The equivalent circuit of transformer is shown in the figure.
No load Components
The noload primary current I_{o} has two components, namely I_{m} and I_{w}.
Where I_{m} = magnetizing component = I_{o} sin φ_{o}
and I_{w} = coreloss component = I_{o} cos φ_{o}.

 I_{w} supplies for the noload losses and is assumed to flow through the noload resistance which is also known as coreloss resistance (R_{o}).
 The magnetizing component, I_{m} is assumed to be flowing through a reactance which is known as magnetizing reactance, X_{o}.
 The parallel combination of R_{o} and X_{o} is also known as the exciting circuit.
From the equivalent circuit of transformer,
R_{o} = V_{1}/I_{w} and X_{o} = V_{1}/I_{m}.
 The coreloss resistance (R_{o}) and the magnetizing reactance (X_{o}) of a transformer are determined by the open circuit test of transformer.
Primary Components

 The resistance R_{1} and reactance X_{1} correspond to the winding resistance (DC resistance) and leakage reactance of the primary winding.
 The total current I_{1} on the primary side is equal to the phasor sum of I_{o} and I_{2}’.
 I_{2}’ = KI^{2} is the additional primary current which flows due to the load connected on the secondary side of the transformer.
Secondary Components
 The resistance R_{2} and reactance X_{2} correspond to the winding resistance and leakage reactance of the secondary winding.
 Load impedance Z_{L} 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
All the components on the secondary side of the transformer are transferred to the primary side as shown in the figure.

 R_{2}’, X_{2}’ and Z_{L}’ are the values of R_{2}, X_{2} and Z_{L} referred to primary respectively.
 The values of these components are obtained as follows:
R_{2}’ = R_{2}/K^{2} , X_{2}’ = X_{2}/K^{2} and Z_{L}’ = Z_{L}/K^{2}
where K = N_{2}/N_{1} (transformation ratio).

 The current I_{2} and voltage E_{2} are also transferred to the primary side as I_{2}’ and E_{2}’ respectively. The expressions for I_{2}’ and E_{2}’ are as follows:
E_{2}’ = E_{2}/K and I_{2}’ = KI_{2}
Equivalent Circuit of Transformer Referred to Secondary
The equivalent circuit of transformer referred to the secondary side is shown in the figure.

 Components R_{1}’, X_{1}’, R_{o}’ and X_{o}’ are the primary components referred to secondary. The expressions for these components are as follows:
R_{1}’ = K^{2}R_{1} , X_{1}’ = K^{2}X_{1}
R_{o}’ = K^{2}R_{o} , X_{o}’ = K^{2}X_{o}

 The primary voltages and currents also get transferred to the secondary side as I_{1}’, V_{1}’, I_{o}’, E_{1}’ respectively and are given by:
I_{1}’ = I_{1}/K , E_{1}’ = KE_{1} , I_{o}’ = I_{o}/K
where K = N_{2}/N_{1} (transformation ratio).
Approximate Equivalent Circuit of Transformer
An approximate equivalent circuit is one which is obtained by shifting the exciting circuit to the left of R_{1} and X_{1} as shown in the figure.
Although this shifting creates an error in the voltage drop across R_{1} and X_{1} yet it greatly simplifies the calculation work and gives much simplified equivalent circuit.

 Now it is possible to combine the resistances R_{1} with R_{2}’ and X_{1} with X_{2}’. So R_{1} and R_{2}’ are combined to obtain the equivalent resistance of transformer referred to the primary R_{01}.
Therefore, R_{01} = R_{1} + R_{2}’ = R_{1} + R_{2}/K^{2}

 Similarly X_{1} and X_{2}’ can be combined to obtain the equivalent reactance of transformer referred to primary X_{01}.
Therefore, X_{01} = R_{1} + R_{2}’ = R_{1} + R_{2}/K^{2}
Now the impedance of the transformer referred to the primary is given by,
Z_{01 }= R_{01} + jX_{01}
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