UNIT2

Magnetic Circuit and Single Phase

Transformer

2.1 ated to magnetic circuit and Comparison between electric and magnetic circuit

Magnetic flux: the total no of lines of force in a magnetic field denoted by Ø andmeasured in Weber’s.

Magnetic flux density [B]= the flux per unit area measured in a plane perpendicular to theflux is defined as the flux density.

It is measured in tesla [T] and donated by B

B =      Tesla / wb /

Magnetic motive force MMF: It is the force that is required for production of flux

MMF = No. Of turns x current

= N x I

= Ampere Turns

=AT

Magnetic field strength / intensity / magnetising force

It is the force experienced by a unit north poles placed at that point in the magnetic field Denoted by H

Measured in Newtown / w­b or AT/n

H =  N/wb

H =

Coulombs Law of Electromagnetic

1st Law- Like poles repels and unlike poles attract

2nd Law- is the force of attraction or repulsion 2 pole a magnetic field in directly proportional to the product of the field strength and inversely proportional to the square of the distance between then i.e.  F X

When K instant which depends upon nature of surrounding medium to the poles andm1 m2 are the pole strength.

Permeability- It is defined as the ability of a material to carry the flux lines. There are three Permeabilities

Absolute Permeability [μ]- It is defined as the ratio of magnetic flux density [B] in a particular medium to the magnetic field strength [H] which produces that flux density it is denoted by μ and measured in henry per meter

   H/M

Permeability of force space or vacuum:

It is ratio of magnetic flux density of force space or vacuum to the magnetic field strength it is denoted by μ0 and measured henry / meter

H/M

The value of μₒ is always constant

μₒ= 4λ x 10-7 H/M

Relative Permeability: it is defined as the ratio flux density in a particular medium to the flux density in air or vacuum conditions the same magnet under identical conditions denoted by μ

μ (with same H)

Expression of μμ= B = μH

μ₀ = B₀ = μ₀H

Now                                          μ

μ =

μ = μ₀μᵣ

Reluctance -it is defined as the opposition to the flow of flux in a material

Reluctance is denoted by S and measured in AT/wb or Siemens

S = ɺ/ μ₀μᵣₐ         - AT/wb

It can also be defined as the ratio of (MMF) to the magnetic flux (Ø)

S =      - AT/wb

Permeance: it is defined as the reciprocal of reluctance the Permeance represents the property of magnetic material to allow the flux to pass through it

Permeance =  - wb/AT

Compare Electrical and magnetic circuit             

Electrical	Magnetic
Current flow of electrons Unit- Ampere	Flux: magnetic lines of force Unit- Weber
I =	Ø = MMF/S
EMF: driving force for current	MMF driving force for flux: AT
Resistance: opposition to the Flow of current	Reluctance: opposition to the flow of flux
R = ƍ	s =
I =	ɸ
Conductance =	Permeance =
Current density ʆ =   A/M2	Flux density B = wb/M2
Electric filed Intensity E =	Magnetic field intensity H =
Voltage drop V = IR	MMF Drop = Ø.S
It is closed path for current	It is closed path for flux
Kirchhoff’s current and voltage Law applicable to electric circuit	Kirchhoff’s flux and MMF laws are applicable to mag circuit

2.2   Series magnetic circuits with air gap, magnetic leakage and fringing

• Direction of Magnetic Field

1. If a straight conductor is held in right hand such that thumb indicates the direction of current and curled fingers indicates the direction of magnetic field

2.     Cork Screw Rule:

Consider right-handed screw when this screw is to be inserted in a wooden plan it is to be rotated in a clockwise direction ɡȴ the direction of advancement of screw indicates the direction of current, then the circular rotational motion of screw indicates direction of magnetic field.

Half part of page no. 28

3.     Magnetic field of long straight conductors

When straight conductor carries a current it produces a magnetic field all along its length. The lines of force are in the form of concentric circles in the planes right angle to the conductor.

4.Magnetic field due to solenoid 

(Large no of coils wounded on iron core)

When the current is passed through the solenoid. The magnetic field is produced as show in above fig.

It is produced outside as well as inside the core of solenoid.

Note that direction of field is reversed due to current direction.

• Rules to find polarity of solenoid

1. Right Hand Thumb Rule

2.     Cork Screw Rule

• Force on current carrying conductor in a magnetic field.

It involves the interaction of magnetic field and current carrying conductor placed in it. The operation sequence is as follow

1. Development of individual field
2. Interaction of two magnetic fields
3. Force exerted on the conduction

1. Development of individual field

• Let a straight conductor is placed in the magnetic fieldproducedbypermanent magnet.
• Let current flowing through the conductor is out of the plane of the paper.
• The magnetic field produced by conductor is shown above

2.     Interaction of two magnetic field

At the top flux lines produced by the magnet and conductor are inoppositedirection to each other and hence cancel each other.

At the bottom individual fields are in same direction they will add each other.

3.     Force excreted on the conductor

The lines of force on the bottom exert a force on the conductor in theupward direction as shown above.

Hence mechanical force is exerted on the conductor from high flux line area towards the low flux line area (top).

• Flemings left Hand Rule for direction of current (for Motor)

If the first 3 fingers of left hand are held mutually at right angle to each other. First finger indicates magnetic field middle finger indicates direction of current and thumb indicated force exerted.

• The magnetically of force experienced by the current carrying conductor placed in a magnetic field is given by

F = B I ɺ sin Ɵ         newton

Where F = Force exerted

B = Flux density

ɺ = length of conductor

I = current

Ɵ = angle between conductor and magnetic field.

The magnetic circuit can be defined asthe closed path traced by magnetic lineof forcesuch magnetic circuit is associated with different magnetic quantities such as MMF, flux, flux density, magnetic field strength

We know that   H =

And B = μ H

Put value of H

B = μ x 

But μ = μₒμ

B = μ₀μ

But B = = B x a

Ø =

• Numerical on F = B I ɻ sin
• Derivation of series magnetic current with air gap   (6 M)

In series magnetic circuit flux is same in each part of circuit

Consider a composite magnetic circuit made from different material of lengths ɻ1,ɻ2, and ɻ3cross sectional area a1, a2 And a3 and relative permeability’s  1 ,2 , 3  resp. With an airgap of length ɻɡ

Total reluctance S = S1 + S2+ S3 + Sg

We know that S =

+ + +

But S = and mmf = S x Ø

mmf = Ø + + + for air

Now  B = 

mmȴ = + + +

But B=μH

H =   = 

Total mmȴ = H1  ɻ1+ H2  ɻ2 + H3  ɻ3 + Hƪɻƪ

• Parallel magnetic circuit, Introduction on page no. 29
• Concept of useful flux leakage flux and magnetic fringing

Leakage flux: the flux which completes its path through the air or the medium surrounding the magnetic circuit instead of completing it through the core and air gap is known as the leakage flux. It is not a useful flux (Øu)

• Useful flux (Øu):

The flux which is available at the air gap and can be utilized for some useful purpose is called as useful flux and denoted by (Øu)

• Leakage coefficient:

The leakage coefficient or leakage factor indicates the percentage or part of total flux lost due to leakage. It is defined as the ratio of total flux (Ø7) to useful / air gap flux Øu

Leakage factor (h) =

It is also called as Hopkinson’s coefficient value is from 1.1 to 1.25

• Magnetic fringing

The tendency of the magnetic flux to spread out at the edges of the air gap is called magnetic fringing

• Effect of fringing

1. Increases cross sectional area of airgap
2. the flux density (B) is reduced

• It can be reduced by selecting a high-quality magnetic material and making the airgap as narrow as possible.

2.3   Faraday's law of electromagnetic induction, Lenz’s law, concept of self and mutual inductance

1. First law: whenever flux linkage with the coil changes an emf is induced in that conductor
2. Second law:  the magnitude of induced emf is equal to the rate of change of flux linkage

• Explanation: suppose a coil has n turns and flux through it change from initial value of Ø1 to Ø2 in line t sec

Initial flux linkage = N Ø

Final flux linkage = NØ2

Induced emfe =

Putting the above equation in differential form

e = rate of change of flux linkage

The direction of this induced emf is given by lenis law which states the polarity of induced emf is always such that it tends to set up a current which flow in such a direction so as to oppose the cause that produces it.

Whenever flux linking a conductor changes an emf is induced in it. This change in flux linkage can be trough about in the following 2 ways

1. The conductor is moved in a stationary magnetic field in such a way that the flux linking is changes in magnitude.

The emf induced in this is called dynamically induced emf.

2.   The conductor is stationary and magnetic field is moving or changing the emf induced in this way is called statically induced emf.

• Statically Induce EMF:

This is technique of generating an emf but here neither the conductor nor the magnetic field are physically moved for EMF generation both are stationary.

• The flux linkage taking place with conductor is changed by changing the magnitude of the current that produces magnetic field.

e.g. Transformers

Statically EMF is subdivided in 2 types:

1. Self-Induced EMF
2. Mutual Induced EMF

Self-Induced EMF

The EMF induced in coil due to change of its own flux linked with it is called as self-Induced EMF

The change in flux is brought by changing the current flowing in coil {using variable resister ‘R’ / or using ac supply}

• Magnitude of self-Induced EMF

Consider a coil haring n Turns carrying a current I amperes

ɡȴ the current in the coil changes the flux linkage of the coil also changes which sets up a self-induced EMF in the coil

We know that

Ø x I

Ø  = K I

As    = K  x I

Rate of flux linkage    = K    x   rate of changes of current

= K x

Now e  = - N

Put value of in above equation.

e = - N k    

e = - N   x x

K =

e = - L

Where L =   = self Inductance

The property of coil that opposes any changes in the amount of current flowing through it is called as well Inductance.

• Coefficient of self-Inductance:

Now L =

We know that Ø =

Ø =

now L = x

L =    replacing Ø

L =

S decreases   L Increases

L is proportional to square of turn NL

Mutually Induced EMF

The emf induced in the coil due to change in current in the neighbouring coil is called as mutually induced EMF

Consider 2 coil 1 and 2 placed closed, adjacent to each other

Current 1 (Variable current) flows in coil 1, flux Ø1  is set upand a part ofthis flux (Ø2) links coil 2. The EMF induced in coil 2 is termed as mutually induced EMF whereas EMF induced in coil 1 is termed as self-induced EMF.

Mutually induced emf is given by

e2 = -N2 

We know that Ø2 x 1

Ø2=K 1and k =

Rate of change of flux in coil 2    = k   x change in current in coil 1

  = K  

Now e2 = - N2   

Replacing value of in above eq. M

e2 = - N2    K  

e2 = - N2    K      x 

e2= - M 

Where

M =       mutual Inductance

• Coefficient of mutual Inductance

M =

Now

2.4   Working principle and construction of Single Phase transformer

2.4.1. Operating principle

It works on principle of mutual Induction ie “when  2 coil are inductively coupled and if current in one coil is changed uniformly then an emf get induced in another coil”

1. When alternating voltage V1 is applied to primary winding am alternating current I1  flows in it producing alternating flux in the core.
2. As per Faradays Law of Electromagnetic Induction 1 an emf E1 is induced in the primary winding  E = N1 
3. The emf induced in the primary winding is nearly equal and opposite to applied voltage V1
4. Assuming leakage flux to be negligible almost whole flux produced in primary winding links with secondary winding thence emf induced in the secondary winding  E2 = N2

2.4.2.               Construction

• There a  2 types of winding

1. Concentric or cylindrical
2. Sandwiched type

1. Cylindrical

L.V. = low voltage  H.V. = high voltage   are mounted on same limb to minimum leakage .

L.V. Winding placed inside and H.V. Winding placed outside with (proper insulation between the winding as it is easy to insulated L.V. Winding) than H.V. Winding.

2.     Sandwiched

The H.V. And L.V. Winding are divided into no. Of small coils and there small windings are interleaved.

(the top and bottom winding are L.V. Coils because they are close to core)

• Transformer tank : wholes assembly of winding and core placed inside the Transformer tank (sheet metal tank) which is filled with Transformer oil or insulating oil which acts as an (insulator or coolant ) MCQ
• Transformer oil : (The function of oil is to remove efficiently the heat generated in core and in winding)
• Moisture should not be allowed which creeps the insulation which achieved by closed Transformer tank.

(To increase cooling surface are tubes or fins are provided)

• Conservator tank : above tank T/F tank there is one small tank in which same empty space is always provided above the oil level. (this space is required for oil to expand or contract due to temperature change) MCQ

However during contraction outside air can have moisture which will deteriorate the insulating properly of oil.

• Breather : the air goes in or out through the breather (To reduce the moisture content of their air . Same drying agents such as (silica gel or) calcium chloride) is used in the breather (The dust particles present in air are also removed by breather)
• Buccholz Relay : (for incipient (slowly increasing) faults

There is pipe connecting rain tank and conservator. On the pipe a protective device called Buccholz Relay is mounted.

When the Transformer is about to be faulty and draw range current the oil becomes very hot and decompose.

During this process different types of gases are liberated.(The Bucchoz Relay get operated by these gases) and gives an alarm to the operator. ɡȴ the fault continues to persist then there lay will trip off main circuit breaker to protect the Transformer.

• Explosion Vent :

An explosion Vent or relief value is the bent-up pipe filled on the main tank.

(The explosion vent consist of aluminium of oil) when the T/F becomes faulty the cooling oil get decomposed and various types of gases are liberated

(ɡȴ the gas pressure exodus certain level then the aluminium of oil (diagram) in explosion vent will burst) to release pressure. They will save main tank from getting damaged.

• Single phase transformer -

(Symbol and principal of operation)

It is a static device which can transfer electrical energy from one ac circuit to another ac circuit without change in frequency

It can increase or decrease the voltage but with corresponding decrease or increase in current

It works on Principle  

“Mutual Induction”

A major application of transformer is to increase voltage before transmitting electrical energy over a long distance through conductors and to again reduce voltage at place where it is to be used.

Symbol

1. Primary winding : (ac supply side) For MCQs

The winding which is connected to supply is called primary side

2.     Secondary winding : (load side) for MCQs

The winding which is connected to load is called as secondary winding

2.5   EMF-equation of Single phase transformer

As primary winding excited by the a sinusoidal alternating voltage an alternating current flows in the winding producing an alternating varying flux Ø

Ø = Øm sin wt

As per Faradays Law of Electromagnetic Induction emf E1 is induced

E1 = N1

E1 = N1  (Ø Sin wt)

= -  N1Øm w  Cos wt

Sin (90-wt)

= - Sin (wt-90)

E1 = N1Øm   w Sin (wt-90)

w =

E1 = N1 Ø m Sin (wt-90)

Max value of E1 = E max

Is when Sin (wt-90) = 1

E1 max = N1 Ø m

Hence rms value of induced EMF in primary winding

E1 rms =   =  

E1 = 4.44 F Ø m N1

Similarly RMS value of induced EMF in secondary wdg Is

E2 = 4.44 F Ø m N2

References:

1. Electrical Technology (Volume I & 2), B L Thereja, 22nd edition, S Chand & Company Ltd

2. Basic Electrical Engineering, V K Mehta, Revised edition, S Chand & Company Ltd

3. Basic Electronics Solid State, B L Thereja, Revised edition, S Chand & Company Ltd

4. Digital Principles and Applications, Albert Malvino , Donald Leach, Tata McGraw Hills Publication

5. Principles of Electronic Devices and Circuits (Analog and Digital), B. L. Theraja , R. S. Sedha , S. Chand publication