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Friday, 16 August 2019

Voltage and Current Relationship [AC Circuit]

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At constant temperature, the current flowing through the conductor is directly proportional to the potential difference (voltage) between the two ends of the conductor. This is ohm’s law.
The relation may be written as,

V = IR

Where V and I now vary with time. When a sinusoidal if I = Imsinώt is applied to a resistor the potential across it.
E = Im R sinώt
    = Vm sinώt


A.C through pure resistor only

A pure resistive circuit is shown in fig, the alternating voltage applied across the resister is
V= Vm sinώt
Let ‘I’ be the alternating current through the circuit
VR= voltage drop across the resister.
V = I ×R
I = V / R
I = Vmsinώ t /R
I = Im sinώ t ------------------------ 2
Im sinώ t = Vmsinώ t / R
Im = Vm sinώ t / R sinώ t,
Im = Vm/ R
From the equ. 1 and 2, the phase angle voltage and current is zero.
Ө = 0

In pure resistive circuit, the circuit is in phase with the voltage .the waveform and vector diagram are shown in the fig (a) and (b)
Instantaneous, power, P = V x I
= Vmsinώ t × Im sinώ t
= Vm Im sin2ώ t

Power = VI watts

Where V and I are R.M.S values

Phase Angle

Phase angle is an angle between the voltage and current.
In a pure resistive current, the voltage and the current in phase with each other hence the phase angle is zero.

Power factor

Power factor = cos
= cos θ [θ=0]
= 1 (Unity)
Power factor is also defined as the ratio of resistance to impedance
cos θ R/Z
Its value cannot be more than one

A.C through pure inductor only

Pure inductive current is shown in fig

When an alternating current flows through a pur inductive coil a back e.m.f is induced due to the inductance of coil. This e.m.f opposes the aplied voltage at every instant since there is no resistance the induced e.m.f will be equal and opposite to the applied voltage.

i.e., Applied voltage = back e.m.f

Applied voltage, V = Vm sinώ t ------------------- 1

Im = Vm/ώL

from equ.2 and 3, we find that the current. Lags behind the applied voltage by 90˚.
the waveform and vector diagram are shown in fig (a) and (b)

Power (P)

V= Vmsinώ t, i= Im sin (ώt-90)
Instantaneous power= V×I= Vmsinώ t× Im sin (ώt-90) = VmIm sin2ώ t

Phase angle

Phase angle is an angle between the voltage and current

In inductive circuit, the angle between the voltage and current. is 90˚
i.e. θ =90˚ The current is always lagging the voltage by 90˚

Power factor

Power factor = cosθ
= cos (90˚)
= 0 (lag) ( θ=90˚ )

AC through pure capacitor only

The circuit shown in the fig is a pure capacitive circuit.

When an alternating voltage is applied to a capacitor the capacitor is charged first in one direction and then in the opposite direction.
V= Vmsinώ t ------------- 1
Q = CV= C Vmsinώ t
Current ,i = dQ/dt
= d(C Vm sinώ t)/dt
= C Vm sinώt . ώ =ώ C Vm sinώ t
= ώ C Vm sinώ t (ώt-90)
I= Im sin (ώt-90) ------------- 2
Im sin (ώt-90) = ώ C Vm sinώ t (ώt-90)
Im = ώ C Vm (or)
Im = Vm/(1/ ώ C)
From the equ, 1 and 2, we find that the current leads the voltage by 90˚ the waveform and vector diagram. Are shown in fig. (a) and (b)

Power (p)

V= Vmsinώ t,
I = Im sin (ώt+90)
Instantaneous power= V x I = Vmsinώ t x Im sin (ώt+90)

Phase angle

Phase angle is an angle between the voltage and current
In inductive circuit, the angle between the voltage and current. is 90˚
i.e. θ =90˚
The current is always lagging the voltage by 90˚

Power factor

Power factor = cosθ
= cos (90˚)
= 0 (lead)

Important Terms:

1. Impedance

It is ratio of the applied voltage to the resulting current.
It is represented by the letter ‘Z’.
Its unit is Ohm.( Ω)

i.e. Z = V/ohm.

2. Admittance

It is defined as the reciprocal of impedance.
It is represented by the letter ‘Y’.
Its unit is mho.

 i.e. Y = 1/ I/V mho

3. Reactance

Inductive reactance, Xl =2πfl
Where f =freq,
L=inductance of the coil
Capacitive reactance, Xc = 1 / 2πfc
Where C= capacitance of the capacitor
Unit of the reactance is Ohm

4. Susceptance

It is defined as the reciprocal of reactance.
It is represented by the letter ‘b’ Its unit is mho

B = 1 / X mho

5. Conductance

It is defined as the reciprocal of resistance.
It is represented by the letter ’g’. Its unit is ‘mho’.

G= 1/R mho

Thursday, 15 August 2019

Open Circuit and Short Circuit Test of Transformer Calculation

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Transformer test

The performance of transformer can be considered on the source of its corresponding circuit which have four main parameters the corresponding resistance R01 as known to primary (or secondary R02 ) ,the corresponding leakage reactance X01 known to primary (or secondary X02 ), the core loss conductance G0 and the magnetizing susceptance B0 .These constants are factors that can be simply calculated by two test.

1. Open circuit test (O.C)
2. Short circuit test (S.C)

1. Open Circuit (O.C) Test on Transformer Calculation

Open circuit test is used

• To determine no load constants R0, X0
To determine core loss

The connection diagram of O.C. test is shown in the fig. The rated voltage is applied to the primary winding, keeping the secondary is open. The readings of voltmeter, Ammeter and wattmeter are recorded. Let the respect readings are given below.

Ammeter reading = I0
Voltmeter reading = V0
Wattmeter reading = W0

W0 represents the power input to the transformer on no load. It is equal to sum of core loss and copper loss. Since the no load current is small, the copper loss,(I20 R01) very small. Hence the copper loss at no load is neglected. Therefore W0 reading shows the core loss.
From this reading R0, X0 are calculated as followed,

V0I0 cosӨ0 = W0
Power factor, cos Ө0 = W0 / V0 I0
Core loss component of no load current IC = I0cosӨ0
Magnetising component of no load current Im = I0sin Ө0
No load circuit constants

R0 = V0 / Ic,
X0 = V0 / Im

2. Short Circuit (S.C ) Test on Transformer Calculation:

Short circuit test is used to

1 determine load constants R01 (or) R02, X01(or) X02
2 determine copper loss at full load

The connection diagram S.C. test is shown in the fig. A reduced voltage is applied to the primary winding and keeping the secondary short-circuited. The applied voltage is gradually increased until full load current flows through the transformer. The reading of ammeter, voltmeter and wattmeter are recorded. Let the respecting readings are Is ,Vs ,Ws.

Here the core loss is negligibly small since the applied voltage is very small. So the wattmeter reading (Ws) will give the full load copper loss of the transformer.

VsIs cosӨs = Ws
Power factor, cosӨs = Ws / VsIs
Impedance, Z01 = Vs / Is
Full load copper loss, Ws = Is2 R01
Total resistance, R01 = Ws/ Is2 ( R01 is total resistance referred to primary side)
Total reactance is primary side, X01 = √ Z012 - R012

Transformer - Operation, Types, EMF Equation

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A transformer is a static electrical machine which transfers electrical energy from one circuit to another circuit without change in its frequency. Due to electromagnetic induction principle the transfer of energy takes place.

Transformer Construction

It consists of three essential parts , they are

1.Primary winding

2.Secondary winding

3.Laminated iron core

I/p - primary
O/p - secondary

Principle of operation

Transformer works on the principle of mutual induction. When an A.C supply is given to primary winding, an alternating flux is set up in the core. This flux cuts both primary and secondary windings. An e.m.f is induced in the primary winding according to self induction principle. According to faradays mutual induction principle, an e.m.f is induced in the secondary winding. if we connect a load to the secondary winding, current will follow through the load. In this way, electrical energy is transferred from the primary to secondary circuit.

Types of transformer

1.Step - down

If the number of turns in the secondary winding is less than that of the primary winding, the e.m.f induced in the secondary winding will be less than the e.m.f induced in the primary winding. This type of transformers is called step down transformers.


If the number of turns in the secondary winding is more than that of the primary winding, the e.m.f induced in the secondary winding will be more than the e.m.f induced in the primary winding. This type of transformers is called step up transformers.

Ideal Transformer

An ideal transformer is static electric machine which transfers electrical energy from one circuit to another circuit without any losses. It consists two purely inductive coil of has loss-free core


1. no winding resistance therefore, there is no I2losses

2. no leakage flux

3. no core losses (or) iron losses in the core.

According to construction, transformer divided into two types

1. core type transformer
2. shell type transformer


In core type transformers the winding surround the core as shown in fig (a) & (b)

1    The core is made up of thin laminated silicon steel.

2    The laminated steel cores are insulated from each other by means of varnish.

3    The laminated core minimizes the eddy current loss.

4    The thickness of lamination varies from 0.35 mm to 0.55 mm

5    Since the core is made up of silicon steel, the hysteresis loss is reduced

6    The cross section of the core may be rectangular for small transformers

7    For large, the cross section of the core should be either square (or) stepped as shown in the fig.

8    The primary and secondary winding of core type transformer are wound helically.

9    Coil is insulated from one another using mica.


In shell type transformers the iron core surrounds the windings.

1. The core is made up of thin laminated silicon steel.

2. The laminated steel cores are insulated from each other by means of varnish.

3. The laminated core minimizes the eddy current loss.

4. The thickness of lamination varies from 0.35 mm to 0.

5. Since the core is made up of silicon steel, the hysteriesis loss is reduced

6. The cross section of the core may be rectangular for small transformers

7. For large, the cross section of the core should be either square (or) stepped as shown in the fig.

8. Coil is insulated from one another using mica.


Consider a transformer having


N1 =primary turns
N2 =secondary turns
Φ = maximum flux in the core
f=freq of the a.c voltage applied

Flux in the core will vary sinusoidal as shown in the waveform

The flux increases from zero value to max value ‘Φm’ is ¼ f second.
The change of flux is ¼ f second = (Φm-0) Weber’s.

Rate of change of flux is the second = Φm / (1/4f) = 4fΦm

Since the flux is varying sinusoidally, the r.m.s value of induced e.m.f is obtained by multiplying the average value with the form factor,

Form factor of sine wave = R.M.S value/average value = 1.11

R.m.s value of e.m.f induced is one turn = 4f Φm*1.11 = 4.44 f Φm

R.m.s value of e.m.f induced in primary winding E1 = 4.44 f Φm N1
R.m.s value of e.m.f induced in secondary winding E2 = 4.44 fΦm N2

In an ideal transformer, e.m.f induced in any winding is equal to the voltage across its terminals on no load.

Applied voltage, V1 = E1
Secondary terminal voltage, V2 E2

Voltage transformation ratio = E1 / E2 =  4.44 f Φm N1 / 4.44 f Φm N2 = N2 / N1 = K

If NN1, k > 1, then the transformer is called step up transformer

If N1 > N2, k < 1, then the transformer is called step down transformer

Current transformation ratio

In an ideal transformer,

Apparent input power = Apparent output power V1I1 = V2I2

I1 / I2 = V2 / V1 = W2 / W1 = K

Wednesday, 14 August 2019

Chemical Properties of Insulating Materials

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1. Chemical Properties: 

Insulating material do sometimes come in contact with chemicals. For example a pole insulator used in the transmission and distribution overhead lines comes in contact with the chemicals like nitrogen, hydrogen, in the atmosphere. When they come in contact with chemicals, the properties of the insulating materials to which it has been designed should not change.

2. Chemical Resistance: 

The insulating materials are chemically affected by the gases, water, acids, alkalies and salts. Chemically a material is a better insulating material if it resists chemical reaction. For example, plastic is mostly used in place of paper insulation in many applications because it is not affected by chemicals and is less hygroscopic. The chemical resistance requirements of insulating materials used in underground cables which are likely to operate under severe chemical condition due to water, salts, acids or alkalies, will be more demanding than those of the insulating materials used in motor winding.

3. Hygrucopicity: 

Many insulators come in contact with atmosphere either during manufacturers, operation or both. The contact of insulation with atmosphere is often so complete that even the less chemically aggressive atmosphere can prove a threat to the smooth running apparatus. The moisture may act on insulator or may be absorbed by the insulation. The process of absorption of moisture is known as Hygroscopicity. This affects the electrical properties adversely, however, there are insulating materials like paraffin, polythene, polytetra-floure ethelene, which are non-hygroscopic.

4. Effects on other Materials: 

The insulating materials are affected by the contact with the conducting and structural materials. If rubber is in contact with copper, chemical action takes place. To avoid it, a coating of tin is applied to copper before putting on the rubber insulation. In oil filled transformers and capacitors, the synthetic insulating oil reacts with the inner walls of the iron tank causing iron particles to mix with the oil and this can badly affect the insulating properties of the oil.

5. Ageing of Insulators: 

Ageing is the long time effect of heat, chemical action and voltage application. These factors decide the natural life of insulators and hence of an electrical apparatus.

Tuesday, 13 August 2019

Thermal Properties of Insulating Materials

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1. Thermal Properties : 

The insulating materials used must be stable within the allowed temperature limits. Certain materials like, waxes, plastics, bitumen compounds and resins are softened at low moderate temperatures. This may cause the deterioration of mechanical properties and the insulation may melt out of the coil windings etc., causing internal short circuits. The chemical changes are accelerated at high temperatures and hence a maximum working temperature is fixed for any type of materials used as insulators. Some organic compounds are damaged by exposure to ultraviolet rays and corona. Ability of temperature to affect such diverse and important properties like electrical properties, mechanical strength, hardness, viscosity, solubility etc., has made the thermal properties all the more important. Hence all the classification of insulating materials are made on the basis of their operating temperature. Some of the thermal properties have been discussed in the succeeding paragraphs.

2. Melting Point : 

The melting point of liquid dielectric used in solids state should be sufficiently high. Melting point is important in specific cases like non-draining compound paper insulating cable. It is desired that in the entire operating temperature of the cable the impregnating compound must not melt to avoid migration of oil. The insulating materials for such purpose should be chosen with a melting point much above that of the operating temperature.

3. Flash Point:

In liquid insulators flash point is an important property to be observed, the insulating material, usually oil, used in the transformer and switchgear should not catch fire at the operating temperature. The materials which are required to withstand high temperature of about 1000°C or so should retain the electrical properties and chemical structures, over the entire range of temperature. Flash point of liquid dielectric is that temperature at which the liquid begins to ignite. Insulating materials which are exposed to arcing should have self extinguishing resistant to cracking or carbonisation of the material.

4. Volatality :

A volatile material cannot act as a good insulator. When a trapped, 11,0 s is evolved from a volatile insulating material subjected to volatile stress, the breakdown of insulator is accerted. Hence material used for insulation should not exhibit volatile property.

5. Thermal Conductivity : 

During the electrical operation heat is generated due to the copper losses within the conductor and its dielectric losses within the insulator. The entire heat produced should be transferred to the outside atmosphere so as to maintain the operating temperature within limits. Hence, an insulator that is used should not have very low thermal conductivity especially in high voltage apparatus where the thickness of insulation is more. Normally most of the insulating materials are poor conductors of heat.

6. Thermal Expansion: 

Thermal expansion is important because of the mechanical effects caused by thermal expansion due to temperature changes. Due to repeated and rapid load cycles of an equipment corresponding expansion and contraction of the insulator occurs leading to the possibility of formation of voids. When two insulating materials are combined to form and insulating system due to two different coefficients of thermal expansion, formation of voids is inevitable. This void formation plays a major role in the breakdown of the insulation. Thermal expansion is of significant importance where heavy currents are involved.

7. Heat Resistance : 

An insulating material should be able to withstand temperature variations within the specified limits without damaging its other properties. An insulating material which retains its properties at high temperatures has got the advantage that current loading can be increased and thus the apparatus can handle more power.

Mechanical Properties of Insulating Materials

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Mechanical Properties of Insulating Materials

Mechanical properties such as impact strength, tensile strength, toughness, hardness, elongation, flexibility, abrasion, resistance etc., have to be considered when choosing an insulating material. Machinability and resistance of splitting are equally important. In the case of varnished products, the bonding property of varnish is important. Some of the mechanical properties which are to be taken care off while selecting the insulating material are dealt in the succeeding paragraphs.

1. Tension and Compression:

The conductors of transmission and distribution systems of overhead lines are supported by means of insulators to avoid leakage of current through the supports to the earth. When a tensile load exists on it, it should be able to withstand and should not give way mechanically.

2. Resistance to Abrasion, Tear, Shear and Impact:

Take the case of the insulator used between the commutator segments which are subjected to abrasive action during the running of the motor. The insulation qualities should be such that it should withstand this abrasive force. The insulating material should be hard and mechanical resistant. In the case of insulating material which is subjected to tear, shear or impact, the damage caused to them will completely put the system out of control and sometimes out of stability. In such cases the insulating material should be capable of withstanding all such forces and should not give way. Importance should be given to these factors while selecting the insulating material for the job.

3. Viscosity : 

In liquid insulators, viscosity plays an important role. It affects the manufacturing process. For example, in paper insulated cables, the temperature at which the oil will penetrate through the paper will depend on its viscosity. Low viscosity liquids are more mobile and hence helps in transmission of heat by easy circulation as in the case of Power transformers and switch gears. Liquid insulations should not contain impurities as it will also affect the viscosity and the performance. The methods used to purify the insulating oil will also depend on the viscosity of the oil.

4. Porosity :

In solid insulators like pole insulators used for transmission and distribution lines, high porosity will increase the moisture holding capacity which is not desired because it adversely affects the electrical properties of the insulator. Therefore, high porosity is not a desired factor. But in certain other applications like in paper which is to be impregnated with oil to increase the insulation capacity, high porosity is desirable and advantageous. Therefore, this factor should be visualised with respect to application and decided as to what should be the level of porosity required for the insulating material.

5. Solubility : 

Certain insulating materials like varnish should be applied only after it is dissolved in proper solvents like acetone. In such cases the insulating material should be soluble in certain suitable solvents, but it should not be soluble in water otherwise the moisture of the atmosphere will be able to remove the applied insulation and cause breakdown.

6. Moisture Absorption : 

The insulating material should not absorb moisture as moisture lowers the electrical resistance and dielectric strength. Due to moisture absorption certain chemical and mechanical effects like swelling warping, corrosion may also occur. Therefore, the insulating materials should not absorb moisture but even if it so, it should be as low as possible without disturbing the electrical characteristic limit.

7. Machinability and Mouldability : 

In the manufacturing of solid insulating material, it should have the property of being easily moulded and machined into the required shape and size.

Monday, 12 August 2019

Factors affecting Dielectric - Constant, Strength and Loss

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Factors affecting Dielectric Strength :

Every electrical apparatus is designed so as to work within a definite range of voltage. If the operating voltage is increased gradually, then at some value of voltage a breakdown will occur puncturing the insulation permanently. The dielectric strength or electric strength or breakdown voltage is, therefore, the minimum voltage which when applied to an insulating material will result in the destruction of its insulating properties.

Dielectric strength is expressed in kV per unit thickness of the insulating material. Breakdown potential is that value of voltage which when applied across one cm or one mm thickness of dielectric medium or insulating medium will breakdown its insulation e.g., the breakdown potential of air is 30 kV/cm which means that the maximum potential difference which 1 cm thickness of air can withstand is 30 kV. If the voltage increases this value then air insulation will breakdown. When an electrical apparatus is designed, the value of dielectric strength is of utmost importance in deciding the thickness of the insulating material. Use of the material of correct dielectric strength results in the reduction of the cost of the apparatus.

The following factors affect the dielectric strength of the insulating material :

(a) Temperature: In case of air dielectric, the dielectric strength decreases with the rise of temperature. In case of liquid dielectrics, the effect varies with the type of oil and its viscosity.

(b) Humidity: It generally decreases the value of dielectric strength. The dielectric strength of some of the insulating materials is shown in Table.

Dielectric Strength of Insulating Materials

Dielectric strength (kilo volts / mm)
Low Voltage Porcelain
1.5 - 4 kV
High Voltage Porcelain
10- 16 kV
80 kV
Asbestos (Paper type)
3.5 kV
Natural Rubber
24 kV
Synthetic Rubber
4.44 kV


Every insulating material has got the general property of storing charge Q when a voltage V is applied across it. The charge Q is proportional to the voltage applied.

i.e. Q α V,
Q = CV

Where C is a constant and is known as the capacitance of the material across which the voltage is applied. Every insulating material behaves as a capacitor. The property of insulating materials that causes the difference in the value of capacitance, physical dimension remaining same, is called the 'dielectric constant or permittivity. It is denoted by E and is expressed as E = Cd / A where C is the capacitance of the material, d is the distance between the two faces, and A is the face area of insulation. Greater the permittivity, greater will be the capacitance of the insulating material. The permittivity of vacuum and air at standard temperature and pressure is about 1.00058 and for all practical purposes it is regarded as unity. The permittivity of solid and liquid insulating materials is given in Table.

Dielectric Constant for Different Insulating Materials

Dielectric Constant
2.5 - 7.7
2.0 - 2.6
2.5 - 6.6
5.4 - 9.9
2.2 – 4.7
2.1 - 2.5
5.7 - 6.8
2.0 - 3.5

Temperature and humidity affect the dielectric constant but to a very small extent. The effect of frequency and applied voltage on dielectric constant is appreciable. While selecting the insulating material for the particular job, permittivity is a prime factor of consideration.

Dielectric Loss:

When an A.C. Voltage is impressed across an ideal insulating material, no power loss takes place and the charging current leads the applied voltage by 90°. But in commercial insulating materials the leakage current does not lead the applied voltage by exactly 90° and hence there is a definite amount of dissipation of energy in the form of heat. The power dissipated is given by P = 2rc fC tan 8 where tan 6 is called the power factor of the dielectric. The power loss is dependent of tan 5 so long as the other factors like voltage, frequency etc., are constant.

Factors Affecting Dielectric Loss :

The following are the factors which affect the dielectric loss in the insulating materials.

(a) Temperature rise increases the dielectric loss.
(b) Moisture increases the dielectric loss.
(c) Voltage increase causes increased dielectric loss.
(d) The loss increases in direct proportion with the frequency of applied voltage.

Dielectric loss plays an important role in high voltage applications. Dielectric loss involves heat generation and heat dissipation. Every application of insulation requires proper understanding of the balance between the heat generation and heat dissipation.