Equivalent Circuit of Transformer

 
The equivalent circuit of transformer is shown in the figure.
 
Equivalent circuit of single phase transformer
 

No load Components

 
The no-load primary current Io has two components, namely Im and Iw.
 
Where Im = magnetizing component = Io sin φo
and Iw = core-loss component = Io cos φo.

  • Iw supplies for the no-load losses and is assumed to flow through the no-load resistance which is also known as core-loss resistance (Ro).
  •  

  • The magnetizing component, Im is assumed to be flowing through a reactance which is known as magnetizing reactance, Xo.
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  • The parallel combination of Ro and Xo is also known as the exciting circuit.
  • From the equivalent circuit of transformer,
     
    Ro = V1/Iw and Xo = V1/Im.

Primary Components

 

  • The resistance R1 and reactance X1 correspond to the winding resistance (DC resistance) and leakage reactance of the primary winding.
  •  

  • The total current I1 on the primary side is equal to the phasor sum of Io and I2’.
  •  

  • I2’ = KI2 is the additional primary current which flows due to the load connected on the secondary side of the transformer.

Secondary Components

 

  • The resistance R2 and reactance X2 correspond to the winding resistance and leakage reactance of the secondary winding.
  •  

  • Load impedance ZL can be resistive, inductive or capacitive.
  •  

  • The equivalent circuit of single phase transformer is further simplified by transferring all the quantities to either primary or secondary side.
  •  

  • This is done in order to make the calculations easy.

Equivalent Circuit of Transformer Referred to Primary

 
Equivalent circuit transformer
 
All the components on the secondary side of the transformer are transferred to the primary side as shown in the figure.

  • R2’, X2’ and ZL’ are the values of R2, X2 and ZL referred to primary respectively.
  •  

  • The values of these components are obtained as follows:
  •  
    R2’ = R2/K2 , X2’ = X2/K2 and ZL’ = ZL/K2
     
    where K = N2/N1 (transformation ratio).

  • The current I2 and voltage E2 are also transferred to the primary side as I2’ and E2’ respectively. The expressions for I2’ and E2’ are as follows:
  •  
    E2’ = E2/K  and  I2’ = KI2

Equivalent Circuit of Transformer Referred to Secondary

 
Equivalent circuit of single phase transformer image
 
The equivalent circuit of transformer referred to the secondary side is shown in the figure.

  • Components R1’, X1’, Ro’ and Xo’ are the primary components referred to secondary. The expressions for these components are as follows:
  •  
    R1’ = K2R1 ,  X1’ = K2X1
     
    Ro’ = K2Ro ,  Xo’ = K2Xo

  • The primary voltages and currents also get transferred to the secondary side as I1’, V1’, Io’, E1’ respectively and are given by:
  •  
    I1’ = I1/K , E1’ = KE1 , Io’ = Io/K
     
    where K = N2/N1 (transformation ratio).

Approximate Transformer Equivalent Circuit

 
Approximate equivalent circuit
 
An approximate equivalent circuit is one which is obtained by shifting the exciting circuit to the left of R1 and X1 as shown in the figure.
 
Although this shifting creates an error in the voltage drop across R1 and X1 yet it greatly simplifies the calculation work and gives much simplified equivalent circuit.

 
Draw exact, approximate equivalent circuit of transformer referred to primary, secondary side
 

Transformer — 6 | Objective Type Question Answers

#1 The voltage transformation ratio of a transformer is equal to the ratio of

secondary induced em.f. to primary induced e.m.f.

#2 Part of the transformer which is most subject to damage from overheating is

winding insulation

#3 If a transformer is switched on to a voltage more than the rated voltage

#4 Auto-transformer makes effective saving on copper and copper losses, when its transformation ratio is

approximately equal to one

#5 Minimum voltage regulation occurs when the power factor of the load is

leading

#6 In a step-down transformer, there is a change of 15 A in the load current. This results In change of supply current of

less than 15 A

#7 The efficiencies of transformers compared with that of electric motors of the same power are

much higher

#8 The short circuit voltage of a transformer mainly depends on the

magnitude of leakage flux

#9 In an ideal transformer, on no-load, the primary voltage is balanced by

the secondary induced e.m.f.

#10 As per the nameplate of a transformer, the secondary normal voltage is 220 V. Which of the following statements about it is correct ?

The no-load voltage is more than 220 V

#11 A transformer is working at its maximum efficiency. Its iron loss is 1 kW. Its copper loss will be

1 kW

#12 A transformer is working at full load and its efficiency is also maximum. Its iron loss is 1 kW, its copper loss at half load will be

0.25 kW

#13 In some transformers the tappings are provided on

H.V. side

#14 In case of transformers using cold rolled grain oriented steel, the area of yoke is taken

equal to that of core

#15 The distribution transformers are designed to keep the iron-losses minimum because

the primary of distribution transformer is energized for all the twenty four hours

#16 Which of the following materials is suitable for the manufacture of trans-former and large turbo alternator ?

Cold rolled grain oriented steel

#17 Which of the following statements is correct ?

transformer operates at a power actor depending on the power factor of the load

#18 A transformer, as compared to an amplifier, cannot increase

the output power

#19 A transformer having a turn ratio 1: 5 and a resistance of 1000 ohm is connected across the secondary terminals, the resistance offered to a current flowing in the primary will be

40 ohms

#20 Which of the following statements about a transformer having a small short-circuit voltage is true?

A high short-circuit current flows through the transformer

#21 Helical coils arc very well suited for

low voltage winding of large rating transformers

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