Short Notes: Single Phase Transformers | Electrical Machines - Electrical Engineering (EE) PDF Download

 Page 1


Single Phase Transformer 
Electrical power transformer is a static device which transforms electrical energy from one circuit to another 
without any direct electrical connection and with the help of mutual induction between two windings. It 
transforms power from one circuit to another without changing its frequency but may be in different voltage level. 
A single-phase transformer is a type of power transformer that utilizes single-phase alternating current, meaning 
the transformer relies on a voltage cycle that operates in a unified time phase.  
The working principle of the single phase transformer is based on the Faraday's law of electromagnetic induction. 
Basically, mutual induction between two or more windings is responsible for transformation action in an electrical 
transformer.  
Faraday's law of electromagnetic induction  
According to Faraday’s law, “Rate of change of flux linkage with respect to time is directly proportional to the 
induced EMF in a conductor or coil”. 
The principle of operation of a transformer has been explained in the following simple steps: 
• As soon as the primary winding is connected to a single–phase supply, an AC current starts flowing through it. 
• An alternating flux is produced in the core by the AC primary current. 
• The alternating flux gets linked with the secondary winding through the core. 
• Now, according to Faraday’s laws of electromagnetic induction this varying flux will induce voltage into the 
secondary winding. 
 
Construction 
The three main parts of a transformer are: 
• Primary Winding: The winding that takes electrical power and produces magnetic flux when it is connected to 
an electrical source. 
• Magnetic Core: This refers to the magnetic flux produced by the primary winding. The flux passes through a low 
reluctance path linked with secondary winding creating a closed magnetic circuit. 
• Secondary Winding: The winding that provides the desired output voltage due to mutual induction in the 
transformer. 
The primary winding is supplied an alternating electrical source. The alternating current through the primary 
winding produces an alternating flux that surrounds the winding. Another winding, also known as the secondary 
winding, is brought close to the primary winding. Eventually, some portion of the flux in the primary will link 
with the secondary. As this flux is continually changing in amplitude and direction, there is a change in flux 
linkage in the second winding as well. According to Faraday’s law of electromagnetic induction, an electromotive 
force (emf) is induced in the secondary winding which is called as induced emf. If the circuit of the secondary 
winding is closed an induced current will flow through it. This is the simplest form of electrical power 
transformation; this is the most basic working principle of a transformer. 
 
 
It consists of two coils of electrical wire called inner and outer windings. The primary is usually known to have 
the higher amount of voltage. Both coils are wrapped around a common closed magnetic iron circuit which is 
referred to as the core. The core is made up of several layers of iron, laminated together to decrease losses. Being 
linked at the common core allows power to be transferred from one coil to the other without an electrical 
connection. When current passes through the primary coil, a magnetic field is created which induces a voltage in 
the secondary coil. Usually, the primary coil is where the high voltage comes in and then is transformed to create 
a magnetic field. The job of the secondary coil is to transform the alternating magnetic field into electric power, 
supplying the required voltage output. 
Page 2


Single Phase Transformer 
Electrical power transformer is a static device which transforms electrical energy from one circuit to another 
without any direct electrical connection and with the help of mutual induction between two windings. It 
transforms power from one circuit to another without changing its frequency but may be in different voltage level. 
A single-phase transformer is a type of power transformer that utilizes single-phase alternating current, meaning 
the transformer relies on a voltage cycle that operates in a unified time phase.  
The working principle of the single phase transformer is based on the Faraday's law of electromagnetic induction. 
Basically, mutual induction between two or more windings is responsible for transformation action in an electrical 
transformer.  
Faraday's law of electromagnetic induction  
According to Faraday’s law, “Rate of change of flux linkage with respect to time is directly proportional to the 
induced EMF in a conductor or coil”. 
The principle of operation of a transformer has been explained in the following simple steps: 
• As soon as the primary winding is connected to a single–phase supply, an AC current starts flowing through it. 
• An alternating flux is produced in the core by the AC primary current. 
• The alternating flux gets linked with the secondary winding through the core. 
• Now, according to Faraday’s laws of electromagnetic induction this varying flux will induce voltage into the 
secondary winding. 
 
Construction 
The three main parts of a transformer are: 
• Primary Winding: The winding that takes electrical power and produces magnetic flux when it is connected to 
an electrical source. 
• Magnetic Core: This refers to the magnetic flux produced by the primary winding. The flux passes through a low 
reluctance path linked with secondary winding creating a closed magnetic circuit. 
• Secondary Winding: The winding that provides the desired output voltage due to mutual induction in the 
transformer. 
The primary winding is supplied an alternating electrical source. The alternating current through the primary 
winding produces an alternating flux that surrounds the winding. Another winding, also known as the secondary 
winding, is brought close to the primary winding. Eventually, some portion of the flux in the primary will link 
with the secondary. As this flux is continually changing in amplitude and direction, there is a change in flux 
linkage in the second winding as well. According to Faraday’s law of electromagnetic induction, an electromotive 
force (emf) is induced in the secondary winding which is called as induced emf. If the circuit of the secondary 
winding is closed an induced current will flow through it. This is the simplest form of electrical power 
transformation; this is the most basic working principle of a transformer. 
 
 
It consists of two coils of electrical wire called inner and outer windings. The primary is usually known to have 
the higher amount of voltage. Both coils are wrapped around a common closed magnetic iron circuit which is 
referred to as the core. The core is made up of several layers of iron, laminated together to decrease losses. Being 
linked at the common core allows power to be transferred from one coil to the other without an electrical 
connection. When current passes through the primary coil, a magnetic field is created which induces a voltage in 
the secondary coil. Usually, the primary coil is where the high voltage comes in and then is transformed to create 
a magnetic field. The job of the secondary coil is to transform the alternating magnetic field into electric power, 
supplying the required voltage output. 
EMF equation for 1ø transformer: - 
When a sinusoidal voltage is applied to the primary winding of a transformer, alternating flux ? m sets up in the 
iron core of the transformer. This sinusoidal flux links with both primary and secondary winding. The function 
of flux is a sine function. The rate of change of flux with respect to time is derived mathematically. 
The derivation of EMF Equation of the transformer is shown below. Let 
• ? m be the maximum value of flux in Weber 
• f be the supply frequency in Hz 
• N 1 is the number of turns in the primary winding 
• N 2 is the number of turns in the secondary winding  
• F is the flux per turn in Weber 
 
 
As shown in the above figure that the flux changes from + ? m to – ? m in half a cycle of 1/2f seconds. 
By Faraday’s Law 
Let E 1 is the emf induced in the primary winding 
 
Where ? = N 1? 
 
Since ? is due to AC supply ? = ? m Sin(wt) 
 
So, the induced emf lags flux by 90 degrees. 
Maximum valve of emf 
 
But w = 2pf 
 
Page 3


Single Phase Transformer 
Electrical power transformer is a static device which transforms electrical energy from one circuit to another 
without any direct electrical connection and with the help of mutual induction between two windings. It 
transforms power from one circuit to another without changing its frequency but may be in different voltage level. 
A single-phase transformer is a type of power transformer that utilizes single-phase alternating current, meaning 
the transformer relies on a voltage cycle that operates in a unified time phase.  
The working principle of the single phase transformer is based on the Faraday's law of electromagnetic induction. 
Basically, mutual induction between two or more windings is responsible for transformation action in an electrical 
transformer.  
Faraday's law of electromagnetic induction  
According to Faraday’s law, “Rate of change of flux linkage with respect to time is directly proportional to the 
induced EMF in a conductor or coil”. 
The principle of operation of a transformer has been explained in the following simple steps: 
• As soon as the primary winding is connected to a single–phase supply, an AC current starts flowing through it. 
• An alternating flux is produced in the core by the AC primary current. 
• The alternating flux gets linked with the secondary winding through the core. 
• Now, according to Faraday’s laws of electromagnetic induction this varying flux will induce voltage into the 
secondary winding. 
 
Construction 
The three main parts of a transformer are: 
• Primary Winding: The winding that takes electrical power and produces magnetic flux when it is connected to 
an electrical source. 
• Magnetic Core: This refers to the magnetic flux produced by the primary winding. The flux passes through a low 
reluctance path linked with secondary winding creating a closed magnetic circuit. 
• Secondary Winding: The winding that provides the desired output voltage due to mutual induction in the 
transformer. 
The primary winding is supplied an alternating electrical source. The alternating current through the primary 
winding produces an alternating flux that surrounds the winding. Another winding, also known as the secondary 
winding, is brought close to the primary winding. Eventually, some portion of the flux in the primary will link 
with the secondary. As this flux is continually changing in amplitude and direction, there is a change in flux 
linkage in the second winding as well. According to Faraday’s law of electromagnetic induction, an electromotive 
force (emf) is induced in the secondary winding which is called as induced emf. If the circuit of the secondary 
winding is closed an induced current will flow through it. This is the simplest form of electrical power 
transformation; this is the most basic working principle of a transformer. 
 
 
It consists of two coils of electrical wire called inner and outer windings. The primary is usually known to have 
the higher amount of voltage. Both coils are wrapped around a common closed magnetic iron circuit which is 
referred to as the core. The core is made up of several layers of iron, laminated together to decrease losses. Being 
linked at the common core allows power to be transferred from one coil to the other without an electrical 
connection. When current passes through the primary coil, a magnetic field is created which induces a voltage in 
the secondary coil. Usually, the primary coil is where the high voltage comes in and then is transformed to create 
a magnetic field. The job of the secondary coil is to transform the alternating magnetic field into electric power, 
supplying the required voltage output. 
EMF equation for 1ø transformer: - 
When a sinusoidal voltage is applied to the primary winding of a transformer, alternating flux ? m sets up in the 
iron core of the transformer. This sinusoidal flux links with both primary and secondary winding. The function 
of flux is a sine function. The rate of change of flux with respect to time is derived mathematically. 
The derivation of EMF Equation of the transformer is shown below. Let 
• ? m be the maximum value of flux in Weber 
• f be the supply frequency in Hz 
• N 1 is the number of turns in the primary winding 
• N 2 is the number of turns in the secondary winding  
• F is the flux per turn in Weber 
 
 
As shown in the above figure that the flux changes from + ? m to – ? m in half a cycle of 1/2f seconds. 
By Faraday’s Law 
Let E 1 is the emf induced in the primary winding 
 
Where ? = N 1? 
 
Since ? is due to AC supply ? = ? m Sin(wt) 
 
So, the induced emf lags flux by 90 degrees. 
Maximum valve of emf 
 
But w = 2pf 
 
Root mean square RMS value is 
 
Putting the value of E 1max in equation (6) we get 
 
Putting the value of p = 3.14 in the equation (7) we will get the value of E 1 as 
 
Similarly, 
 
Now, equating the equation (8) and (9) we get 
 
The above equation is called the turn ratio where K is known as transformation ratio. 
The equation (8) and (9) can also be written as shown below using the relation 
(?m = B m x A i) where A i is the iron area and B m is the maximum value of flux density. 
 
For a sinusoidal wave 
                                                       
Losses in Transformer 
In any electrical machine, 'loss' can be defined as the difference between input power and output power. 
An electrical transformer is an static device, hence mechanical losses (like windage or friction losses) are absent 
in it. A transformer only consists of electrical losses (iron losses and copper losses). Transformer losses are similar 
to losses in a DC machine, except that transformers do not have mechanical losses. 
Losses in transformer are explained below - 
 
(I) Core Losses or Iron Losses 
Eddy current loss and hysteresis loss depend upon the magnetic properties of the material used for the construction 
of core. Hence these losses are also known as core losses or iron losses. 
? Hysteresis loss in transformer: Hysteresis loss is due to reversal of magnetization in the transformer 
core. This loss depends upon the volume and grade of the iron, frequency of magnetic reversals and value 
of flux density. It can be given by, Steinmetz formula: 
W h= ?B max
1.6
fV (watts) 
where, 
Page 4


Single Phase Transformer 
Electrical power transformer is a static device which transforms electrical energy from one circuit to another 
without any direct electrical connection and with the help of mutual induction between two windings. It 
transforms power from one circuit to another without changing its frequency but may be in different voltage level. 
A single-phase transformer is a type of power transformer that utilizes single-phase alternating current, meaning 
the transformer relies on a voltage cycle that operates in a unified time phase.  
The working principle of the single phase transformer is based on the Faraday's law of electromagnetic induction. 
Basically, mutual induction between two or more windings is responsible for transformation action in an electrical 
transformer.  
Faraday's law of electromagnetic induction  
According to Faraday’s law, “Rate of change of flux linkage with respect to time is directly proportional to the 
induced EMF in a conductor or coil”. 
The principle of operation of a transformer has been explained in the following simple steps: 
• As soon as the primary winding is connected to a single–phase supply, an AC current starts flowing through it. 
• An alternating flux is produced in the core by the AC primary current. 
• The alternating flux gets linked with the secondary winding through the core. 
• Now, according to Faraday’s laws of electromagnetic induction this varying flux will induce voltage into the 
secondary winding. 
 
Construction 
The three main parts of a transformer are: 
• Primary Winding: The winding that takes electrical power and produces magnetic flux when it is connected to 
an electrical source. 
• Magnetic Core: This refers to the magnetic flux produced by the primary winding. The flux passes through a low 
reluctance path linked with secondary winding creating a closed magnetic circuit. 
• Secondary Winding: The winding that provides the desired output voltage due to mutual induction in the 
transformer. 
The primary winding is supplied an alternating electrical source. The alternating current through the primary 
winding produces an alternating flux that surrounds the winding. Another winding, also known as the secondary 
winding, is brought close to the primary winding. Eventually, some portion of the flux in the primary will link 
with the secondary. As this flux is continually changing in amplitude and direction, there is a change in flux 
linkage in the second winding as well. According to Faraday’s law of electromagnetic induction, an electromotive 
force (emf) is induced in the secondary winding which is called as induced emf. If the circuit of the secondary 
winding is closed an induced current will flow through it. This is the simplest form of electrical power 
transformation; this is the most basic working principle of a transformer. 
 
 
It consists of two coils of electrical wire called inner and outer windings. The primary is usually known to have 
the higher amount of voltage. Both coils are wrapped around a common closed magnetic iron circuit which is 
referred to as the core. The core is made up of several layers of iron, laminated together to decrease losses. Being 
linked at the common core allows power to be transferred from one coil to the other without an electrical 
connection. When current passes through the primary coil, a magnetic field is created which induces a voltage in 
the secondary coil. Usually, the primary coil is where the high voltage comes in and then is transformed to create 
a magnetic field. The job of the secondary coil is to transform the alternating magnetic field into electric power, 
supplying the required voltage output. 
EMF equation for 1ø transformer: - 
When a sinusoidal voltage is applied to the primary winding of a transformer, alternating flux ? m sets up in the 
iron core of the transformer. This sinusoidal flux links with both primary and secondary winding. The function 
of flux is a sine function. The rate of change of flux with respect to time is derived mathematically. 
The derivation of EMF Equation of the transformer is shown below. Let 
• ? m be the maximum value of flux in Weber 
• f be the supply frequency in Hz 
• N 1 is the number of turns in the primary winding 
• N 2 is the number of turns in the secondary winding  
• F is the flux per turn in Weber 
 
 
As shown in the above figure that the flux changes from + ? m to – ? m in half a cycle of 1/2f seconds. 
By Faraday’s Law 
Let E 1 is the emf induced in the primary winding 
 
Where ? = N 1? 
 
Since ? is due to AC supply ? = ? m Sin(wt) 
 
So, the induced emf lags flux by 90 degrees. 
Maximum valve of emf 
 
But w = 2pf 
 
Root mean square RMS value is 
 
Putting the value of E 1max in equation (6) we get 
 
Putting the value of p = 3.14 in the equation (7) we will get the value of E 1 as 
 
Similarly, 
 
Now, equating the equation (8) and (9) we get 
 
The above equation is called the turn ratio where K is known as transformation ratio. 
The equation (8) and (9) can also be written as shown below using the relation 
(?m = B m x A i) where A i is the iron area and B m is the maximum value of flux density. 
 
For a sinusoidal wave 
                                                       
Losses in Transformer 
In any electrical machine, 'loss' can be defined as the difference between input power and output power. 
An electrical transformer is an static device, hence mechanical losses (like windage or friction losses) are absent 
in it. A transformer only consists of electrical losses (iron losses and copper losses). Transformer losses are similar 
to losses in a DC machine, except that transformers do not have mechanical losses. 
Losses in transformer are explained below - 
 
(I) Core Losses or Iron Losses 
Eddy current loss and hysteresis loss depend upon the magnetic properties of the material used for the construction 
of core. Hence these losses are also known as core losses or iron losses. 
? Hysteresis loss in transformer: Hysteresis loss is due to reversal of magnetization in the transformer 
core. This loss depends upon the volume and grade of the iron, frequency of magnetic reversals and value 
of flux density. It can be given by, Steinmetz formula: 
W h= ?B max
1.6
fV (watts) 
where, 
 ? = Steinmetz hysteresis constant 
 V = volume of the core in m
3
 
? Eddy current loss in transformer: In transformer, AC current is supplied to the primary winding which 
sets up alternating magnetizing flux. When this flux links with secondary winding, it produces induced emf 
in it. But some part of this flux also gets linked with other conducting parts like steel core or iron body or 
the transformer, which will result in induced emf in those parts, causing small circulating current in them. 
This current is called as eddy current. Due to these eddy currents, some energy will be dissipated in the 
form of heat. 
 (II) Copper Loss in Transformer 
Copper loss is due to ohmic resistance of the transformer windings.  Copper loss for the primary winding is 
I 1
2
R 1 and for secondary winding is I 2
2
R 2. Where, I 1 and I 2 are current in primary and secondary winding 
respectively, R 1 and R 2 are the resistances of primary and secondary winding respectively. Cu loss is proportional 
to square of the current, and current depends on the load. Hence copper loss in transformer varies with the load. 
 
Efficiency of Transformer 
Just like any other electrical machine, efficiency of a transformer can be defined as the output power divided by 
the input power. That is efficiency = output / input. 
Transformers are the most highly efficient electrical devices. Most of the transformers have full load efficiency 
between 95% to 98.5%. As a transformer being highly efficient, output and input are having nearly same value, 
and hence it is impractical to measure the efficiency of transformer by using output / input. A better method to 
find efficiency of a transformer is using, 
efficiency = (input - losses) / input = 1 - (losses / input). 
Condition for Maximum Efficiency 
Let,     Copper loss = I12R1,   Iron loss = Wi 
 
Hence, efficiency of a transformer will be maximum when copper loss and iron losses are equal. 
That is Copper loss = Iron loss. 
 
 
All Day Efficiency of Transformer 
As we have seen above, ordinary or commercial efficiency of a transformer can be given as 
Page 5


Single Phase Transformer 
Electrical power transformer is a static device which transforms electrical energy from one circuit to another 
without any direct electrical connection and with the help of mutual induction between two windings. It 
transforms power from one circuit to another without changing its frequency but may be in different voltage level. 
A single-phase transformer is a type of power transformer that utilizes single-phase alternating current, meaning 
the transformer relies on a voltage cycle that operates in a unified time phase.  
The working principle of the single phase transformer is based on the Faraday's law of electromagnetic induction. 
Basically, mutual induction between two or more windings is responsible for transformation action in an electrical 
transformer.  
Faraday's law of electromagnetic induction  
According to Faraday’s law, “Rate of change of flux linkage with respect to time is directly proportional to the 
induced EMF in a conductor or coil”. 
The principle of operation of a transformer has been explained in the following simple steps: 
• As soon as the primary winding is connected to a single–phase supply, an AC current starts flowing through it. 
• An alternating flux is produced in the core by the AC primary current. 
• The alternating flux gets linked with the secondary winding through the core. 
• Now, according to Faraday’s laws of electromagnetic induction this varying flux will induce voltage into the 
secondary winding. 
 
Construction 
The three main parts of a transformer are: 
• Primary Winding: The winding that takes electrical power and produces magnetic flux when it is connected to 
an electrical source. 
• Magnetic Core: This refers to the magnetic flux produced by the primary winding. The flux passes through a low 
reluctance path linked with secondary winding creating a closed magnetic circuit. 
• Secondary Winding: The winding that provides the desired output voltage due to mutual induction in the 
transformer. 
The primary winding is supplied an alternating electrical source. The alternating current through the primary 
winding produces an alternating flux that surrounds the winding. Another winding, also known as the secondary 
winding, is brought close to the primary winding. Eventually, some portion of the flux in the primary will link 
with the secondary. As this flux is continually changing in amplitude and direction, there is a change in flux 
linkage in the second winding as well. According to Faraday’s law of electromagnetic induction, an electromotive 
force (emf) is induced in the secondary winding which is called as induced emf. If the circuit of the secondary 
winding is closed an induced current will flow through it. This is the simplest form of electrical power 
transformation; this is the most basic working principle of a transformer. 
 
 
It consists of two coils of electrical wire called inner and outer windings. The primary is usually known to have 
the higher amount of voltage. Both coils are wrapped around a common closed magnetic iron circuit which is 
referred to as the core. The core is made up of several layers of iron, laminated together to decrease losses. Being 
linked at the common core allows power to be transferred from one coil to the other without an electrical 
connection. When current passes through the primary coil, a magnetic field is created which induces a voltage in 
the secondary coil. Usually, the primary coil is where the high voltage comes in and then is transformed to create 
a magnetic field. The job of the secondary coil is to transform the alternating magnetic field into electric power, 
supplying the required voltage output. 
EMF equation for 1ø transformer: - 
When a sinusoidal voltage is applied to the primary winding of a transformer, alternating flux ? m sets up in the 
iron core of the transformer. This sinusoidal flux links with both primary and secondary winding. The function 
of flux is a sine function. The rate of change of flux with respect to time is derived mathematically. 
The derivation of EMF Equation of the transformer is shown below. Let 
• ? m be the maximum value of flux in Weber 
• f be the supply frequency in Hz 
• N 1 is the number of turns in the primary winding 
• N 2 is the number of turns in the secondary winding  
• F is the flux per turn in Weber 
 
 
As shown in the above figure that the flux changes from + ? m to – ? m in half a cycle of 1/2f seconds. 
By Faraday’s Law 
Let E 1 is the emf induced in the primary winding 
 
Where ? = N 1? 
 
Since ? is due to AC supply ? = ? m Sin(wt) 
 
So, the induced emf lags flux by 90 degrees. 
Maximum valve of emf 
 
But w = 2pf 
 
Root mean square RMS value is 
 
Putting the value of E 1max in equation (6) we get 
 
Putting the value of p = 3.14 in the equation (7) we will get the value of E 1 as 
 
Similarly, 
 
Now, equating the equation (8) and (9) we get 
 
The above equation is called the turn ratio where K is known as transformation ratio. 
The equation (8) and (9) can also be written as shown below using the relation 
(?m = B m x A i) where A i is the iron area and B m is the maximum value of flux density. 
 
For a sinusoidal wave 
                                                       
Losses in Transformer 
In any electrical machine, 'loss' can be defined as the difference between input power and output power. 
An electrical transformer is an static device, hence mechanical losses (like windage or friction losses) are absent 
in it. A transformer only consists of electrical losses (iron losses and copper losses). Transformer losses are similar 
to losses in a DC machine, except that transformers do not have mechanical losses. 
Losses in transformer are explained below - 
 
(I) Core Losses or Iron Losses 
Eddy current loss and hysteresis loss depend upon the magnetic properties of the material used for the construction 
of core. Hence these losses are also known as core losses or iron losses. 
? Hysteresis loss in transformer: Hysteresis loss is due to reversal of magnetization in the transformer 
core. This loss depends upon the volume and grade of the iron, frequency of magnetic reversals and value 
of flux density. It can be given by, Steinmetz formula: 
W h= ?B max
1.6
fV (watts) 
where, 
 ? = Steinmetz hysteresis constant 
 V = volume of the core in m
3
 
? Eddy current loss in transformer: In transformer, AC current is supplied to the primary winding which 
sets up alternating magnetizing flux. When this flux links with secondary winding, it produces induced emf 
in it. But some part of this flux also gets linked with other conducting parts like steel core or iron body or 
the transformer, which will result in induced emf in those parts, causing small circulating current in them. 
This current is called as eddy current. Due to these eddy currents, some energy will be dissipated in the 
form of heat. 
 (II) Copper Loss in Transformer 
Copper loss is due to ohmic resistance of the transformer windings.  Copper loss for the primary winding is 
I 1
2
R 1 and for secondary winding is I 2
2
R 2. Where, I 1 and I 2 are current in primary and secondary winding 
respectively, R 1 and R 2 are the resistances of primary and secondary winding respectively. Cu loss is proportional 
to square of the current, and current depends on the load. Hence copper loss in transformer varies with the load. 
 
Efficiency of Transformer 
Just like any other electrical machine, efficiency of a transformer can be defined as the output power divided by 
the input power. That is efficiency = output / input. 
Transformers are the most highly efficient electrical devices. Most of the transformers have full load efficiency 
between 95% to 98.5%. As a transformer being highly efficient, output and input are having nearly same value, 
and hence it is impractical to measure the efficiency of transformer by using output / input. A better method to 
find efficiency of a transformer is using, 
efficiency = (input - losses) / input = 1 - (losses / input). 
Condition for Maximum Efficiency 
Let,     Copper loss = I12R1,   Iron loss = Wi 
 
Hence, efficiency of a transformer will be maximum when copper loss and iron losses are equal. 
That is Copper loss = Iron loss. 
 
 
All Day Efficiency of Transformer 
As we have seen above, ordinary or commercial efficiency of a transformer can be given as 
 
But in some types of transformers, their performance cannot be judged by this efficiency. For example, distribution 
transformers have their primaries energized all the time. But, their secondaries supply little load all no-load most 
of the time during day (as residential use of electricity is observed mostly during evening till midnight). 
That is, when secondaries of transformer are not supplying any load (or supplying only little load), then only core 
losses of transformer are considerable and copper losses are absent (or very little). Copper losses are considerable 
only when transformers are loaded. Thus, for such transformers copper losses are relatively less important.  The 
performance of such transformers is compared based on energy consumed in one day. 
 
All day efficiency of a transformer is always less than ordinary efficiency of it. 
Auto Transformer 
An Auto Transformer is a transformer with only one winding wound on a laminated core. An auto transformer 
is like a two winding transformer but differ in the way the primary and secondary winding are interrelated. A part 
of the winding is common to both primary and secondary sides. On load condition, a part of the load current is 
obtained directly from the supply and the remaining part is obtained by transformer action. An Auto transformer 
works as a voltage regulator. 
Explanation of Auto Transformer with Circuit Diagram 
In an ordinary transformer, the primary and the secondary windings are electrically insulated from each other but 
connected magnetically as shown in the figure below and in auto transformer the primary and the secondary 
windings are connected magnetically as well as electrically. In fact, a part of the single continuous winding is 
common to both primary and secondary. 
 
Figure A: Ordinary Two Winding Transformer 
There are two types of auto transformer based on the construction. In one type of transformer, there is continuous 
winding with the taps brought out at convenient points determined by desired secondary voltage and in another 
type of auto transformer, there are two or more distinct coils which are electrically connected to form a continuous 
winding. The construction of Auto transformer is shown in the figure below. 
 
Figure B: Auto – Transformer