armature emf and this cumulative phenomenon continues until the excitation reaches to the
rated value
...
Series wound generators
B
...
Compound wound generators
Series Wound Generator

In these type of generators, the field windings are connected in series with armature
conductors as shown in figure below
...
As series field winding carries full load current it is designed with relatively few
turns of thick wire
...
5Ω )
...
In shunt wound generators the voltage in the field
winding is same as the voltage across the terminal
...
So, Ia=Ish + IL The effective power across the load will be
maximum when IL will be maximum
...
For this purpose the resistance of the shunt field winding generally kept high
(100 Ω) and large no of turns are used for the desired emf
...

In shunt wound generators, output voltage is inversely proportional with load current
...
This
combination of windings is called compound wound DC generator
...
One winding is placed in
series with the armature and the other is placed in parallel with the armature
...


Short Shunt Compound Wound DC Generator
The generators in which only shunt field winding is in parallel with the armature winding
as shown in figure
...


Shunt field current, Ish=V/Rsh Armature current, Ia= series field current, Isc=
IL+Ish Voltage across the load, V=Eg-Ia Ra-Isc Rsc=Eg-Ia (Ra+Rsc) [∴Ia=Ics] Power
generated, Pg= Eg?Ia Power delivered to the load, PL=V?IL In a compound wound
generator, the shunt field is stronger than the series field
...
On the other hand if
series field opposes the shunt field, the generator is said to be differentially compound
wound
...
D C Motor

A motor is an electrical machine which converts electrical energy into mechanical
energy
...
The direction of
this force is given by Fleming's left hand rule and it's magnitude is given by F = BIL
...

Fleming's left hand rule: If we stretch the first finger, second finger and thumb of our
left hand to be perpendicular to each other AND direction of magnetic field is represented by
the first finger, direction of the current is represented by second finger then the thumb
represents the direction of the force experienced by the current carrying conductor
...
The principle of working of a DC motor is that "whenever a current carrying
conductor is placed in a magnetic field, it experiences a mechanical force"
...
Where,
B = magnetic flux density, I = current and L = length of the conductor within the magnetic
field
...

The direction of rotation of a this motor is given by Fleming’s left hand rule, which
states that if the index finger, middle finger and thumb of your left hand are extended

mutually perpendicular to each other and if the index finger represents the direction of
magnetic field, middle finger indicates the direction of current, then the thumb represents
the direction in which force is experienced by the shaft of the DC motor
...
Here we unlike a generator we supply
electrical energy to the input port and derive mechanical energy from the output port
...
If the direction of current in the wire is reversed,
the direction of rotation also reverses
...


Here in a DC motor, the supply voltage E and current I is given to the electrical port or
the input port and we derive the mechanical output i
...
torque T and speed ω from the
mechanical port or output port
...
So from the picture above we can well understand that motor is just the
opposite phenomena of a DC generator, and we can derive both motoring and generating
operation from the same machine by simply reversing the ports
...
Hence, this classification is valid
for both: DC generators and DC motors
...
This makes two broad categories of dc machines; (i)
Separately excited and (ii) Self-excited
...
That means the field winding is electrically separated from the
armature circuit
...

They are used in laboratories for research work, for accurate speed control of DC motors
with Ward-Leonard system and in few other applications where self-excited DC generators

are unsatisfactory
...
A PMDC
motor may be used in a small toy car
...

In self-excited type of DC generator, the field winding is energized by the current
produced by themselves
...
So, initially, current induces in the armature conductors of a dc
generator only due to the residual magnetism
...

Self-excited machines can be further classified as –
Series wound – In this type, field winding is connected in series with the armature
winding
...
That is
why series winding is designed with few turns of thick wire and the resistance is kept very
low (about 0
...

Shunt wound – Here, field winding is connected in parallel with the armature winding
...
Shunt winding is made with a
large number of turns and the resistance is kept very high (about 100 Ohm)
...

Compound wound – In this type, there are two sets of field winding
...
Compound wound
machines are further divided as Short shunt – field winding is connected in parallel with only the armature winding
...


Chapter – 8
...

Stator: As its name indicates stator is a stationary part of induction motor
...

Rotor: The rotor is a rotating part of induction motor
...
The rotor in single phase induction motor is of squirrel
cage rotor type
...

Stator of Single Phase Induction Motor
The stator of the single phase induction motor has laminated stamping to reduce eddy
current losses on its periphery
...
In order to reduce the hysteresis losses, stamping are made up of silicon
steel
...

1
...

As the number of turns per coil can be easily adjusted with the help of concentric coils,
the mmf distribution is almost sinusoidal
...
Except for shaded pole motor, the asynchronous motor has two stator windings
namely the main winding and the auxiliary winding
...

Rotor of Single Phase Induction Motor

The construction of the rotor of the single phase induction motor is similar to the squirrel
cage three phase induction motor
...
The slots are not made parallel to each other but are bit skewed as the skewing
prevents magnetic locking of stator and rotor teeth and makes the working of induction
motor more smooth and quieter
...
These aluminium or copper bars are called rotor conductors and are placed in
the slots on the periphery of the rotor
...
In order to provide mechanical strength
these rotor conductor are braced to the end ring and hence form a complete closed circuit
resembling like a cage and hence got its name as "squirrel cage induction motor"
...
The
absence of slip ring and brushes make the construction of single phase induction motor very
simple and robust
...


When single phase ac supply is given to the stator winding of single phase induction
motor, the alternating current starts flowing through the stator or main winding
...
This main flux also links
with the rotor conductors and hence cut the rotor conductors
...
As the rotor circuit is closed
one so, the current starts flowing in the rotor
...
This
rotor current produces its own flux called rotor flux
...

Now there are two fluxes one is main flux and another is called rotor flux
...

Why Single Phase Induction Motor is not Self Starting?
According to double field revolving theory, any alternating quantity can be resolved into
two components, each component have magnitude equal to the half of the maximum
magnitude of the alternating quantity and both these component rotates in opposite
direction to each other
...
e if one φm / 2 is rotating in
clockwise direction then the other φm / 2 rotates in anticlockwise direction
...
According to the double field revolving theory,
this alternating flux, φm is divided into two components of magnitude φm /2
...
Let us call
these two components of flux as forward component of flux, φf and backward component of
flux, φb
...


Now at starting, both the forward and backward components of flux are exactly opposite
to each other
...
So, they
cancel each other and hence the net torque experienced by the rotor at starting is zero
...

Methods for Making Single Phase Induction as Self Starting Motor

From the above topic we can easily conclude that the single phase induction motors are
not self starting because the produced stator flux is alternating in nature and at the starting
the two components of this flux cancel each other and hence there is no net torque
...
Then the induction motor will
become self starting
...
When these two fluxes
interact with each other they will produce a resultant flux
...
Once the motor starts running,
the additional flux can be removed
...
Depending upon the methods for making asynchronous motor as Self
Starting Motor, there are mainly four types of single phase induction motor namely,

1
...

3
...


Split phase induction motor,
Capacitor start inductor motor,
Capacitor start capacitor run induction motor,
Shaded pole induction motor
...
These are
also called asAsynchronous Motors, because an induction motor always runs at a speed
lower than synchronous speed
...

There basically 2 types of induction motor depending upon the type of input supply (i) Single phase induction motor and
(ii) Three phase induction motor
...
But in aninduction motor only the stator winding is fed with an AC supply
...

This alternating flux revolves with synchronous speed
...




The relative speed between stator RMF and rotor conductors causes an induced emf in
the rotor conductors, according to the Faraday's law of electromagnetic induction
...
That is why such motors are called as induction motors
...
)



Now, induced current in rotor will also produce alternating flux around it
...
The direction of induced rotor current, according
to Lenz's law, is such that it will tend to oppose the cause of its production
...
Thus the
rotor rotates in the same direction as that of stator flux to minimize the relative



velocity
...

This is the basic working principle of induction motor of either type, single phase of 3
phase
...


where, f = frequency of the spply
P = number of poles
Slip:
Rotor tries to catch up the synchronous speed of the stator field, and hence it rotates
...
If rotor catches up the stator speed,
there wont be any relative speed between the stator flux and the rotor, hence no induced
rotor current and no torque production to maintain the rotation
...
That is why the rotor rotates at speed which is always less the
synchronous speed
...


Balanced Load

A balanced load is a term that is used to identify the establishment of a state of
equilibrium with electrical power flow, weight distribution during the shipment of goods, and
even the process of creating an logical flow on a factory assembly line
...
A balanced load also is designed to allow
the greatest degree of safety for those working with or near the load itself
...

This is often accomplished by using some type of phase system that helps to regulate the
flow of power through the components
...
The same general idea holds true for an air conditioning
system, where the load is balanced based on the work that the components must perform in
order to heat and cool an interior space efficiently
...
It is usually done by electricians when installing a new service
panel (breaker box), rewiring a house, or adding multiple circuits during a remodel
...

An unbalanced load occurs when there is significantly more power drawn on one side
of the panel than the other
...

Electrical Service Basics
Most homes have a type of electrical service called single-phase, three-wire
...
The wires connect to the home's service panel, and
each hot wire provides 120-volt power to one of the two hot bus bars in the panel
...
A single-pole circuit breaker
connects to only one bus bar and provides 120 volts to a circuit
...

Like the utility service wires, each branch circuit has one or two hot wires and a
neutral wire
...
From there, the power goes back onto the utility grid via the utility
service neutral
...


Single-pole breakers usually are rated for 15 or 20 amps
...
The amperage rating is the main factor used to
balance the loads in the service panel
...
) served by the circuits and when that equipment is
typically used
...
By contrast, a whole-house fan (attic fan)
has a relatively consistent power drawn and is used only during warm weather and usually
at night or early in the morning
...
One circuit supplies a refrigerator that draws 8 amps; the other
circuit supplies a chest freezer that draws 7 amps
...
To balance the load of the two circuits, the breakers should be on different hot bus
bars, or "legs," of the service panel
...
In this case, the current on
the neutral would be 1 amp: 8 – 7 = 1
...
The goal is
to have the current on the neutral be as low as possible—for safety, energy-efficiency, and
other reasons (that's a big subject for another article)
...
That would be an unbalanced load and preferably avoided
...
In most panels, the breaker slots on each side of the panel alternate between the hot
bus bars (legs)
...

If they're on the same side but have a slot in between them, they will connect to the
same leg
...
Each
leg provides 120 volts for a total of 240 for the circuit
...
Therefore,
when you're laying out circuits for the house, the goal is to have roughly equal amperage
draw on both legs of the panel
...
The arrangement of the winding is so as to produce a rotating
magnetic field
...

Problems Encountered During Motor Starting:
The most basic feature of an Induction motor is its self starting mechanism
...
As per the Lenz law, the rotor will start rotating in a direction so as to
oppose the flow of electric current and this gives a torque to the motor
...


Motor Starting Period Vs Steady State Running Period
During this self starting period, as torque increases, a large amount of current flows in
the rotor
...
Hence there is a need to control the motor starting
...

Objectives of Star-Delta Technique Motor Starter are:



Reduce high starting current and along these lines forestall motor from overheating
Provide over-burden and no-voltage assurance

Star Delta Starter:
In star delta starting, the motor is connected in STAR mode throughout the starting
period
...


Star Delta Motor Control Power Circuit
Components of a Star-Delta Starter:
Contactors: The Star- Delta starter circuit comprises of three contactors: Main, star and
delta contactors
...

Timer: The contactors are regulated by a timer incorporated with the started
...
By any chance if star and delta contactors are actuated at the
same time, the motor will be damaged
...
In the event that the temperature goes past a preset quality, the
contact is open and power supply is cut in this manner ensuring the motor
...
After a time interval the
timer signs to the star contactor to head off to the open position and the primary, delta
contactors to head off to the shut position, accordingly structuring delta circuit
...
Hence, the line current drawn by the
motor at starting is decreased to one-third as contrasted with starting current with the
windings associated in delta
...

The timer controls conversion from star connection to delta connection
...

Terminal Connections in Star and Delta Configurations:
L1, L2 and L3 are the 3-phase line voltages, which are given to primary contactor
...
In star mode of motor windings, the
primary contactor associate the mains to essential winding terminals U1, V1 and W1
...

Notwithstanding when the primary contactor is shut supply arrives at terminals A1, B1, C1
and consequently the motor windings are energized in star-mode
...
After
the timer achieves the specified time period, the star contactor is de-energized and delta
contactor is energized
...

That is for delta association, fulfilling end of one winding is to be joined with beginning end
of the other winding
...

Types of Star Delta Starter:
There are two types of star-delta starters, open and close
...
As the name proposes,
in this strategy motor windings are open throughout the transition time of altering the

windings from a star mode with a delta mode
...

Merits:
Open transition starter is very easy to implement in terms of cost and circuitry, it does
not require additional voltage educing equipment
...
Electrically, the outcome of the momentary peaks
in current could cause force vacillations or misfortunes
...
e
...

Star Delta Closed Transition Starter:
In this starter, the transfer from the star to delta modes is made without disengaging
motor from the line
...
The extra components incorporate a contactor and few
transition resistors
...
A fourth contactor is additionally used to place the resistor in circuit
before opening the star contactor and afterward evacuating the resistors once the delta
contactor is closed
...

Merit:
There is a reduction in the incremental current surge, which results from transition
...

Demerit:
In addition to requiring more switching devices, the control circuit is more complicated
due to the need to carry out resistor switching
...


Full load current in Open Transition and Closed Transition

Example of Star-Delta Starter:
A Star-Delta starter is generally used to reduce start current of the motor
...

From the circuit, we used a supply of 440volts to start a motor
...
In this, we
explained the working by using lamp instead of motor for easy understanding
...
During delta operation after the timer works the lights might glow with full
intensity showing full supply voltage of 440volts
...


Block Diagram by Edgefx Kits
Photo Credit:





Motor starting period Vs Steady state running period by myelectrical
Star Delta Motor Control Power Circuitby by s1
...

Construction of a synchronous motor is similar to an alternator (AC generator)
...

Synchronous motors are available in a wide range, generally rated between 150kW to
15MW with speeds ranging from 150 to 1800 rpm
...
Just like any other motor, it consists of a stator and a rotor
...
The stator has axial slots inside, in which three
phase stator winding is placed
...

The rotor in synchronous motors is mostly of salient pole type
...
The direct current excites the rotor winding and creates
electromagnetic poles
...
The figure
above illustrates the construction of a synchronous motor very briefly
...
The 3 phase AC supply produces rotating magnetic field in stator
...
Consider a two
pole synchronous machine as shown in figure below
...
If the
rotor position is such that, N pole of the rotor is near the N pole of the stator (as
shown in first schematic of above figure), then the poles of the stator and rotor will
repel each other, and the torque produced will be anticlockwise
...
But at this very soon, rotor can not rotate with the
same angle (due to inertia), and the next position will be likely the second schematic in
above figure
...

Hence, the rotor will undergo to a rapidly reversing torque, and the motor will not
start
...
Now, the rotor will undergo unidirectional torque
...

Characteristic Features Of A Synchronous Motor





Synchronous motor will run either at synchronous speed or will not run at all
...
(As Ns = 120f / P)
Synchronous motors are not self starting
...

They can operate under any power factor, lagging as well as leading
...


Application Of Synchronous Motor




As synchronous motor is capable of operating under either leading and lagging power
factor, it can be used for power factor improvement
...

It is used where high power at low speed is required
...


Chapter – 9
...
All these elements are linear and passive in nature;
i
...
they consume energy rather than producing it and these elements have a linear
relationship between voltage and current
...
The RLC circuit exhibits the property of resonance in same way
as LC circuit exhibits, but in this circuit the oscillation dies out quickly as compared to LC
circuit due to the presence of resistor in the circuit
...

Since all these components are connected in series, the current in each element
remains the same,

Let VR be the voltage across resistor, R
...

VC be the voltage across capacitor, C
...

XC be the capacitive reactance
...
So, voltages in each
component are not in phase with each other; so they cannot be added arithmetically
...
For drawing the phasor
diagram for RLC series circuit, the current is taken as reference because, in series circuit the
current in each element remains the same and the corresponding voltage vectors for each
component are drawn in reference to common current vector
...
The parallel RLC circuit is exactly opposite to the series RLC circuit
...
The total current drawn from the supply is not equal to mathematical sum of the
current flowing in the individual component, but it is equal to its vector sum of all the
currents, as the current flowing in resistor, inductor and capacitor are not in the same phase
with each other; so they cannot be added arithmetically
...

IC is the current flowing in the capacitor, C in amps
...

Is is the supply current in amps
...
Therefore, for drawing phasor diagram, take voltage
as reference vector and all the other currents i
...
The current through each element can be found using Kirchhoff's Current Law, which
states that the sum of currents entering a junction or node is equal to the sum of current
leaving that node
...
e
...
So in parallel RLC circuit, it
is convenient to use admittance instead of impedance
...

1
...

2
...

The magnetic field in the inductor is built by the current, which gets provided by the
discharging capacitor
...
In some cases at
certain frequency called resonant frequency, the inductive reactance of the circuit becomes
equal to capacitive reactance which causes the electrical energy to oscillate between the
electric field of the capacitor and magnetic field of the inductor
...
In RLC circuit, the presence of resistor causes these oscillation s to die
out over period of time and it is called as the damping effect of resistor
...


When resonance occurs, the inductive reactance of the circuit becomes equal to
capacitive reactance, which causes the circuit impedance to be minimum in case of series
RLC circuit; but when resistor, inductor and capacitor are connected in parallel, the circuit
impedance becomes maximum, so the parallel RLC circuit is sometimes called as anti
resonator
...
A Capacitor consists of two Conducting Plates separated by
an Insulating Material or Dielectric
...


Figure 1: Basic structure of the Capacitor

Figure 2: Schematic symbol of the Capacitor
When a Capacitor is connected to a circuit with Direct Current (DC) source, two
processes, which are called "charging" and "discharging" the Capacitor, will happen in
specific conditions
...
Both Plates get the equal and opposite charges and an increasing
Potential Difference, vc, is created while the Capacitor is charging
...


Figure 3: The Capacitor is Charging
A Capacitor is equivalent to an Open-Circuit to Direct Current, R = ∞, because once the
Charging Phase has finished, no more Current flows through it
...


When the Capacitor disconnected from the Power Supply, the Capacitor is discharging
through the Resistor RD and the Voltage between the Plates drops down gradually to zero,
vc = 0, Figure 4
...

The product of Resistance R and Capacitance C is called the Time Constant τ, which
characterizes the rate of charging and discharging of a Capacitor, Figure 5
...

Capacitors are found in almost all electronic circuits
...

For example, a Capacitor is a storehouse of energy in photoflash unit that releases the
energy quickly during short period of the flash
...
As the charge
increases, the voltage rises, and eventually the voltage of the capacitor equals the voltage
of the source, and current stops flowing
...


Discharging
Consider the following circuit:

In the circuit, the capacitor is initially charged and has voltage V0 across it, and the
switch is initially open
...
The voltage across a capacitor discharging through a resistor
as a function of time is given as:

where V0 is the initial voltage across the capacitor
...
The function completes

63% of the transition between the initial and final states at t = 1RC, and completes over
99
...

The voltage and current of the capacitor in the circuits above are shown in the graphs
below, from t=0 to t=5RC
...
A positive current flows into the
capacitor from this terminal; a negative current flows out of this terminal
...
Note that the current through the
capacitor can change instantly at t=0, but the voltage changes slowly
...
Once the magnetic field is up and no longer changing, the inductor acts like
a short circuit
...
Since the inductor is
acting like a short circuit at steady state, the voltage across the inductor then is 0
...


After we cut out the voltage source, the voltage across the inductor is I0 * R, but the
higher voltage is now at the negative terminal of the inductor
...
The
current flowing through the inductor at time t is given by:

where I0 = − Vs / R
...

The voltage and current of the inductor for the circuits above are given by the graphs
below, from t=0 to t=5L/R
...
A positive current flows into the inductor from this terminal; a
negative current flows out of this terminal:

Inductor
Voltage

Current

Charge

Discharge

Remember that for an inductor, v(t) = L * di / dt
...


Chapter – 10
...

The reason for transforming the voltage to a much higher level is that higher
distribution voltages implies lower currents for the same power and therefore lower I2R
losses along the networked grid of cables
...


A Typical Voltage Transformer
The Voltage Transformer can be thought of as an electrical component rather than an
electronic component
...

The transformer does this by linking together two or more electrical circuits using a
common oscillating magnetic circuit which is produced by the transformer itself
...

Mutual induction is the process by which a coil of wire magnetically induces a voltage
into another coil located in close proximity to it
...

Transformers are capable of either increasing or decreasing the voltage and current
levels of their supply, without modifying its frequency, or the amount of Electrical
Power being transferred from one winding to another via the magnetic circuit
...
For this tutorial we
will define the primary side of the transformer as the side that usually takes power, and the
secondary as the side that usually delivers power
...

These two coils are not in electrical contact with each other but are instead wrapped
together around a common closed magnetic iron circuit called the core
...

The two coil windings are electrically isolated from each other but are magnetically
linked through the common core allowing electrical power to be transferred from one coil to
the other
...

Single Phase Voltage Transformer

In other words, for a transformer there is no direct electrical connection between the
two coil windings, thereby giving it the name also of an Isolation Transformer
...
While the job of the secondary
winding is to convert this alternating magnetic field into electrical power producing the
required output voltage as shown
...
A single-phase transformer can operate to either increase or decrease the
voltage applied to the primary winding
...

When it is used to ‘decrease’ the voltage on the secondary winding with respect to the
primary it is called a Step-down transformer
...
In other words, its output is identical with
respect to voltage, current and power transferred
...

The difference in voltage between the primary and the secondary windings is achieved
by changing the number of coil turns in the primary winding ( NP ) compared to the number
of coil turns on the secondary winding ( NS )
...
This ratio,
called the ratio of transformation, more commonly known as a transformers ‘turns ratio’,
( TR )
...

It is necessary to know the ratio of the number of turns of wire on the primary winding
compared to the secondary winding
...
This means in this
example, that if there are 3 volts on the primary winding there will be 1 volt on the
secondary winding, 3 volts-to-1 volt
...

Transformers are all about ‘ratios’
...
In other words for a transformer: ‘turns ratio = voltage ratio’
...

Transformer Basics Example No1
A voltage transformer has 1500 turns of wire on its primary coil and 500 turns of wire
for its secondary coil
...


This ratio of 3:1 (3-to-1) simply means that there are three primary windings for every
one secondary winding
...

Transformer Basics Example No2
If 240 volts rms is applied to the primary winding of the same transformer above, what
will be the resulting secondary no load voltage
...

Then the main purpose of a transformer is to transform voltages at preset ratios and
we can see that the primary winding has a set amount or number of windings (coils of wire)
on it to suit the input voltage
...
In other words, one coil turn on the secondary to one coil turn on the
primary
...
Likewise, if it is required that
the secondary voltage is to be lower or less than the primary, (step-down transformer) then
the number of secondary windings must be less giving a turns ratio of N:1 (N-to-1)
...
But if the two windings are electrically isolated from each other, how is this secondary
voltage produced’
We have said previously that a transformer basically consists of two coils wound
around a common soft iron core
...
The strength of the magnetic field builds up as the current flow
rises from zero to its maximum value which is given asdΦ/dt
...
This magnetic
flux links the turns of both windings as it increases and decreases in opposite directions
under the influence of the AC supply
...
When current is
reduced, the magnetic field strength reduces
...
The amount
of voltage induced will be determined by: N
...
Also this induced voltage has the same frequency as the primary winding
voltage
...
As a result,
the total induced voltage in each winding is directly proportional to the number of turns in
that winding
...

If we want the primary coil to produce a stronger magnetic field to overcome the cores
magnetic losses, we can either send a larger current through the coil, or keep the same
current flowing, and instead increase the number of coil turns ( NP ) of the winding
...

So assuming we have a transformer with a single turn in the primary, and only one
turn in the secondary
...
That is, each winding supports the same number of volts
per turn
...

Φ - is the flux density in webers
This is known as the Transformer EMF Equation
...

Also please note that as transformers require an alternating magnetic flux to operate
correctly, transformers cannot therefore be used to transform or supply DC voltages or
currents, since the magnetic field must be changing to induce a voltage in the secondary
winding
...

If a transformers primary winding was connected to a DC supply, the inductive
reactance of the winding would be zero as DC has no frequency, so the effective impedance
of the winding will therefore be very low and equal only to the resistance of the copper
used
...

Transformer Basics Example No3
A single phase transformer has 480 turns on the primary winding and 90 turns on the
secondary winding
...
1T when 2200
volts, 50Hz is applied to the transformer primary winding
...
The maximum flux in the core
...
The cross-sectional area of the core
...
The secondary induced emf
...
Transformers are
rated inVolt-amperes, ( VA ), or in larger units of Kilo Volt-amperes, ( kVA )
...
Thus, in an ideal transformer the Power
Ratio is equal to one (unity) as the voltage, V multiplied by the current, I will remain
constant
...
Although the transformer can step-up (or step-down) voltage, it cannot
step-up power
...
Then
we can say that primary power equals secondary power, ( PP = PS )
...

Note that since power loss is proportional to the square of the current being
transmitted, that is:I2R, increasing the voltage, let’s say doubling ( 2 ) the voltage would
decrease the current by the same amount, ( 2 ) while delivering the same amount of power
to the load and therefore reducing losses by factor of 4
...

Transformer Basics ‘ Efficiency
A transformer does not require any moving parts to transfer energy
...
However,
transformers do suffer from other types of losses called ‘copper losses’ and ‘iron losses’ but
generally these are quite small
...

Copper losses represents the greatest loss in the operation of a transformer
...

Iron losses, also known as hysteresis is the lagging of the magnetic molecules within
the core, in response to the alternating magnetic flux
...

Their reversal results in friction, and friction produces heat in the core which is a form
of power loss
...

The intensity of power loss in a transformer determines its efficiency
...
Then the resulting efficiency of a transformer is equal to the
ratio of the power output of the secondary winding, PS to the power input of the primary
winding, PP and is therefore high
...

Real transformers on the other hand are not 100% efficient and at full load, the efficiency of
a transformer is between 94% to 96% which is quiet good
...
The efficiency, η of a transformer is given as:
Transformer Efficiency

where: Input, Output and Losses are all expressed in units of power
...
Then the efficiency equation
above can be modified to:

It is sometimes easier to remember the relationship between the transformers input,
output and efficiency by using pictures
...
This arrangement represents the actual position of each quantity in the
efficiency formulas
...
Hence these losses are also known as core
losses or iron losses
...
This loss depends upon the volume and grade of the iron,
frequency of magnetic reversals and value of flux density
...
6fV (watts)

where,

η = Steinmetz hysteresis constant
V = volume of the core in m3



Eddy current loss in transformer: In transformer, AC current is supplied to the
primary winding which sets up alternating magnetizing flux
...
But some part of this flux also gets
linked with other conducting parts like steel core or iron body or the transformer,
which will result in induced emf in those parts, causing small circulating current in
them
...
Due to these eddy currents, some energy
will be dissipated in the form of heat
...
This means that the power
supplied at the input terminal should be exactly equal to the power supplied at the output
terminal, since efficiency can only be 100% if the output power is equal to the input power
with zero energy losses
...
Similarly, since
the output power of a transformer is never exactly equal to the input power, due a number
of electrical losses inside the core and windings of the transformer, so we never get to see a
100% efficient transformer
...
e
...
So
there are two primary types of electrical losses in the transformer:
1
...
Iron losses
Other than these, some small amount of power losses in the form of ‘stray losses’
are also observed, which are produced due to the leakage of magnetic flux
...
So these are also known as ohmic losses or I2R losses, where ‘I’ is the current
passing through the windings and R is the internal resistance of the windings
...

Mathematically, these copper losses can be defined as:
Iron losses
These losses occur in the core of the transformer and are generated due to the
variations in the flux
...
And since they do not change like the load, so these losses
are also constant
...
Eddy Current losses
2
...
During this process, the other conduction

materials of which the core is composed of; also gets linked with this flux and an emf is
induced
...
So such losses are
called Eddy Current losses and are mathematically expressed as:
Pe = Ke f² Kf² Bm²
Where;


Ke = Constant of Eddy Current



Kf² = Form Constant



Bm = Strength of Magnetic Field
Hysteresis Loss
Hysteresis loss is defined as the electrical energy which is required to realign the
domains of the ferromagnetic material which is present in the core of the transformer
...
For their proper realignment, some external energy supply, usually in the form of
current is required
...

Mathematically, they can be defined as;
>Ph = Kh Bm1
...


Efficiency

Efficiency of Transformer
Transformer efficiency may be defined as the ratio between Output and Input
...
e
...
But the values of both input and Output should be same in unites (i
...
in Watts,
kilowatts, megawatts etc)
But note that a transformer has very high efficiency because the losses occur in
transformer is very low
...
The best way to find the transformer
efficiency is that, first determine the losses in transformer and then calculate the
transformer efficiency with the help of these losses
...
… (As Input = Output +Losses)
Efficiency = η= Output / (Output +Cupper Losses + Iron Losses)
You may also find the Efficiency by the following formula
Efficiency = η= Output / Input
Efficiency = η = (Input – Losses) / Input ……
...
But the
efficiency doesn’t depend on VA i
...
it would be expressed in Power Watts (kW) not in kVA
...
And the efficiency would be maximum on
unity (1) Power factor
...
R1or I22R2
Iron Loss=Wi = Hysteresis Loss + Eddy Current Loss

WI = WH + WE
Suppose to Primary Side…
Primary Input = P1 = V1I1 Cosθ1
Efficiency = η = Output / Input
Efficiency = η = (Input – Losses) / input …
...
R1 – WI)/ V1 I1 Cosθ1
Taking LCM
Efficiency = η = 1- (I12
...
R1 /V1Cosθ1) – (WI/ V1 I1 Cosθ1)
Differentiate both sides with respect to I1
Dη/ dI1 = 0 – ( R1 /V1 Cosθ1) + (WI/V1 I12 Cosθ1)
Dη/ dI1= – ( R1 /V1 Cosθ1) + (WI/V1 I12 Cosθ1)
For Maximum Efficiency, the value of (Dη/ dI1) should be Minimum i
...

Dη/ dI1 = 0
The above Equation can be written as
R1 / (V1 Cosθ1) = (WI/V1 I12 Cosθ1)
Or
WI = I12
...
e
...
Therefore, with proper designing,
maximum efficiency can be attained at any desired load i
...
Copper loss and Iron Loss can
be equaled
...

Those distribution transformers which supply electrical energy to lighting and other
general circuits, their primary energize for 24 hours, but the secondary windings does not
energize all the time
...
I
...
secondary windings supply
eclectic power for very small load or no load for maximum time in 24 hours
...

Therefore it realizes the necessity to design a transformer in which the core loss
should be low
...
In this
type of transformers, we can track their performance only by all day efficiency
...
On the base of usable energy, we
estimate the all day efficiency for a specific time (During the 24 hours =one day)
...

All Day Efficiency = Output (in kWh)/Input (in kWh)
To understand about the all day efficiency, we must know about the load cycle i
...
how
much load is connected, and for how much time (in 24 hours)
...
Semi-Conductor

Semiconductor

A semiconductor is a substance, usually a solid chemical element or compound, that can
conduct electricity under some conditions but not others, making it a good medium for the
control
of
electrical
current
...

The specific properties of a semiconductor depend on the impurities, or dopants, added
to it
...
A Ptypesemiconductor carries current predominantly as electron deficiencies called holes
...
In a
semiconductor material, the flow of holes occurs in a direction opposite to the flow of
electrons
...
Silicon is the best-known of these, forming the basis
of most integrated circuits (ICs)
...
Of these, gallium arsenide
(GaAs) is widely used in low-noise, high-gain, weak-signal amplifying devices
...
A single integrated circuit (IC), such as a microprocessor chip, can do the
work of a set of vacuum tubes that would fill a large building and require its own electric
generating plant
...

In fact semiconductor technology is present in almost every area of modern day technology
and as such semiconductor theory is a very important element of electronics
...
It
is the fundamental building block of semiconductor diodes and transistors and a number of
other electronic components
...
As it has two electrodes it receives its
name - diode
...
Vast numbers of diodes are manufactured each year, and of course the
semiconductor diode is the basis of many other devices apart from diodes
...
This makes the semiconductor PN junction diode one of the key enablers in
today's electronics technology
...
This means that both ends have different
characteristics
...

Where the two areas meet the electrons fill the holes and there are no free holes or
electrons
...
In view of
the fact that this area is depleted of charge carriers it is known as the depletion region
...
Different effects are noticed dependent
upon the way in which the voltage is applied to the junction
...
Similarly
electrons move towards the positive voltage and jump the depletion layer
...


The semiconductor diode PN junction with forward bias
If the voltage is applied to the semiconductor diode in the opposite sense no current
flows
...
Similarly the electrons are attracted towards the positive
potential which is applied to the N type region
...

Accordingly no current flows
...


The characteristic of a diode PN junction

In the forward direction (forward biased) it can be seen that very little current flows until
a certain voltage has been reached
...
This voltage varies from one type of
semiconductor to another
...
2 or 0
...
6 volts
...
6 volts across most
small current diodes when they are forward biased
...

From the diagram it can be seen that a small amount of current flows in the reverse
direction (reverse biased)
...
Typically it may be a
pico amps or microamps at the most
...

This reverse current results from what are called minority carriers
...
Early
semiconductors has relatively high levels of minority carriers, but now that the manufacture
of semiconductor materials is very much better the number of minority carriers is much
reduced as are the levels of reverse currents
...
The most common kind of diode in modern circuit
design is the semiconductor diode, although other diode technologies exist
...
The
term ‘diode’ is customarily reserved for small signal devices, I ≤ 1 A
...


Semiconductor diode schematic symbol: Arrows indicate the direction of electron
current flow
...

(Figure below)

Diode operation: (a) Current flow is permitted; the diode is forward biased
...

When the polarity of the battery is such that electrons are allowed to flow through the
diode, the diode is said to be forward-biased
...
A diode may be
thought of as like a switch: ‘closed’ when forward-biased and ‘open’ when reverse-biased
...
This is because the diode symbol was invented by engineers,
who predominantly use conventional flow notation in their schematics, showing current as
a flow of charge from the positive (+) side of the voltage source to the negative (-)
...

Diode behavior is analogous to the behavior of a hydraulic device called a check valve
...


Hydraulic check valve analogy: (a) Electron current flow permitted
...

Check valves are essentially pressure-operated devices: they open and allow flow if
the pressure across them is of the correct ‘polarity’ to open the gate (in the analogy
shown, greater fluid pressure on the right than on the left)
...

Like check valves, diodes are essentially "pressure-" operated (voltage-operated)
devices
...
Let’s take a closer look at the simple battery-diodelamp circuit shown earlier, this time investigating voltage drops across the various
components in Figurebelow
...
(b) Reverse biased
...
If the battery’s polarity is reversed,
the diode becomes reverse-biased, and drops all of the battery’s voltage leaving none for
the lamp
...
The most
substantial difference is that the diode drops a lot more voltage when conducting than the
average mechanical switch (0
...

This forward-bias voltage drop exhibited by the diode is due to the action of the
depletion region formed by the P-N junction under the influence of an applied voltage
...
(Figure below (a)) The depletion
region is almost devoid of available charge carriers, and acts as an insulator:

Diode representations: PN-junction model, schematic symbol, physical part
...

The cathode bar, nonpointing end, at (b) corresponds to the N-type material at (a)
...

If a reverse-biasing voltage is applied across the P-N junction, this depletion region
expands, further resisting any current through it
...

Conversely, if a forward-biasing voltage is applied across the P-N junction, the
depletion region collapses becoming thinner
...
In order for a sustained current to go through the diode; though, the depletion
region must be fully collapsed by the applied voltage
...


Inceasing forward bias from (a) to (b) decreases depletion region thickness
...
7 volts, nominal
...
3 volts
...
Forward voltage
drop remains approximately constant for a wide range of diode currents, meaning that
diode voltage drop is not like that of a resistor or even a normal (closed) switch
...

Actually, forward voltage drop is more complex
...
It is commonly known as thediode
equation:

The term kT/q describes the voltage produced within the P-N junction due to the
action of temperature, and is called thethermal voltage, or Vt of the junction
...
Knowing this, and assuming a ‘nonideality’
coefficient of 1, we may simplify the diode equation and re-write it as such:

You need not be familiar with the ‘diode equation’ to analyze simple diode circuits
...
This is why many textbooks simply say the voltage drop across a
conducting, semiconductor diode remains constant at 0
...
3 volts for
germanium
...
Also, since temperature is a factor in the diode equation, a forward-biased
P-N junction may also be used as a temperature-sensing device, and thus can only be
understood if one has a conceptual grasp on this mathematical relationship
...
In actuality, a very small amount of current can and does go through a
reverse-biased diode, called the leakage current, but it can be ignored for most purposes
...
If the applied reverse-bias voltage becomes too great, the diode will experience
a condition known as breakdown (Figure below), which is usually destructive
...
Like forward voltage, the PIV rating of a diode
varies with temperature, except that PIV increases with increased temperature
and decreases as the diode becomes cooler’exactly opposite that of forward voltage
...

Technical feats previously requiring relatively large, mechanically fragile, power-hungry
vacuum tubes were suddenly achievable with tiny, mechanically rugged, power-thrifty
specks of crystalline silicon
...
Understanding
how transistors function is of paramount importance to anyone interested in
understanding modern electronics
...
Discussions of holes and electrons are better left to another
chapter in my opinion
...
I don’t mean to downplay the importance of understanding
semiconductor physics, but sometimes an intense focus on solid-state physics detracts
from understanding these devices’ functions on a component level
...
’ If these concepts are unclear to you, it is best to refer to earlier
chapters in this book before proceeding with this one
...
Each layer
forming the transistor has a specific name, and each layer is provided with a wire contact
for connection to a circuit
...


BJT transistor: (a) PNP schematic symbol, (b) physical layout (c) NPN symbol, (d) layout
...
For any given state of operation, the
current directions and voltage polarities for each kind of transistor are exactly opposite
each other
...
In other words,
transistors restrict the amount of current passed according to a smaller, controlling
current
...
The small
current thatcontrols the main current goes from base to emitter, or from emitter to base,
once again depending on the kind of transistor it is (PNP or NPN, respectively)
...
(Figure below)

Small Base-Emitter current controls large Collector-Emitter current flowing against
emitter arrow
...
In other words, two types of charge
carriers’electrons and holes’comprise this main current through the transistor
...
This is the first and foremost rule in the use of transistors: all
currents must be going in the proper directions for the device to work as a current
regulator
...

Conversely, the large, controlled current is referred to as the collector current because it
is the only current that goes through the collector wire
...

No current through the base of the transistor, shuts it off like an open switch and
prevents current through the collector
...
Collector
current is primarily limited by the base current, regardless of the amount of voltage
available to push it
...




---