BEAM & GAIN
BASIC ELECTRICAL
THREE PHASE vs SINGLE PHASE SUPPLY
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Presently 3-ø AC system is very popular and being used worldwide for power
generation, power transmission, distribution and for electric motors.
Three phase system has the following advantages as compare to single phase
system:
1. Power to weight ratio of 3-ø alternator is high as compare to 1-ø
alternator. Means for generation for same amount of Electric Power, the
size of 3-ø alternator is small as compare to 1-ø Alternator. Hence, the
overall cost of alternator is reduced for generation of same amount of
power. Moreover, of due to reduction in weight, transportation and
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BASIC ELECTRICAL
installation alternator become convenient and less space is required to
accommodate the alternator in power house.
2. For electric power transmission and distribution of same amount of
power, the requirement of conductor material is less in 3-ø system as
compare to 1-ø system. Hence, the 3-ø transmission and distribution
system is economical as compare 1-ø system.
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3. Let us consider the power produced by single phase supply and 3-phase
supply at unity power factor. Wave form of power produce due 1-phase
supply at unity power factor is shown in figure (C) and Wave form of
power produced due to 3-phase supply is shown in figure (D) below.
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BASIC ELECTRICAL
&
From power wave forms shown in figure (C) and (D) above it is clear that in 3phase system, the instantaneous power is always constant over the cycle results
in smooth and vibration free operation of machine. Whereas in 1-ø system the
instantaneous power is pulsating hence change over the cycle, which leads to
vibrations in machines.
BE
A
M
Power to weight ratio of three phase induction motor is high as compare
to single phase induction motor. Means for same amount of Mechanical
Power, the size of three phase induction motor is small as compare to single
phase induction motor. Hence, the overall cost of induction motor is reduced.
Moreover, due to reduction in weight, transportation and installation of
induction motor become convenient and less space is required to accommodate
the Induction motor.
3-phase induction motor is self-started as the magnetic flux produced by 3phase supply is rotating in nature with constant magnitude. Whereas 1-ø
induction motor is not self-started as the magnetic flux produced by 1-ø supply
is pulsating in nature. Hence, we have to make some arrangement to make the
1-ø induction motor self-started. Which further increase the cost of 1-ø
induction motor.
3-phase motor is having better power factor and efficiency as compare to 1-ø
motor.
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Power to weight ratio of 3-phase transformer is high as compare to 1-ø
transformer. Means for same amount of Electric Power, the size of 3-phase
transformer is small as compare to 1-ø transformer. Hence, the overall cost of
transformer is reduced. Moreover, due to reduction in weight, transportation and
installation of transformer become convenient and less space is required to
accommodate the transformer.
If fault occurs in any winding of 3-phase transformer, the rest of two winding
can be used in open delta to serve the 3-phase load which is not possible in 1-ø
transformer. This ability of 3-phase transformer further increase the reliability
of 3-phase transformer.
IN
A 3-phase system can be used to feed a 1-ø load, whereas vice-versa is not
possible.
&
GA
DC rectified from 3-phase supply is having the ripple factor 4% and DC
rectified from 1-ø supply is having the ripple factor 48.2 %. Mean DC rectified
from 3-ø supply contains less ripples as compare to DC rectified from 1-ø
supply. Hence the requirement of filter is reduced for DC rectified from 3-phase
supply. Which reduce the overall cost of convector.
M
From above it clear the 3-phase system is more economical, efficient, reliable
and convenient as compare to 1-ø system.
BE
A
There are two types of system available in electric circuit, single phase and
three phase system. In single phase circuit, there will be only one phase, i.e the
current will flow through only one wire and there will be one return path called
neutral line to complete the circuit. So in single phase minimum amount of
power can be transported. Here the generating station and load station will also
be single phase. This is an old system using from previous time. In 1882, new
invention has been done on polyphase system, that more than one phase can be
used for generating, transmitting and for load system. Three phase circuit is
the polyphase system where three phases are send together from the generator to
the load. Each phase are having a phase difference of 120°, i.e 120° angle
electrically. So from the total of 360°, three phases are equally divided into 120°
each. The power in three phase system is continuous as all the three phases are
involved in generating the total power. The sinusoidal waves for 3 phase system
is shown below4
BSNL JE STUDY MATERIAL
BEAM & GAIN
BASIC ELECTRICAL
GA
IN
The three phases can be used as single phase each. So if the load is single phase,
then one phase can be taken from the three phase circuit and the neutral can be
used as ground to complete the circuit.
Why Three Phase is preferred Over Single Phase?
BE
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There are various reasons for this question because there are numbers of
advantages over single phase circuit. The three phase system can be used as
three single phase line so it can act as three single phase system. The three
phase generation and single phase generation is same in the generator except the
arrangement of coil in the generator to get 120° phase difference. The conductor
needed in three phase circuit is 75% that of conductor needed in single phase
circuit. And also the instantaneous power in single phase system falls down to
zero as in single phase we can see from the sinusoidal curve but in three phase
system the net power from all the phases gives a continuous power to the load.
Till now we can say that there are three voltage source connected together to
form a three phase circuit. And actually it is inside the generator. The generator
is having three voltage source s which are acting together in 120° phase
difference. If we can arrange three single phase circuit with 120° phase
difference, then it will become a three phase circuit. So 120° phase difference is
must otherwise the circuit will not work, the three phase load will not be able to
get active and it may also cause damage to the system. The size or metal
quantity of three phase devices is not having much difference. Now if we
consider the transformer, it will be almost same size for both single phase and
three phase because transformer will make only the linkage of flux. So the three
phase system will have higher efficiency compared to single phase because for
the same or little difference in mass of transformer, three phase line will be out
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whereas in single phase it will be only one. And losses will be minimum in
three phase circuit. So overall in conclusion the three phase system will have
better and higher efficiency compared to the single phase system. In three phase
circuit, connections can be given in two types:
1. Star connection
2. Delta connection
Star Connection
GA
IN
In star connection, there is four wire, three wires are phase wire and fourth is
neutral which is taken from the star point. Star connection is preferred for long
distance power transmission because it is having the neutral point. In this we
need to come to the concept of balanced and unbalanced current in power
system.
BE
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When equal current will flow through all the three phases, then it is called as
balanced current. And when the current will not be equal in any of the phase,
then it is unbalanced current. In this case, during balanced condition there will
be no current flowing through the neutral line and hence there is no use of the
neutral terminal. But when there will be unbalanced current flowing in the three
phase circuit, neutral is having a vital role. It will take the unbalanced current
through to the ground and protect the transformer. Unbalanced current affects
transformer and it may also cause damage to the transformer and for this star
connection is preferred for long distance transmission. The star connection is
shown below-
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BASIC ELECTRICAL
&
GA
In star connection, the line voltage is √3 times of phase voltage. Line voltage is
the voltage between two phases in three phase circuit and phase voltage is the
voltage between one phase to the neutral line. And the current is same for both
line and phase. It is shown as expression below
BE
A
M
If a balance symmetrical load is connected across three phase voltage system in
parallel, then the three currents will flow in neutral wire which quantities would
be same, but they would be differ by 120° (out of phase), hence the vector sum
of these three currents = 0. i.e.
IR + IY + IB = 0 ……………. Victorially
The voltage between any two terminals or Voltage between Line and Neutral
(Star Point) is called Phase voltage or Star voltage. And the voltage between
two Lines is called Line to Line Voltage or Line Voltage
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BASIC ELECTRICAL
Voltage, Current and Power Values in Star Connection (Y)
1. Line Voltages and Phase Voltages in Star Connection
We know that the Line Voltage between Line 1 and Line 2 (from fig 3a) is
VRY = VR – VY …. (Vector Difference)
VRY = 2 x VPH x Cos (60°/2)
&
= 2 x VPH x Cos 30°
GA
Hence, if VR = VY = VB = VPH, then
IN
Thus, to find vector of VRY, increase the Vector of VY in reverse direction as
shown in the dotted form in the below fig 2. Similarly, on the both ends of
vector VR and Vector VY, make perpendicular dotted lines which look like a
parallelogram as shown in fig (2). The Diagonal line which divides the
parallelogram into two parts, showing the value of VRY. The angle between
VY and VR vectors is 60°.
= 2 x VPH x (√3/2) …… Since Cos 30° = √3/2
Similarly,
BE
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VYB = VY – VB
M
= √3 VPH
= √3 VPH
And
VBR = VB – VR
= √3 VPH
Hence, it is proved that VRY = VYB = VBR is line voltages VL in Star Connection,
Therefore, in Star Connection;
VL = √3 VPH or VL = √3 EPH
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BEAM & GAIN
It is seen from the fig 2 that;
GA
IN
BASIC ELECTRICAL
Line voltages are 120° apart from each other

Line voltages are 30° leading from the corresponding phase voltages

The angle Ф between line currents and respective line voltages are
(30°+Ф), i.e. each line current is lagging (30°+Ф) from the corresponding
line voltage.
BE
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
2. Line Currents and Phase Currents in Star Connection
It is seen from the fig (3a) that each line is in series with individual phase
winding, therefore, the value of line current is same as in Phase windings to
which the line is connected. i.e.;

Current in Line 1 = IR

Current in Line 2 = IY

Current in Line 3 = IB
Since, the flowing currents in all three lines are same, and the individual current
in each line is equal to the corresponding phase current, therefore;
IR = IY = IB = IPH …. The phase current
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BASIC ELECTRICAL
Line Current = Phase Current
IL = IPH
3. Power in Star Connection
GA
IN
In simple words, the value of Line Current and Phase Current is same in Star
Connection.
&
In a three phase AC circuit, the total True or Active power is the sum of the
three phase power. Or the sum of the all three phase powers is the Total Active
or True Power.
M
Hence, total active or true power in a three phase AC system;
BE
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Total True or Active Power = 3 Phase Power
Or
P = 3 x VPH x IPH x CosФ
….. Eq … (1)
Good to Know: Where Cos Φ = Power factor = the phase angle between Phase
Voltage and Phase Current and not between Line current and line voltage.
We know that the values of Phase Current and Phase Voltage in Star
Connection;
IL = IPH
VPH = VL /√3 ….. (From VL = √3 VPH)
Putting these values in power eq……. (1)
P = 3 x (VL/√3) x IL x CosФ …….….
(VPH = VL /√3)
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BASIC ELECTRICAL
P = √3 x√3 x (VL/√3) x IL x CosФ ….… {3 = √3x√3}
P = √3 x VL x IL x CosФ
Hence proved;
Power in Star Connection,
P = 3 x VPH x IPH x CosФ or
P = √3 x VL x IL x CosФ
Similarly,
IN
Total Reactive Power = Q = √3 x VL x IL x SinФ
GA
Good to know: Reactive Power of Inductive coil is taken as Positive (+) and
that of a Capacitor as Negative (-).
Also, the total apparent power of the three phases
Total Apparent Power = S = √3 x VL x IL
&
Or, S = √ (P2 + Q2)
M
Delta Connection
BE
A
In delta connection, there is three wires alone and no neutral terminal is taken.
Normally delta connection is preferred for short distance due to the problem of
unbalanced current in the circuit. The figure is shown below for delta
connection. In the load station, ground can be used as neutral path if required.
In this system of interconnection, the starting ends of the three phases or coils
are connected to the finishing ends of the coil. Or the starting end of the first
coil is connected to the finishing end of the second coil and so on (for all three
coils) and it looks like a closed mesh or circuit as shown in fig
In more clear words, all three coils are connected in series to form a close mesh
or circuit. Three wires are taken out from three junctions and the all outgoing
currents from junction assumed to be positive.
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BASIC ELECTRICAL
In Delta connection, the three windings interconnection looks like a short
circuit, but this is not true, if the system is balanced, then the value of the
algebraic sum of all voltages around the mesh is zero.
When a terminal is open, then there is no chance of flowing currents with basic
frequency around the closed mesh.
Good to Remember: at any instant, the EMF value of one phase is equal to the
resultant of the other two phases EMF values but in the opposite direction.
BE
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Delta or Mesh Connection System is also called Three Phase Three Wire
System (3-Phase 3 Wire) and it is the best and suitable system for AC Power
Transmission.
In delta connection, the line voltage is same with that of phase voltage. And the
line current is √3 times of phase current. It is shown as expression below,
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BASIC ELECTRICAL
Voltage, Current and Power Values in Delta Connection (Δ)
IN
1. Line Voltages and Phase Voltages in Delta Connection
M
If the line voltage between;
&
GA
It is seen from fig 2 that there is only one phase winding between two terminals
(i.e. there is one phase winding between two wires). Therefore, in Delta
Connection, the voltage between (any pair of) two lines is equal to the phase
voltage of the phase winding which is connected between two lines. Since the
phase sequence is R → Y → B, therefore, the direction of voltage from R phase
towards Y phase is positive (+), and the voltage of R phase is leading by
120°from Y phase voltage. Likewise, the voltage of Y phase is leading by 120°
from the phase voltage of B and its direction is positive from Y towards B.
BE
A
Line 1 and Line 2 = VRY
Line 2 and Line 3 = VYB
Line 3 and Line 1 = VBR
Then, we see that VRY leads VYB by 120° and VYB leads VBR by 120°.
Let’s suppose,
VRY = VYB = VBR = VL …………… (Line Voltage)
Then
VL = VPH
I.e. in Delta connection, the Line Voltage is equal to the Phase Voltage.
2. Line Currents and Phase Currents in Delta Connection
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BASIC ELECTRICAL
It will be noted from the below (fig-2) that the total current of each Line is equal
to the vector difference between two phase currents flowing through that line.
i.e.;

Current in Line 1= I1 = IR – IB

Current in Line 2 =I2 = IY – IR

Current in Line 3 =I3 = IB – IY
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{Vector Difference}
The current of Line 1 can be found by determining the vector difference
between IR and IB and we can do that by increasing the IB Vector in reverse, so
that, IR and IB makes a parallelogram. The diagonal of that parallelogram shows
the vector difference of IR and IB which is equal to Current in Line 1= I1.
Moreover, by reversing the vector of IB, it may indicate as (-IB), therefore, the
angle between IR and -IB (IB, when reversed = -IB) is 60°. If,
IR = IY = IB = IPH …. The phase currents
Then;
The current flowing in Line 1 would be;
IL or I1 = 2 x IPH x Cos (60°/2)
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= 2 x IPH x Cos 30°
= 2 x IPH x (√3/2) …… Since Cos 30° = √3/2
= √3 IPH
i.e. In Delta Connection, The Line current is √3 times of Phase Current
Similarly, we can find the reaming two Line currents as same as above. i.e.,
I2 = IY – IR … Vector Difference = √3 IPH
I3 = IB – IY … Vector difference = √3 IPH
IN
As, all the Line current are equal in magnitude i.e.
Hence
IL = √3 IPH
&
It is seen from the fig above that;
GA
I1 = I2 = I3 = IL
The Line Currents are 120° apart from each other

Line currents are lagging by 30° from their corresponding Phase Currents

The angle Ф between line currents and respective line voltages is
(30°+Ф), i.e. each line current is lagging by (30°+Ф) from the
corresponding line voltage.
BE
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
3. Power in Delta Connection
We know that the power of each phase
Power / Phase = VPH x IPH x CosФ
And the total power of three phases;
Total Power = P = 3 x VPH x IPH x CosФ ….. (1)
We know that the values of Phase Current and Phase Voltage in Delta
Connection;
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BEAM & GAIN
BASIC ELECTRICAL
IPH = IL / /√3 ….. (From IL = √3 IPH)
VPH = VL
Putting these values in power eq……. (1)
P = 3 x VL x ( IL/√3) x CosФ …… (IPH = IL / /√3)
P = √3 x√3 x VL x ( IL/√3) x CosФ …{ 3 = √3x√3 }
P = √3 x VLx IL x CosФ …
Hence proved;
Power in Delta Connection,
IN
P = 3 x VPH x IPH x CosФ …. or
P = √3 x VL x IL x CosФ
GA
Good to Know: Where Cos Φ = Power factor = the phase angle between Phase
Voltage and Phase Current and not between Line current and line voltage.
Good to Remember:
&
In both Star and Delta Connections, The total power on balanced load is same.
Good to know:
M
I.e. total power in a Three Phase System = P = √3 x VL x IL x CosФ
BE
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Balanced System is a system where:

All three phase voltages are equal in magnitude

All phase voltages are in phase by each other i.e. 360°/3 = 120°

All three phase Currents are equal in magnitude

All phase Currents are in phase by each other i.e. 360°/3 = 120°

A three phase balanced load is a system in which the load connected
across three phases are identical.
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BASIC ELECTRICAL
In three phase circuit, star and delta connection can be arranged in four different
ways1. Star-Star connection
2. Star-Delta connection
3. Delta-Star connection
4. Delta-Delta connection
GA
IN
But the power is independent of the circuit arrangement of the three phase
system. The net power in the circuit will be same in both star and delta
connection. The power in three phase circuit can be calculated from the
equation below,
Since, there is three phases,
so the multiple of 3 is made in the normal power equation and the PF is power
factor. Power factor is a very important factor in three phase system and some
times due to certain error, it is corrected by using capacitors.
BE
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Comparison between Star and Delta Connections
Star (Y) Connection
Delta (Δ) Connection
In STAR connection, the starting or
finishing ends (Similar ends) of three
coils are connected together to form the
neutral point. A common wire is taken out
from the neutral point which is called
Neutral.
In DELTA connection, the opposite ends
of three coils are connected together. In
other words, the end of each coil is
connected with the start of another coil,
and three wires are taken out from the
coil joints
There is a Neutral or Star Point
No Neutral Point in Delta Connection
Three phase four wire system is derived
Three phase three wire system is derived
from Star Connections (3-Phase, 4
from Delta Connections (3-Phase, 3
Wires System) We may Also derived 3
Wires System)
Phase 3 Wire System from Star
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Connection
Line Current is Equal to Phase Current. Line Voltage is Equal to Phase Voltage.
i.e.
i.e.
Line Current = Phase Current
Line Voltage = Phase Voltage
IL = IPH
VL = VPH
Line Voltage is √3 times of Phase Line Current is √3 times of Phase
Voltage. i.e.
Current. i.e.
VL = √3 VPH
IL = √3 IPH
GA
IN
The Total Power of three phases could The Total Power of three phases could
be found by
be found by
P = √3 x VL x IL x CosФ …. Or
P = √3 x VL x IL x CosФ … or
P = 3 x VPH x IPH x CosФ
P = 3 x VPH x IPH x CosФ
The speeds of Delta connected motors
The speeds of Star connected motors are
are high because each phase gets the
slow as they receive 1/√3 voltage.
total of line voltage
M
&
In Star Connection, the phase voltage is
In Delta connection, The phase voltage
low as 1/√3 of the line voltage, so, it
is equal to the line voltage, hence, it
needs low number of turns, hence,
needs more number of turns.
saving in copper.
BE
A
Low insulation required as phase voltage Heavy insulation required as Phase
is low
voltage = Line Voltage.
In Power Distribution and industries,
In Power Transmission, Star Connection
Delta Connection is general and typical
system is general and typical to be used.
to be used.
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STAR DELTA TRANSFORMATIONS
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BASIC ELECTRICAL
54
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
55
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
56
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
57
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
58
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
59
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
60
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
61
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
62
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
63
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
64
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
65
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
66
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
67
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
68
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
69
BSNL JE STUDY MATERIAL
BEAM & GAIN
BASIC ELECTRICAL
BE
A
M
&
GA
IN
PHASE CONTROLLED RECTIFIERS OR CONVERTERS
70
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
71
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
72
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
73
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
74
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
75
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
76
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
77
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
78
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
79
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
80
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
81
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
82
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
83
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
84
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
85
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
86
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
87
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
88
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
89
BSNL JE STUDY MATERIAL
BEAM & GAIN
BE
A
M
&
GA
IN
BASIC ELECTRICAL
90
BSNL JE STUDY MATERIAL