Vijay Balu Raskar E.T. Notes

Electrical Notes…..
EELDAD

“Vijay B. Raskar
 What qualities do successful engineers
have?
Strong in mathematics and science.
Highly analytical and detail oriented.
Imaginative and creative.
Good communication skills.
Enjoy working in teams.
Enjoy building or improving the way things work.

 TECHNIQUE TO CLEAR ELECTRICAL TECHNOLOGY
SUBJECT
IMPORTANT CHAPTERS IN ELECTRICAL
TECHNOLOGY WITH HIGHER WAITAGE:
( HIGHER TO LOWER PRIORITY TO STUDY)

1) SINGLE PHASE A.C.CIRCUITS
2) SINGLE PHASE TRANSFORMERS
3) D.C.MOTORS
4) D.C.CIRCUITS
5) THREE PHASE A.C. CIRCUITS
6) A.C. FUNDAMENTALS
7) INSTALLATION, EARTHING AND
TROUBLESHOOTING
8) FRACTIONAL HORSE POWER MOTORS

Vijay Raskar
1

Electrical Notes….. “Vijay B. Raskar”
8898443014 , vijayraskar2003@yahoo.co.in
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INDEX
S. CHAPTER NUMBER PAGE WEIGHTAGE
NO. NUMBER
1 IMP FORMULAES
2 D.C. MOTORS
3 INSTALLATIONS,
EARTHING AND
TROUBLESHOOTING
4 SINGLE PHASE
TRANSFORMER
5 A.C.
FUNDAMENTALS
6 D.C. CIRCUITS
7 SINGLE PHASE A.C.
CIRCUITS
8 THREE PHASE A.C.
CIRCUITS
9 FRACTIONAL
HORSE POWER
MOTORS
10 Theorems
(Problems)

NOTE:
Problems are very important with theory.
Subject is very easy if practice.
Use technique to solve the problems.
More practice = More marks.
Use calculator and it is very essential to clear
“ELECTRICAL SUBJECT”.

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Derivation is also important.
Solve previous question papers.
Any doubts or query ask any time.

1. IMPORTANT FORMULAES
D.C. CIRCUITS
V = I*R
R =  (/ A )
G = 1/ R
SERIES CIRCUIT: R = R1 + R2 + …..Rn
PARALLEL CIRCULT: R = (R1 + R2) / (R1*R2)
KCL = I 0
KVL = V  0
LOOP METHOD = MESH ANALYSIS = IR METHOD
USE CLOCK WISE DIRECTION
R = + to - Take –ve
R = - to + Take +ve
V = OPPOSITE SYMBOLE
I = SAME SYMBOLE
NODAL ANALYSIS = V/R METHOD
USE OUTGOING EVERYTIME
I = INCOMING = TAKE +VE
I = OUTGOING = TAKE –VE
V = OPPOSITE SYMBOLE
STAR –DELTA:
R12 = R1R2 + R2R3 + R3R1
R3
R23 = R1R2 + R2R3 + R3R1
R1
R31 = R1R2 + R2R3 + R3R1
R2
DELTA-STAR:
R1 = R12 * R31
R12 + R23 + R31
R2 = R12 * R23
R12 + R23 + R31
R3 = R23 * R31

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R12 + R23 + R31

A.C. FUNDAMENTALS

f=1/T
  t
  2f
Instantaneous value of e.m.f. or standard equation of e.m.f. =
e = Em Sin 
e = Em Sin t
e = Em Sin 2f (NOTE: e = V)
Instantaneous value of current or standard equation of current =
i = Im Sin 
i = Im Sin t
i = Im Sin 2f
Heat produced in the nth interval = i₂²R(t / n) UNIT: Joules
Irms = 0.707 * Imax
Imax = 2 * Irms
Vrms = 0.707 * Vmax
Vmax = 2 * Vrms
Maximulvalue
Peak factor = = 1.414
R.M .S .value
R.M .S .value
Form factor = = 1.11
Averagevalue
V 1  V 2  V 3  ...  Vn
Vavg =
n

SINGLE-PHASE A.C. CIRCUITS
PURELY RESISTIVE A.C.CIRCUIT:
 i = ImSin t
 v = VmSin t
 P = V*I = V²/R = I²*R
PURELY INDUCTIVE A.C.CIRCUIT:

 i = ImSin( t - )
2

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 v = VmSin t
PURELY CAPACITIVE A.C.CIRCUIT:

 i = ImSin( t + )
2
 v = VmSin t
V = I*R
VL = I*XL
Vc = I*XC
XL = L = 2fL
1 1
XC = =
C 2fC
FOR R-L CIRCUIT
 VR = I*R
 VL = I*XL
 V = I*Z
 Z² = R² + XL²
R
 POWER FACTOR = COSᴓ =
Z
 P = V*I*COSᴓ
FOR R-C CIRCUIT
 VR = I*R
 Vc = I*Xc
 V = I*Z
 Z² = R² + Xc²
R
Z
 P = V*I*COSᴓ
FOR R-L-C CIRCUIT
 VR = I*R
 VL = I*XL
 Vc = I*Xc
 V = I*Z
 Z² = R² + (XL-Xc)² If XL < Xc
 Z² = R² + X² If XL = Xc
R
Z
 P = V*I*COSᴓ

THREE PHASE A.C. CIRCUITS

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STAR CONNECTION:
 LINE CURRENT = PHASE CURRENT
 LINE E.M.F. = 3 * PHASE E.M.F. (VOLTAGE = E.M.F.)
DELTA CONNECTION:
 LINE CURRENT = 3 * PHASE CURRENT
 LINE E.M.F. = PHASE E.M.F. (VOLTAGE = E.M.F.)
POWER FOR STAR & DELTA:
P = 3 * LINE VOLTAGE * LINE CURRENT * COSᴓ
P = 3 * VL * IL * COSᴓ
R = Z * COSᴓ
X = Z * Sinᴓ

Output
Efficiency = *100
Input
Reactive power = Q = 3 * VL * IL * Sinᴓ

SINGLE PHASE TRANSFORMER
E.M.F. EQUATION OF TRANSFORMER:
 e = 4.44 * ᴓm * f * N
 For primary winding: e1 = 4.44 * ᴓm * f * N₁
 For secondary winding: e2 = 4.44 * ᴓm * f * N₂
m
 Bm = Maximum flux density =
Area
V 2 V1
Voltage regulation:
V2
EFFICIENCY OF TRANSFORMER:
 OUTPUT POWER = INPUT POWER – LOSSES
 INPUT POWER = OUTPUT POWER + LOSSES
 INPUT POWER = V2I2 * COSᴓ +Pi + Pcu
Output
 Efficiency = *100
Input
 EFFICIENCY AT FULL LOAD =
X * FULLLOADRATING * p. f .
( X * FULLLOADRATING * p. f .)  Pi  ( X * X * Pcu )
TOTAL COPPER LOSS = I₁²R₁ + I₂²R₂
HYSTERESIS LOSS = Ph = Kh * Bm¹·⁶ * f * v

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EDDY CURRENT LOSS = Pe = Ke * Bm² * f² * t² * v
OUTPUT POWER = kVA * p.f.

2. D.C. MOTORS
 Voltage equation of the motor:
 V = Eb  IaRa
 Eb = ZNP FOR LAP (A = P) & WAVE WINDING (A=2)
60 A
 T = 0.159 *  * Z * Ia * P
A
 SHUNT MOTOR:
 Ish = Vsh
Rsh
 Ia = I  Ish
 Eb  V  IaRa
 SERIES MOTOR:
 Ia  I
 Eb  V  Ia( Ra  Rse)
 SHORT-SHUNT COMPOUND MOTOR:
 V’ = V  I * Rse
 Ish  V '
Rsh
 Ia  I  Ish
 Eb  V ' IaRa
 LONG-SHUNT COMPOUND MOTOR:
 Ish  V
Rsh
 Ia  I  Ish
 Eb  V  Ia( Ra  Rse)
 If  Ia
Then, N1  Eb1* 2 = Eb1 * Ia 2
N2 Eb 2 * 1 Eb 2 * Ia1

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(B.E.ELECTRICAL)

2. SINGLE PHASE A.C. CIRCUITS
Q.1 Derive the relationship between voltage and current in pure resistive circuits.
ANS:

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 Consider a purely resistive circuit.
 It contains pure resistance.
 Alternating voltage is applied across resistance.
 v = VmSin 
   t ………………………………………………………(1)
 Current is set up in the circuit.
 By ohm’s law, V = IR
VmSin  = IR
VmSin
:. I =
R
 The current is maximum when Sin  1
 :. Im = Maximum current
Vm
 Im =
R
 i = Im Sin
 i  Im Sint
 From phasor diagram, Current is in phase with voltage.
 Angle between current and voltage is zero.
   0

CONCLUSION:
 In purely a.c. resistive circuit, the current is in phase with voltage.
 Ohm’s law is applicable.
POWER:
 Power is a product of current and voltage.
 P = V*I
 P = VmSin * Im Sin
= Vm Im sin ² 
= Vm Im sin ² t
Vm Im 1  cos t
= (1  cos 2t ) …………………..( sin ² t  )
2 2

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Vm Im Vm Im
=  cos 2t
2 2
 Fluctuating part is a cosine wave.
 Cosine curve of frequency is double that of voltage and current waves.
 Therefore, average power is zero.
Vm Im
 P= 0
2
Vm Im
P=
2
Vm Im Maximumvalue
P= (R.M.S. Value = )
2 2 2
P = V*I
P = VI = I²R = V² / R WATTS

Q.2 Derive the relationship between voltage and current in pure inductive circuits.
ANS:

 Consider a purely inductive coil* with Inductance L henries.
 Inductance having negligible ohmic resistance.
 A.c. supply is connected across inductance.

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 V  VmSin
 V  VmSint ………………………(1)
 The resulting a.c is set up in the coil.
 E.m.f. is induced in it.
 E.m.f. of self induction is,
di
e  L
dt
di
v = e  L …………………….(2)
dt
 Ohmic resistance is negligible.
 Substitute (1) in (2)
di
VmSint  L
dt
Vm
di  Sint.dt
L
Integratin g ,
 cos t
NOTE: Integration of  sin t 

Vm
 di  L
Sint.dt
Vm (  cos t )
i=
L 

 VmSin (  t )
i 2
L


VmSin (t  )
i 2 ………………………(3)
L

Im is Maximum when Sin (t  ) 1
2
Vm
Im 
L
Substitute in (3)

i  Im Sin (t  )
2
This equation is shows,
 Current will be sinusoidal.
 Current lag behind the voltage by 90

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Vm
Im 
L
I V

0.707 0.707L
V
I
L
XL = L

POWER:
P = VI

P  VmSint * Im Sin (t  )
2

P  Vm Im Sint * Sin (t  )
2
P  Vm Im Sint * ( Cost )

P  Vm Im Sint * Cost

Vm Im
P Sin 2t
2
:. Sin curve of frequency double that of voltage and current waves.
Therefore, Average power is zero.
CONCLUSION:
The average demand for power in a purely inductive circuit over the whole period is always
zero.

Q.3 Derive the relationship between voltage and current in pure capacitive circuits.
ANS:

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 Capacitor is connected across a.c. supply.
 When applied voltage increases capacitor charging.
 When applied voltage decreases capacitor discharging.
 A.c. supply is connected across capacitor.
 V  VmSin
 V  VmSint ………………………(1)
 C = Capacitor
 We have, Charge = Capacitor * Voltage
Q=C*V
Q = C* VmSint
 We have, Charge = Current * Time
 Small charge = dQ on a capacitor plate in small time (dt)
 Therefore,
Charge = Current * Time
dQ = i*dt
dQ
i
dt
d
i  (CVmSint )
dt

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d
i  CVm ( Sint ) d
dt ………….( Sint  Cost
dt
i  CVm (Cost )


i  CVmSin (t  )
2

Current reaches maximum value, when Sin (t  ) 1
2
Im  CVm
Substitute ,

i  Im Sin (t  )
2
CONCLUSION:
Current varies sinusoidally and leads the applied voltage by 90.

POWER:
P = VI

P  VmSint * Im Sin (t  )
2

P  Vm Im Sint * Sin (t  )
2
P  Vm Im Sint * Cost
Sin 2t
P  Vm Im
2
Power curve is purely sin wave of frequency double that of voltage and current.
Average power is zero.

Q.4 Explain power factor in detail.
ANS:
R
 Power factor = Cos 
Z
TruePower VICos
 Power factor =   Cos
ApparantPo wer VI
 Power factor is defined as the ratio of True power to Apparent Power.
 The numerical value of the cosine of the phase angle between voltage and current.
 Power factor is always less than one.
 Nature of power factor is decided by lead or lag of the current with respect to voltage.
 Capacitive circuit = Lead
 Inductive circuit = Lag
 Power factor is also expressed as percentage.

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Q.5 What is a Choking coil?
ANS:
 It consists of a coil wound on a laminated iron core.
 In practice, a.c. circuit have negligible small capacitance.
 Such circuits come under R-L series circuit.
 Its inductance is very high in comparison with its ohmic resistance.
 Resistance and inductance are not physically separate.
 Such a coil is always equal to R-L series circuit.
 In many cases, we require low voltage. Hence, Reduction is obtained by choking coil.
 Choking coil is connected in series with circuit.
 Choking coil is used in fluorescent tube circuit.
 Its having very little loss as compare with simple resistor used in phase.
 Choking coil reduces the circuit current.
 Choking coil is also used as current limiting device.
 It also used as simple resistor due to small loss.

Q.6 What is Active power, Reactive power and Power triangle?
ANS:
 Active power (P):
 It is the product of applied voltage and active component of the current.
 P  VICos
 Unit: Watts or Kilo-watts
 Reactive Powers (Q):
 It is the product of applied voltage and reactive component of the current.
 P  VISin 
 Unit: Volt-Ampere or Kili-Volt-Ampere
 Power Triangle:

 All three sides of impedance triangle are multiplied by I²
 From power triangle,

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S  (P2  Q 2 )
P  SCos
Q  SSin
 Inductive Reactive power is always negative.
 Capacitive Reactive power is always positive.

3. SINGLE PHASE TRANSFORMERS
Q.1 State and explain the principle of transformer?
ANS: STATEMENT: The operation of a transformer is based on the principle of mutual
induction between two circuits linked by a common magnetic field.
EXPLAINATION:

 See the elementary transformer.
 There are two windings PRIMARY and SECONDARY.
 They are separated and wound on common laminated steel core.
 Vertical portion of core where windings are placed is called as LIMB.
 Top and bottom portions are called as YOKES.
 Primary winding is connected across mains and output is receives from secondary
windings.

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 “ When the supply is flows from primary windings, alternate voltage circulates an
alternating current through it.
 The current flowing through primary windings produces the alternating flux (ᴓ)
 This varying flux is linked with secondary windings through iron core and induces
an e.m.f. (Electro Magnetic Force).
 E.m.f. is induced accordance to Faraday’s law of electromagnetic induction.
 a.c. current in the primary winding produces an e.m.f. in the secondary winding.
This phenomenon is called as mutual induction.
 E.m.f. induced in the secondary winding is known as mutual induce e.m.f. or
e.m.f. of mutual induction.
 Frequency remains same at both sides.
 Transformer operation is possible only in alternating currents and not for direct
current.”

Q.2 Explain types of transformer.
ANS:
There are three types of transformers depending upon the core and windings.

a) Core Type Transformer
b) Shell type transformer
c) Berry type transformer

EXPLAINATION:

1) Core Type Transformer:

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Figure: Core type transformer
 This core transformer is having rectangular frame and provides a single
magnetic circuit.
 The windings are normally cylindrical in form and concentric, low-voltage
winding being placed near the core.
 Both windings are uniformly distributed over two limbs of the core.
 Therefore, Neutral core is very effective.
 The coils can be withdrawn for repairs by dismantling lamination of the
top yoke.

2 ) Shell type transformer:

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 Shell type transformer provides double magnetic circuit.
 The windings are normally sandwitch type.
 Windings are placed on central limb of the core.
 H.V. and L.V. coils are wound in the form of pancakes and they are interleaved.
 The windings are near to the yoke of the core is L.V. windings only.
 The windings are placed on the central limb which gives mechanical protection to the
winding.
 Natural cooing is poor.
 During repairing, large numbers of laminations are to be dismantled.

3) Berry Type Transformer:

 Berry type transformer distributes the magnetic circuit.
 Magnetic circuits are independent.
 The core is constructed in such a fashion that its yokes radiate out from the
centre just like the spokes of a wheel.
 The windings are near to the yoke of the core is L.V. windings only.

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 The windings are placed on the central limb which gives mechanical
protection to the winding.
 Natural cooing is poor.
 During repairing, large numbers of laminations are to be dismantled.

Q.3 Derive the e.m.f. equation of the transformer?
ANS:

 We know that, primary winding is connected to a.c. supply and secondary
winding is connected to the load.
 When current is flowing through the primary winding flux is induced in the
core.
 Flux is linked with secondary winding and produced e.m.f. by mutual
induction.
 In the primary winding, E.m.f is induced due to self induction.

MATHEMATICAL EXPRESSIONS: Where,

 N1 = Number of turns on the primary winding.
o N2 = Number of turns on the secondry winding.
 ᴓm = Maximum flux in weber
 f = Frequency in Hz
 Figure shows one cycle of the sinusoidal flux.
 :. Average value of change of flux = maximum flux / time = ᴓm / (1/4f)
 Average value of change of flux = 4 X ᴓm X f weber per second.
 Average e.m.f. = 4 X ᴓm X f Volts
 We have, form factor = 1.11
 :. R.M.S. value of e.m.f. induced in each turn : 1.11 X average value
: 1.11 X 4 X ᴓm X f

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R.M.S. value of e.m.f. induced in each turn : 4.44 X ᴓm X f …….(1)

 R.M.S. value of induced e.m.f. for primary winding: E1
 E1 = Induced e.m.f. each turn X number of turns of P Winding (from (1))
 E1= 4.44 X ᴓm X f X N1 VOLTS
 Similarly,
This is the transformer equation.

OR
 ᴓ = ᴓm sinwt ………………………..(1)
 according to Faraday’s electromagnetic induction,
 e = -N dᴓ
dt
 N = 1 (For e.m.f. per turn)
 e = - dᴓ
dt
 e = - d (ᴓm sinwt) (From 1)
dt
 e = -w ᴓm coswt (derivative of sinwt = wcoswt)
 e = w ᴓm sin(wt – (π/2)) volts ………….(2)
 maximum induced e.m.f. per turn = w ᴓm
= 2πf ᴓm volts (w = 2πf) ….(3)
 We have,
R.M.S. value =0.707 X Maximum value
 R.M.S. value =0.707 X 2πf ᴓm volts
 Similarly,
This is the transformer equatio

Q.4 Explain properties of ideal transformer or define ideal transformer?
ANS: PROPERITIES OF IDEAL TRANSFORMER:

 It has no losses.
 Its winding has no ohmic resistance.
 There is no magnetic leakage.
 The permeability f the core is so high.
 Required very low current to produce flux in the core.

Q.5 EXPLAIN Transformer losses or its type.
ANS:

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 Electrical energy is transfer from one circuit to another.
 Some energy is always lost.
 All the losses in the transformer are ultimately converted into heat.
 Therefore, transformer is provided with cooling system to protect the insulation of the
windings.
 There are two types of losses in the transformer:

1) COPPER LOSS:
 TOTAL COPPER LOSS = I₁² R₁ + I₂²R₂
Where, I₁ & R₁ : For primary
I₂ & R₂ : For secondary
 Copper conductor is used for winding.
 Loss of power caused by resistance of the winding.
 Power loss is proportional to the square of the current flowing through
the windings.
 It is ultimately utilized in heating the windings.
 Copper loss is proportional to the current and square of the KVA output.
2) CORE OR IRON LOSS:

a) Hysteresis loss:
 Hysteresis loss = Ph = Kh X Bm¹·⁶ X f X v volts
Where,
Kh = constant
Bm = Maximum flux density in tesla
f = frequency
v = volume of the magnetic material
 This loss is takes place in the transformer core.

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 It is continuously subjected to rapid reversals of magnetization by the
alternating flux.
b) Eddy current loss:
 Eddy current loss= Pe = Ke X Bm² X f² X v X t² watts
Where,
Ke = constant
Bm = Maximum flux density in tesla
f = frequency
v = volume of the magnetic material
t = thickness of the laminations
 Core losses together are nearly constant and independent of the
magnitude of the current.
 They can be reduced by choosing silicon steel having small values of
Kh and Ke.

Q.6 Explain Auto-Transformers. Also, explain its applications.
ANS:

 Auto-transformer having only one winding on a laminated magnetic core.
 Winding is common for both primary and secondary circuits.
 Ordinary two winding transformer, it can be used as step up and step down
transformer.
 V1, N1 for primary side and V2, N2 For secondary side.
 If neglecting the losses, leakage reactance and magnetizing current,
We have, V2 = I1 = N2 = K
V1 I2 N1

APPLICATION:

 For starting squirrel-cage induction motors & synchronous motors.

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 For interconnection of a.c. systems.
 As booster to raise the voltage in a.c. feeders.
 For furnace transformers for getting suitable supply voltage.
 As variacs for getting continuously variable supply a.c. voltage.

Q.7 What are the advantages and disadvantages of auto-transformers?
ANS: ADVANTAGES OF AUTO-TRANSFORMER:

 Its cheaper.
 Copper require very less for windings.
 Transformation ratio is approaches unity.
 Its regulation is better than two winding transformer.
 Efficiency of transformer is high.
 I²R Losses are less.
 The resistance and leakage reactance is less.

DISADVANTAGES OF AUTO-TRANSFORMER:

 There is always risk of electrical shock.
 When it is used in high-voltage circuit, possibilities of electrical shocks.
 Therefore, Low voltage and high voltage sides are not electrically separated.

Q.8 Explain isolation transformers.
ANS: Definition: The transformer which are specially designed to provide electrical isolation
between the primary and secondary circuits without changing voltage and current levels.
EXPLAINATION:

 The isolation transformer is frequently used to isolate one portion of an electrical
system from another.
 These systems are physically separated.
 They are magnetically couple to each others.
 Electrical isolation provided between primary and secondary circuits.
 Isolation transformer is a 1:1 transformer and is used only for the purpose of electrical
isolation.

FUNCTIONS OF ISOLATION TRANSFORMERS:

1) Isolation transformers isolate and protect the sensitive and expensive
equipments from electrical system grounds.
2) Isolation transformers protect the delicate and expensive equipments against
voltage spikes.

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4. D.C.MOTORS
Q.1 Explain the working principle of operation of a d.c. generator.
ANS: Generator: Which converts mechanical energy into electrical energy either ac or dc.
Principle of Generator: “When a conductor is moved in magnetic field or magnetic field moved
with respect to the conductor. According to Faraday’s law of electromagnetic induction,
electromotive force is set up in the conductor”

 There is relative motion between a conductor and a magnetic field.
 Voltage will always be generated in the conductor.
 A.C. Generators are normally known as alternators.

CONSTRUCTION:

 It consists of a single turn rectangular conducting coil (AB) like copper or aluminum.
 Coil / conductor is placed in between two poles (S & N POLE).
 Coil is placed in such a way that to rotate at constant speed in uniform magnetic field.
 The coil is also known as armature of the alternator.
 The ends of the armature coil are connected to rings called slip rings. i.e. R1 & R2
 Two carbon brushes pressed against the slip rings.
 The slip rings collect the current and carry it to the external resistor (R).

OPERATION: Current supplied by alternator is necessarily alternating.

 Unidirectional or direct current is desired.
 Before external circuit, alternating current must be rectified or commutated.
 Rectification can be done by replacing the slip-rings R1 and R2 of the alternator.
 Where, M is shown in figure “COMMUTATOR”.
 Commutator is made by conducting material which is cuts in two equal halves or
segments.
 Segments are insulated by thin sheet of mica or some other insulating material.
 The ends of the armature coil AB are joined to these segments.
 The external load resistor R is connected to the split ring M through brushes B1 and B2.

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ACTION OF A COMMUTATOR:

 When coil is undergoing for first half cycle, current flowing from load(R) (C to D).
 For next half cycle, its reverses with position of a and b terminals.
 Again for next cycle, current is flowing from C to D and so on.
 Direction of current through the external circuit is same.
 In the commercial d.c. generator, by using number of coils evenly distributed
around the armature core and connecting these coils to commutator having a
corresponding number of segments, a more steady direct current is obtained in
the external circuit.

Q.2 Explain the working principle of operation of a d.c. Motor.
ANS: CONSTRUCTION:

 Armature coil is supplied with direct current through the brushes B1 and B2.

WORKING / OPERATION:

 Unidirectional torque is produced in the d.c. motor.
 There are three positions to understand it.
 Torque developed at different position of the coil.
 By Flemming’s left hand rule, conductor moves upwards as well as downwards.
 Conductor is placed between the two poles.
 The computer plays very important role in the operation of the d.c.motor.

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POSITION-1

 Plane of the coil lies parallel to a magnetic field.
 The direction of current in the conductor is plane of paper from North to South.
 Therefore, conductor is moves downwards from N side and upwards from S side.
 They are moves as per the Fleming’s left hand rule.
 These two upward and downward forces are produces the torque.
 Torque tending to rotate the coil about its axis in a counterclockwise direction.
 Perpendicular distances between the two forces are maximum. Hence, torque is also
maximum.

POSITION-2

 In this position, the two forces being opposite to each others.
 Therefore, the perpendicular distances between two forces are zero.
 Therefore, torque is zero.
 Hence, coil tends to remain stationary in this position. Because of its inertia.

POSITION-3

 After crosses position-2, at same time. The direction of the current in the coil is reversed
by the commutator.
 Therefore, coil continues to experience the torque in the counterclockwise direction
only.
 Commutator reverse the current in each conductor of the armature as it passes from
one pole to another.

Q.3 Explain back e.m.f. or counter e.m.f.

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ANS: e.m.f. = Electro Motive Force.

 Current carrying conductor of the armature winding is placed in the magnetic field.
 Magnetic field is produced by field winding.
 When armature conductor starts rotating, flux cuts and emf is induced.
 Emf is induced according to Faraday’s law of electromagnetic induction.
 According to Lenz’s law, emf is opposes the applied voltages.
 Therefore, it is known as back emf .
 Counter emf is opposes the applied voltage across the armature.
 The net or total voltage in the armature circuit is difference between the two. i.e. V-Eb
 By ohm’s law, V=IR
 Eb = V-IaRa
i.e. V=Eb+IaRa ……………..Voltage equation of motor
Where, Ia = Armature current.
Eb= back emf
Ra=Armature resistance
V=Applied voltage
 Voltage equation of the transformer is shows, Voltage is not depends on resistance or
Armature current but also, depends on back emf.
 Back emf of motor = Eb = ᴓZNP
60A

Q.4 Explain the types of d.c. motors.

ANS:

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 There are three types of D.C.Motors.
1. A d.c. shunt motors
2. A d.c. series motors
3. Compound motors
a) A short-shunt compound motor
b) A long-shunt compound motor

EXPLANATION:

A) SHUNT MOTORS:
 Z-ZZ is a field winding.
 A-AA is a armature winding.
 When field winding is parallel to armature winding. It is said to be “Shunt motor”.

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 Shunt means parallel.
 In shunt motor Z-ZZ (field) winding has large number of turns of the fine gauge copper
wire.
 The field winding has high resistance to limit field current to a small value.
 This is helpful to reduce the power loss in the field circuit.
 Ish = V / Rsh
 Ia = I – Ish
 Eb = V – IaRa

B) SERIES MOTORS:
 Y-YY is a field winding.
 When field winding is series with armature winding. It is said to be “Series motor”.
 In series motor Y-YY (field) winding has few turns of copper wire for a low resistance.
 Field current being large which is equal to motor current.
 The required flux can be produced by small number of turns.
 Ia = I
 Eb = V – Ia(Ra+Rse)

C) COMPOUND MOTORS:
 A compound motor is a combination of shunt and series motor.
 Both shunt and series windings are employed.
 Both windings are wounded on same poles.
 Y-YY is a series field winding.
 Z-ZZ is a shunt field winding.
 Where, Y-YY is in series with A-AA and in parallel with Z-ZZ. It is said to be short
shunt compound motor.
 Short shunt compound:
V’ = V-IRse
Ish = V’ / Rsh
Ia = I – Ish
Eb = V’ – IaRa = V – Irse -IaRa
 Where, Z-ZZ is connected across A-AA and in series with YY. It is said to be long-
shunt compound motor
 long-shunt compound motor:
Ish = V / Rsh
Ia = I – Ish
Eb = V’ – Ia(Ra + Rse)
Where, Eb = Back emf.
Ia = Armature Current.

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Rse = Series resistance.
Ish = shunt field current.

Q.5 Explain characteristics of D.C.Motors. (for 4-5 Marks)
ANS: There are three characteristics of d.c. motors.

1) T vs Ia
2) N vs Ia
3) T vs N

EXPLAINATION:

1) T vs Ia :
T  Ia
Where, T = Torque
Ia = Armature current
 In dc motor, torque is directly proportional to armature current.
 The curve which shows the relation between the Torque (T) and the armature
current (Ia).
2) N vs Ia :
N  Ia
Where, N = Speed
 In dc motor, speed is directly proportional to armature current.
 The curve which shows the relation between the Speed (N) and the armature
current (Ia).
3) T vs N:
T N
Where, T = Torque
N = Speed
 In dc motor, torque is directly proportional to speed.
 The curve which shows the relation between the Torque (T) and the Speed (N).

Q.6 Explain the characteristics of D.C.Motor with one type in details.
ANS: There are three characteristics of d.c. motors.

1) T vs Ia
2) N vs Ia
3) T vs N

EXPLAINATION:

1) T vs Ia:
T  Ia

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Where, T = Torque
current (Ia).
2) N vs Ia
N  Ia
Where, N = Speed
 In dc motor, speed is directly proportional to armature current.
 The curve which shows the relation between the Speed (N) and the armature
current (Ia).
3) T vs N:
T N
Where, T = Torque
N = Speed
 In dc motor, torque is directly proportional to speed.
 The curve which shows the relation between the Torque (T) and the Speed (N).

There are three characteristics of d.c. shunt motors.

1) T vs Ia
2) N vs Ia
3) T vs N

EXPLAINATION:
Let us see D.C.SHUNT MOTOR CHARACTERISTICS

1) T vs Ia :

 T  Ia
Where, T = Torque
current (Ia).

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 Whenever, Torque increases as Armature current increases.
2) N vs Ia:
N  Ia
Where, N = Speed

 In dc motor, Speed is directly proportional to armature current.
 The curve which shows the relation between the speed (N) and the armature
current (Ia).
 Whenever, Armature current increases speed decreases.
 N  ( Eb /  )
 N  Eb  V - IaRa
 Ia increases , back emf is reduces. Therefore, speed downs.
 Hence, the curve is slightly drooping.
 Drop in speed from no load to full load being very small.
3) T vs N:
T N

Where, N = Speed
T = Torque
 In dc motor, Torque (T) is directly proportional to speed (N).
 The curve which shows the relation between the Torque (T) and the speed (N).

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 Whenever, Torque increases speed decreases.
 N  ( Eb /  )
 N  Eb  V - IaRa
 Ia increases , back emf is reduces. Therefore, speed downs.
 Hence, the curve is slightly drooping.
 Drop in speed from no load to full load being very small.
 This type of speed characteristic is generally known as shunt characteristics.

Q.7 Explain D.C. Series motor characteristics.
ANS: There are three characteristics.

1) T vs Ia
2) N vs Ia
3) T vs N

EXPLAINATION: Let us see D.C.SERIES MOTOR CHARACTERISTICS

1) T vs Ia:
  Ia
T   Ia  I²a

 Before saturation of the magnetic circuit,   Ia
 The torque is proportional to the square of armature current.
 Characteristic of D.C.Series motor is like parabola.
 After saturation of the magnetic circuit,  remains constant.
 Hence, T  
 Characteristic is straight line after the saturation.
 At low speed, series motors produced a high torque.
 Where large torque is required, d.c. series motors are used.
2) N vs Ia:

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 N  ( 1 / Ia).
 Speed is inversely proportional to the armature current.
 N  (Eb /  )  (1 /  )  ( 1 / Ia)
 Therefore, Speed is inversely proportional to the armature current.
 Eb = V – Ia (Ra + Rse)
 Ia (Ra + Rse) is very small.
 Eb is nearly constant.
 See the characteristics, Its rectangular.
 The curve shows, the series motor is variable speed motor.
 On load or no-load it can be rise the speed.
 The centrifugal force developed at such a high speed can damage the motor.
 Hence, the d.c. series motor is never started without some mechanical load on it
or never run on light load.
3) T vs N:

 Curve shows that, torque increases with speed deceases.
 Speed of the motor falls as the torque increases.
 This type of characteristics is known as series characteristics.

Q.8 Explain speed control of d.c. motors or explain armature voltage control method.
ANS: We have,

 N  (Eb /  )
 Eb = V – IaRa

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 N  ((V – IaRa )/  )
 Armature Resistance is very small.
 Therefore, IaRa is also small.
 :. N  ( V /  )
 Speed of d.c. motor is directly proportional to Applied voltage and inversely
proportional to flux.

There are two basic methods to vary the speed of d.c. motor.

1. Armature Voltage control
2. Flux control

Let us see in details.

1. Armature Voltage Control:

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EXPLAINATION:

 When Applied Voltage across the armature winding changes then speed changes.
 Speed of d.c. motor is depends on applied voltage.
 Applied voltage is constant.
 Variable Resistance is connected across armature winding with voltage.
 Variable resistance (R) is called as controller in this method.
 As external resistance is increased , voltage applied across the armature decreases and
speed falls.
 i.e. R = Increases, V = Decreases
N = Decreases or falls.
 We can use this method for to use motor at different speeds.
 This method having few merits and demerits.

MERITS OF ARMATURE VOLTAGE CONTROL METHOD:

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 It is very simple method.
 Any speed can obtained.
 Below normal speed (to crawing)

DEMERITS OF ARMATURE VOLTAGE CONTROL METHOD:

 Efficiency of the motor reduces due to power wastage in the controller.
 Controller is costly.
 Proper heat dissipation is required.

APPLICATION:

 This method is used, where slow speed require.
 Printing machine
 Cranes
 Trams, Hoist etc..

Q.9 Explain speed control of d.c. motors or explain flux control method.
ANS:

 N  (Eb /  )
 Eb = V – IaRa
 N  ((V – IaRa )/  )
 Armature Resistance is very small.
 Therefore, IaRa is also small.
 :. N  ( V /  )
 Speed of d.c. motor is directly proportional to Applied voltage and inversely
proportional to flux.

There are two basic methods to vary the speed of d.c. motor.
3. Armature Voltage control
4. Flux control

Let us see in details.

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2. FLUX CONTROL:

 By changing flux speed can be vary.
 The flux per pole is depends on field current.
 To change the field current, variable resistor is used.
 Variable resistor is called as field regulator in this method.
 In shunt motor, Field resistor is connected in series with field winding of d.c. shunt
motor.
 When resistance increases, current and flux reduces. Then speed increases.
 And vice versa for speed in d.c. shunt motor.
 In series motor, Field resistor is connected in parallel with field winding of d.c. shunt
motor.
 Resistance is called as diverter in d.c. series motor.
 When resistance increases, current and flux reduces. Then speed increases.

MERITS OF ARMATURE FLUX CONTROL METHOD:

 Speed above normal can be obtained with ease.
 Method is more convenient.
 This method is economical and efficient.
 Low power loss due to low resistance value.

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Q. 10 What are the application of D.C. Motors?

ANS: APPLICATION OF D.C. MOTORS:

 D.C. Shunt Motors: D.C. Shunt Motors having constant speed.
 Drilling machines
 Grinders
 Planers
 Metal cutting machines
 Wood working machines
 Fans
 Blowers
 Compressors
 Conveyors
 Vacuum cleaners
 Centrifugal and reciprocal pumps etc.
 D.C. Series Motors: Those machines require high starting torque.
 Traction
 Lifts
 Cranes
 Hoists
 D.C. Series Motors are commonly used for conveyors and in rolling mills.
 D.C. Compound Motors:
 Driving of steel rolling mills
 Elevators
 Punches
 Shears
 Conveyors
 Heavy planers
 Presses etc.
 Cumulative compound motors are suitable for high starting torque and for
particular under fluctuating load conditions.
 Differential Compound motors have low starting torque. They are in actual
practice.

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5. D.C. CIRCUITS
Q. 1 What is ohm’s law? Or what fundamental relation does Ohm’s law express? Give the
three forms in which the law may be expressed?
ANS: OHM’S LAW: “The current flowing through a solid conductor is directly proportional to
the difference of potential across the conductor and inversely proportional to its resistance,
temperature remains constant”.
EXPRESSIONS:

I  V/ R
I = (V/ R)*CONSTANT
: . V = IR …………..Ohm’s law equation
Where, V= Voltage, Unit: Volt (V)
I= Current, Unit: Ampere (A)
R= Resistance, Unit: Ohm (  )

Q.2 Define the terms resistance, specific resistance, conductance and specific conductance?
ANS: (1) Definition of resistance: “It is defined as the property of a substance by virtue of
which it opposes the flow of current through it.
Unit of resistance is Ohm (  )
Pure metals means less resistance and vice versa.
(2) Definition of specific resistance: “It is the resistance of a specimen piece of a material
having unit length and unit cross-sectional area”.
:. It is also called as resistivity.
:. R =  . L / A
Where, R = Resistance
 = Specific resistance
l = Length
A = Area
Unit: Ohm-meter

(3) Definition of conductance (G): “It is the reciprocal of resistance”
Where resistance is measure of opposition offered by the conductor to the flow of current, the
conductance is measure which current may flow through a conductor.
Unit of conductance is Mho (  )¯¹
(4) Definition of specific conductance: “It is the reciprocal of the specific resistance”
G = 1 / R =  .A / l
Where, R = Resistance
 = Specific resistance

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l = Length
A = Area
Unit of specific conductance or conductivity: siemens/meter.

Q.3 what are the factors on which the resistance of a material depends?
ANS: The resistance of a conductor depends upon the following factors:
(i) Type and nature of material: The resistance varies from material to material. Based
on capacity to carry free electrons. Example: silver is the best resistance and iron
offers high resistance.
(ii) Purity and hardness also affects the resistance. Pure metal less resistance and vice
versa.
(iii) Length of the conductor: The resistance of a conductor is directly proportional to the
length. Resistance of the longer wire is greater.
(iv) Cross sectional area: The resistance of a conductor is inversely proportional to the
area.
(v) Temperature: The resistance is directly proportional to the temperature.
In most materials, resistance increases with temperature.

 NOTE: CURRENT: The rate of transfer of electric charge per unit time.
 CHARGE = CURRENT X TIME
 VOLTAGE OR P.D.: The difference between the electric potentials or pressure at any two
given points in the electric circuit.
 e.m.f.(ELECTROMOTIVE FORCE): A p.d. generated by a source of electrical energy across
its terminals which tends to produce an electric current in a circuit.
 P.d = work done per charge.

Q.4 Derive the expression for equivalent resistance of a circuit having several resistance
connected (i) in series and (ii) parallel.
ANS:
(i) SERIES CIRCUITS:

DERIVATION:

 Consider the three resistances R1, R2 and R3 connected in series as shown in circuit
diagram.
 They are connected in series.
 Current flowing through the circuit is “I” and voltage across each resistance is V1, V2
and V3 across R1, R2 and R3 respectively.

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From circuit,
V = V1 + V2 + V3 …………….(1)
By Ohm’s law,
V = IR (Substitute in equation 1)
:. IR = IR1 + IR2 + IR3
IR = I ( R1 + R2 + R3 )
Hence,
R = R1 + R2 +R3
In general,
R = R1 + R2 + R3 +…..Rn

SUMMARY
 The same current flows through each resistance in turn.
 The supply voltage is sum of the individual voltage drops across the resistances.
 The total or equivalent resistance is sum of all the connected resistances.

(ii) PARALLEL CIRCUITS:

DERIVATION:

 Consider the three resistances R1, R2 and R3 connected in series as shown in circuit
diagram.
 They are connected in series.
 Current flowing through the circuit is “I” and voltage across each resistance is V1, V2
and V3 across R1, R2 and R3 respectively.

I = I1 + I2 + I3 …….(1)
By ohm’s law,
V = IR
I = V / R (Substitute in equation 1)

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:. V/R = V/R1 + V/ R2 + V/R3
V/R = V1/ R1 + V2/ R2 + V 3/ R3
V/R = V/ R1 + V/ R2 + V / R3 …………………………. (V=V1=V2=V3)
V/R = V(1/ R1 + 1 / R2 + 1 / R3) Hence,
1/R = 1 / R1 + 1 / R2 + 1 / R3
In general,
1/ R = 1 / R1 + 1 / R2 + 1 / R3 ……1 / Rn

SUMMARY
 The same potential difference is applied across all of the resistances.
 The total current drawn from the supply is equal to the sum of the currents flowing
through the individual resistances.
 The total or equivalent resistance is sum of all individual reciprocals of resistances.

Q.5 Classify the electrical networks.
ANS:
In an electrical networks or circuit, there are sources of energy and parameters like
resistors, capacitors and inductors etc.
The behavior of entire network depends on these elements. Accordingly, they can be
classified as,
(i) Linear Circuits
(ii) Non-linear Circuits
(iii) Bilateral Circuits
(iv) Unilateral Circuits and
(v) Active Networks
(vi) Passive networks

(i) Linear Circuits: Circuits whose parameters are always constant at any condition like
variation in voltage and currents etc.
Current is directly proportional to voltage.
(ii) Non-linear Circuits: Circuits whose parameters changes with variation in current and
voltages.
(iii) Bilateral Circuits: Circuit whose characteristic is same as direction of operation like
transmission line.
It has same relationship between current and voltage for current flowing in either
direction.
(iv) Unilateral Circuits: Circuits whose characteristics are dependent on the direction of
its operation is called unilateral circuits. E.g. vacuum diodes which allow the current
at one direction.
(v) Active Circuits: Having source of energy in the circuit. It may be either voltage or
current.
(vi) Passive networks: A networks contains no source of energy.

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6. THREE PHASE A.C. CIRCUITS
Q. 1 Define symmetrical system and phase Sequence.
ANS: Symmetrical system:
 When e.m.f .s of the same frequency in different phases.
 They are equal in magnitude.
 They are displaced from one another by equal phase angles.
Phase Sequence:
 E.m.f. of three phases are reach at its maximum value.
 It is essential for finding the direction of rotation of a.c. machines, parallel operation of
alternator and transformer etc.

Q.2 Write a short notes on “three phase supply system”.
ANS:
 THREE PHASE SUPPLY SYSTEM:
 For single phase system, there are two wires. Phase and neutral.
 For three phase alternator, there are three independent armature phases.
 Total six wires are required for three phase alternator. See the figure.
 The arrangement is more expensive.
 In actual practice, three armature windings are interconnected to reduced the numbers
of wires.

(a) THREE PHASE AND THREE WIRE SYSTEM:

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 Three phases are connected at a common point N.
 Where, N = Neutral
 R,Y & B are three phases.
 Such an arrangement is called Ster or wye (Y) connection.
 Fig (b) is star connected.
(b) 3-phase,3-wire, Delta or mesh-connected System:

 Each phase is connected to other phase end.
 Its closed loop.
 Fig (b) is known as delta or mesh connection.
(C) 3-phase,4-wire system:

 This system is used for low voltage distribution of electrical power.
 It provides 3-phase medium voltage supply for heavy industrial loads.
 It also provides a low voltage supply for lighting, heating and domestic loads.

Q.3 Write a short notes on “balanced load”.
ANS:

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 The load on a 3-phase system may be star or delta connected.
 If all phases impedances of the three phases load are exactly identical in respect of
magnitude and their nature. It is called as balanced load.
 The lighting and heating loads are resistive in nature.
 The lighting and heating loads are connected between line and neutral.
 The electricity is distributed on three phase of equal loads.
 In such condition, all single phase loads forms a balanced star-connected load.

Q.3 Write a short notes on “balanced system”.
ANS: A 3-phase system is balanced when it possesses following characteristics:
1) The three phase e.m.f.s are equal and displaced by 120 electrical degrees.
2) Impedance in any one phase should be identical as compare with other two phases.
3) The resulting currents in different phases with same phase angles.
4) Power and reactive power flow should be equal in each phase.

Q.4 Derive the voltage, current and power relations in star connections in a star connection.
ANS:

EXPLAINATION:
 Star connection is shown in figure (a).

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 Em.f. generated in each phase on the armature of the alternator is known as phase
e.m.f. and corresponding current as phase current.
 PHASE e.m.f.s = Vph = Vr = Vy = Vb = coming out from two phases.
 N = Neutral point.
 PHASE CURRENT: Iph = Ir = Iy = Ib
 LINE e.m.f.s = VL = VRY = VYB = VBR
 LINE CURRENTS IL = IR = IY = IB
 Balanced 3-phase inductive load is assumed.
 :. Phasor diagram is shown in figure (b).
 VRY = Vr – Vy
 VYB = Vy – Vb
 VBR = Vb – Vr
 VOLTAGE:
In star connection, From phasor diagram,
VL = VRY = 2Vph*cos30
3
= 2*Vph*
2
:. VL = 3 Vph
 CURRENT: Line current = Phase Current
 IL = Iph
 POWER: P = V*I
P = 3*Power supplied by each phase
P = 3* Vph*Iph* Cos
VL
P = 3* *IL* Cos
3
P = 3 * VL*IL* Cos

Q.5 Derive the voltage, current and power relations in delta connections in a delta
connection.
ANS:

48

___________________________________________________________________
EXPLANATION:
 Delta connection is shown in figure (a).
 Em.f. generated in each phase on the armature of the alternator is known as phase
e.m.f. and corresponding current as phase current.
 PHASE e.m.f.s = Vph = Vr = Vy = Vb = coming out from two phases.
 N = Neutral point.
 PHASE CURRENT: Iph = Ir = Iy = Ib
 LINE e.m.f.s = VL = VRY = VYB = VBR
 LINE CURRENTS IL = IR = IY = IB
 Balanced 3-phase inductive load is assumed.
 :. Phasor diagram is shown in figure (b).
 VOLTAGE: Line voltage = Phase voltage
 CURRENT: In delta connection, From phasor diagram,
IL = IR = 2Iph*cos30
3
= 2*Iph*
2
:. IL = 3 Iph
 POWER: P = V*I
P = 3*Power supplied by each phase
P = 3* Vph*Iph* Cos
VL
P = 3* *IL* Cos
3
P = 3 * VL*IL* Cos
Q.6 Solve all problems based on star connection and delta connection.

49

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7. A.C. FUNDAMENTAL
Q.1 What is an alternating current? Compare it with a direct current.
ANS: Alternating current is one which periodically passes through a definite cycle of changes in
respect of magnitude as well as direction.
Or
Alternating current is current which flows periodically through a definite cycle of changes in
respect of magnitude as well as direction.

Direct current: d.c. is that current which flows continuously in one direction and has constant
magnitude with respect to time.

Comparison between a.c. and d.c. or advantages of a.c.
1. The ac voltage can be raised or lowered very easily by using transformer. In dc, not so
easy and economical.
2. Construction and operating costs per kilowatt are low.
3. We can build up high voltage, high speed a.c. generators with large capacities. It is not
possible in dc.
4. Due to adoption of high voltages, a.c. transmission is always efficient and economical.
Because, higher the voltages lesser the current through transmission.
5. ac motors are simple in construction, cheaper and more efficient than dc.
6. ac can be easily converted to dc for the application like traction, search lights,
projections etc.

Q.2 What is the principle of Generator? Also, Explain generation of alternating current and
voltage.
ANS:
Generator: Which converts mechanical energy into electrical energy either ac or dc.

Principle of Generator:
“When a conductor is moved in magnetic field or magnetic field moved with respect to the
conductor. According to Faraday’s law of electromagnetic induction, electromotive force is set
up in the conductor”

50

___________________________________________________________________


CONSTRUCTION:


OPERATION:

 Assume that the armature coil is rotating in an anticlockwise direction.
 According to Faraday’s law of electromagnetic induction e.m.f. is produced in them.

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 The magnitude of this e.m.f. is depend on position of coil.
 Let us consider few positions of the coil:

POSITION 1:
 At ϴ = 0
 This is the initial position of the coil
 The plane of the coil is perpendicular to the magnetic field .
 The conductor of the coil move parallel to the magnetic field.
 There is no flux cutting. So, no emf is generated in the conductor.
 No current flows.

 POSITION 2:
 At ϴ= 0 to ϴ= 90
 Coil is rotates from 0 to 90
 Both the conductor of the coil move at right angles to the magnetic field.
 There is maximum flux cutting. So, there is maximam emf generated in the conductor.
 Emf is generated from 0 to maximum.
 The emf’s in both conductor being in series. Therefore , total emf is sum of two emfs.
 The voltages are equal and twice than one of the conductor.
 The current is varies as the emf varies.
 More and more lines of force are ct by the conductors.
 According to fleming’s right hand rule, the direction of induced current is towards the
observer (conductor A) and away from observer (conductor B).
 Therefore,, current flowing through resistor from the terminal C to the terminal D.

POSITION 3:
 At ϴ= 90 to ϴ= 180
 Coil is rotates from 90 to 180.
 Conductor again moves parallel to the field.
 The lines of force cut by the conductor gradually reduces.
 Hence, emf is decreases.
 Therefore, current through external resistor is zero.
 In this, during first half cycle the conductor moves in the same direction through the
magnetic field.
 Therefore, polarity of generated e.m.f. is same and current flows through the external
resistor from C to D.

 POSITION 4:
 At ϴ= 180 to ϴ=270
 As the coil rotates beyond position 3.
 The direction of the cutting lines of force through the magnetic field reverses.

52

___________________________________________________________________
 Conductor A cuts up and conductor B cuts down through the field.
 Both the polarity of generated e.m.f. and current is reverse.
 By fleming’s left hand rule, direction of current in conductor A is away and for B
towards.
 Current flows through D to C.
 Similar to position 2, emf in the coil is maximum in position 4.
 In general, the variations in the magnitude of emf of the alternator is exactly similar to
those in first half revoltion.
 Current supplied by alternator is necessarily alternating.
 Unidirectional or direct current is desired.
 Before external circuit, alternating current must be rectified or commutated.
 Rectification can be done by replacing the slip-rings R1 and R2 of the alternator.
 Where, M is shown in figure “COMMUTATOR”.
 Commutator is made by conducting material which is cuts in two equal halves or
segments.
 Segments are insulated by thin sheet of mica or some other insulating material.
 The ends of the armature coil AB are joined to these segments.

The external load resistor R is connected to the split ring M through brushes B1 and B2.

ACTION OF A COMMUTATOR:
 When coil is undergoing for first half cycle, current flowing from load(R) (C to D).
 For next half cycle, its reverses with position of a and b terminals.
 Again for next cycle, current is flowing from C to D and so on.
 Direction of current through the external circuit is same.
 In the commercial d.c. generator, by using number of coils evenly distributed
around the armature core and connecting these coils to commutator having a
corresponding number of segments, a more steady direct current is obtained in
the external circuit.

GRAPHICAL REPRESENTATION OF E.M.F. OR CURRENT:

53

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Q.3 Derive the equation of the alternating voltages and currents?
ANS:

Generator: Which converts mechanical energy into electrical energy either ac or dc.

Principle of Generator:
“When a conductor is moved in magnetic field or magnetic field moved with respect to the
conductor. According to Faraday’s law of electromagnetic induction, electromotive force is set
up in the conductor”


CONSTRUCTION:


DERIVATION:
Let,
B= Flux density of the magnetic field (teslas)
l = Length of the conductor (metres)
r = Radius of circular path (metres)
ῳ = Angular velocity of the coil (radians / second)
v = Linear velocity of the coil sides ( metres / second)

when the coil lies in YOY plane and zero e.m.f.
then, angle ϴ = ῳt ……………………………………………………………..(1)

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After some time coil rotates at angle ϴ. It resolved two components (1) horizontal (v.cosϴ) and
(2) vertical (v.sinϴ).
Therefore,
E.M.F. generated in each coil side: B.l.v.sinϴ volts ……………….(2)
Total e.m.f. generated in the coil = e
:. e = 2 B.l.v.sinϴ volts ……………………………………….(3)
When coil will be horizontal plane then ϴ = 90 and conductor cuts maximum flux (Em)
:. Em = 2 B.l.v.sinϴ
= 2 B.l.v.sin90
= 2 B.l.v.1 ( sin90 = 1)
= 2 B.l.v volts
Therefore, the standard equation of the voltage or e.m.f,
e = Em.sinϴ
e= Em.sinῳt
e = Em.sin(2π.f.t)
e = Em.sin(2π.t / T)
Similarly, we can write for current,
i = Im.sinϴ
i = Im.sinῳt
i = Im.sin(2π.f.t)
i = Im.sin(2π.t / T)

Q.4 Define peak factor, form factor, waveform, cycle, periodic time, frequency and
amplitude.
ANS:
(i) PEAK FACTOR:
“ It is the ratio of maximum value to the R.M.S. value of an alternating quantity”.
It is also called as crest or amplitude factor.

Peak factor = maximum value
R.M.S. value
Where, R.M.S. value = 0.707 X Maximum value
Maximum value = √2 X R.M.S. value
Substitute in peak factor,
Peak factor = maximum value
0.707 X Maximum value
Peak factor = 1.4144
(ii) Form factor:
“ It is the ratio of R.M.S. value to the average value of an alternating quantity”.
Form factor = R.M.S. value
Average value
Where,

55

___________________________________________________________________
Average value = 0.637 X maximum value
R.M.S. value = 0.707 X Maximum value
Substitute in form factor,
Form factor = 0.707 X Maximum value
0.637 X maximum value
= 1.11
(iii) waveform:
“ It is the pictorial representation of an alternating quantity in a graphical form”.
(iv) cycle:
“Each repetition of a complete set of changes undergone by the alternating quantity is called
cycle”.
(v) Periodic time:
“ It is the time required by an alternating quantity to complete its one cycle”.
It is denoted as “T” in seconds.
(vi) Frequency:
“ The number of cycle completed per second by an alternating quantity is known as frequency”.
It is denoted as “f” in hurtz.
f=1/T
(vii) Amplitude:

The maximum value attained by an alternating quantity during it’s positive or
negative half cycle”.

56

___________________________________________________________________
8. INSTALLATION, EARTHING AND TROUBLE
SHOOTING

Q.1) Briefly describe the different types of wires used in the electrical wiring work. How these
wires normally specified?
ANS: There are nearly (commonly) seven types of wires.
They are as follows:

1) V.I.R.
2) C.T.S. / T.R.S.
3) Lead Sheathed Wires
4) P.V.C. Wires
5) Weather Proof Wires
6) Flexible Wires
7) Cables

Explanation:

1) V.I.R. (Vulcanised India Rubber wires):
 It consists of a tinned conductor coated with rubber insulation.
 The thickness of rubber varies i.e. 250 or 660 V.
 Insulation is not moisture & heat proof.
 Conductor is covered with heat & moisture resistant bitumen compound.
 It is finished with wax for cleanliness & smoothness.
 These wires are single core.
 These wires are rarely used.
 Cheaper cost.
2) C.T.S. (Cab Tyre Sheathed ) or T.R.S.(Tough Rubber Sheathed):
 It consists of rubber insulation conductor but additional tough rubber is used.
 Tough rubber is provides protection against moisture ,chemical fumes, wear &
tear.
 These wires are single core, twin core & three core.
3) Lead Sheathed wires:
 It consists of rubber or paper insulation conductor but additional tough rubber is
used with an outer sheath of lead or lead alloy.
 It gives protection against moisture, atmospheric corrosion, wear & tear.
 These wires are single & multicore.
 Quite heavy & costly.
4) P.V.C. (Poly Vinyl Chloride wires):
 Conductors are insulated with P.V.C.

57

___________________________________________________________________
 P.V.C is non-hygroscopic, tough,durable,resistant to corrosion & chemical inert.
 These wires are sufficient to give mechanical protection.
 P.V.C. being a thermoplastic, softens at high temperature.
 It should not used for giving connection to heating appliance.
5) Weather Proof Wires:
 It is used for outer service lines.
 Wires are costly.
 Its conductor consist of three braids of fibrous yarn with water proof compound
are used.
 They are cheap.
 They are resistant to varying atmospheric conditions.
6) Flexible wires:
 It consists of two separately insulated stranded conductors.
 Stranded conductors are used for flexibility.
 Rubber or P.V.C. are used or insulation.
 They are available in the two parallel twin and twisted twin forms.
 Easy to handles.
 Good flexibility.
 Used for holders, household portable appliances, like heater, irons, table lams,
etc.
7) Cables:

“It is defined as a length of a single insulated or two or more insulated
conductors, each having its own insulation and all put together”.
 It is used for distribution purpose.
 They are laid along the wall poles (Aerial cables)
 These cables are insulated with V.I.R. or P.V.C. or varnish cambric.
 They are mechanically sound and weather proof.

58

___________________________________________________________________
 V.I.R and P.V.C are used for outdoor works.
 They are designed for underground laying (Underground cables).
 They are costly.

CONDUCTOR or CORE:

 It has one central core or a number of cores i.e. 2,3,3⅟2 or 4.
 It is made up of tinned stranded copper or aluminum conductor.
 Stranding gives flexibility to the cable.

INSULATION:

 Insulating materials are impregnated paper or vulcanized bitumen or
varnished cambric.
 Impregnated paper is used for high-voltage cables.

METALLIC SHEATH:

 Lead alloy or aluminum sheath is provided over the insulation.
 Insulation provides mechanical protection & preventing entry of
moisture in the insulation.

BEDDING:

 Bedding consists of a layer of fibrous material.
 It protects from corrosion & mechanical injury.

ARMOURING:

 It consist of one or two layers of galvanized steel wire or steel tape.
 During laying, it provides protection from mechanical injury.

SERVING:

 A layer of fibrous material like jute cloth.
 It protects from atmospheric condition.

Q.2) What is fuse? Explain the principle of operation of a fuse and its type.
ANS: FUSE:

 Fuse is a current interrupting device or type of sacrificial over current protection device.
 Fuse is an essential component which is a metal wire or strip that melts when too much
current flows through the circuit.
 It starts melts when fault is occurred, excess current flows, short circuit, overload,
device failure etc.

59

___________________________________________________________________
 Short circuit means, where there is a direct connection between live wire to neutral
wire.

GENERAL CONSTRUCTION:

 Small piece of wire connected between two terminals on the insulated base.

FUNCTION OF THE FUSE:

 When the fuse is inserted in a circuit to be protected.
 Fuse carries normal current safely without heating.
 Whenever excess current flows then it melts due to rapid overheating.
 It disconnects the load during faults or over current or short circuit.
 The fuse is in effect a safety value for the electrical circuit.

FUSE ELEMENT:

 It is metal like tin, lead, copper, aluminum, zinc, silver and antimony.
 The most preferred lead-tin alloy is found more suitable for this purpose.
 Tin-alloy = lead (37%) + alloy(63%)
 Normally, tin-alloy wire is not used beyond 10 amps because of higher current.

TYPES OF FUSES:
There are two types.

1) Semi-enclosed or Rewirable type fuse.
2) H.R.C. Cartridge Fuse.
EXPLAINATION:
1) Semi-enclosed or Rewirable type fuse:

CONSTRUCTION:
 Fuse element is semi-enclosed.
 It is also known as kit-kat type fuse.
 Where, E = fuse element

60

___________________________________________________________________
S = Screws
C = contacts
B’ = Porcelain fuse bridge
B’’ = base.
 E = Short length of fuse wire depending upon the ratings.
 B’ = wire is threaded in the hole.
 B’’ = Incoming and outgoing is connected to this bridge.
 C = contacts

OPERATION:

 Fuse wire is in series with the circuit to be protected.
 During fault, fuse element resist and heat is developed.
 Current rises and fuse is starts melting.
 After some time its breaks and circuits to be protects.

APPLICATION:

 Commonly used in domestic installation and the other circuits.
 It is used to be protects low values of faults.

2) HIGH RUPTURING CAPACITY CARTRIDGE FUSES:

Where, E = Fuse element
C = cartridge
M = Metal end caps
P = Pure quartz
B = Contact blades
 E = Silver or copper made.
 Fuse element is totally enclosed and hermetically sealed inside the container
called Container.
 C = Cearamic material or epoxy-resins made.
 End of the enclosed fuse elements are connected to the metal end caps (M)
normally of brass.

61

___________________________________________________________________
 The fuse body is filled with powdered pure quartz.
 Some form of the indication is provided on it.

OPERATION:

 When the fuse is inserted in the circuit to be protected.
 It carries the normal working current safely without heating.
 When a fault occurs, fuse element starts melting due to excess of current flow through
it.
 The metal released in the vapour form diffuses with the quartz powder.
 The chemical reaction between the two substance of high electrical resistance like an
insulator.
 An indicator consists of resistance wire of fine gauge connected in parallel with the fuse
element.

APPLICATION:

 Due to increasing loads and size of the network, H.R.C. replacing with rewirable fuse.
 They are used in industrial installayion and low-voltage distribution.

Q.3) Compare the different methods of wiring with respect to their application, cost and life?
ANS: There are total five different types of wirings:
PARTICULAR CLEAT WOODEN T.R.S./ C.T.S. LEAD CONDUIT
WIRING CASING & WIRING SHEATHED WIRING
CAPPING WIRING
Durability of Short life Fairly long life Long life Long life Very long
life
Mechanical Poor Good Fair Good Very good
Protection protection protection protection protection protection
Appearance Shabby Neat Neat Neat Good
Type of Semi-skilled Highly skilled Skilled Skilled Highly skilled
labour
required
Cost Low Medium Medium Costly than High
capping or
C.T.S. wiring
Possibility of Nil Poor Good Very Good Poor or fair
hazards
Application Temporary General Most widely Damp Concealed
installation Indoor work used in situation type wiring
indoor wiring

62

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Q.4) Explain conduit wiring? Or What are the various types of conduit used in conduit wiring?
ANS: CONDUIT WIRING:
V.I.R or P.V.C. wires are run through black enameled or galvansed metallic tubing called
conduit.
There are two types of conduits:

1) Thin wall conduits
2) Rigid conduits
1) Thin wall conduits:
 These are light gauge iron conduit with seam along its length.
 The seam may be open type.
 There is no mechanical adhesion between its two edges.
 These edges are brazed together for damp proof.
2) Rigid conduit:
 These are heavy gauge iron conduit.
 Conduits are solid drawn or with welded seam.
 Join fittings are always threaded.
 Conduits are more costly.
 Conduits are used for medium pressure circuits.
 Also used in places where good mechanical protection & absolute protection
from moisture is required.

There are two types of Conduit wiring. They are as follows,

 Surface conduit wiring
 Concealed conduit wiring
a) Surface conduit wiring:
 Conduits are fixed on the walls.
 By using saddles screwed to rawl plugs or wood plugs.
 In damp situation, they are separated by small wooden blocks.
 Conduit piping is kept at earth potential by proper earthing.

63

Vijay Balu Raskar E.T. Notes

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