Basically, an equivalent circuit is representing all the parameters of the transformer in a form of a circuit or diagrammatical manner. The equivalent circuit of the transformer can be used to understand the behavior of the transformer under various conditions. Calculation of various parameters of the transformer like resistance, reactance, impedance on the primary and secondary side can be done easily which inturn also used for determining the regulation, efficiency, and losses of the transformer.

## Equivalent Circuit of a Transformer :

Consider a transformer with V_{1} and I_{2} are the primary voltage and current. Similarly, V_{1} and I_{2} are the secondary voltage and current. Let, E_{1} and E_{2} are the EMFs induced in primary and secondary windings respectively as shown below.

For the above transformer, the equivalent circuit with having transformation ratio K is shown below.

In the above circuit diagram, the primary current of the transformer serves two components I_{o} and I_{2}. The no-load current I_{o}, also known as the magnetizing current also produces flux and magnetizes the core with losses in the core.

- The core losses (hysteresis loss and eddy-current loss) are represented by a non-inductive resistance R
_{o} taking working component I_{w}. The current I_{w}, component current of I_{o} flow through the resistance R_{o} such that,
- The emf E
_{1} induced in the primary winding due to flux produced by the magnetizing current I_{Î¼}. The magnitude of emf E_{1} will be less and in opposition to the applied voltage V_{1}. The reactance X_{o} due to flux Î¦, which is connected in parallel to the resistance R_{o} is such that,

_{o}taking working component I_{w}. The current I_{w}, component current of I_{o}flow through the resistance R_{o}such that,_{1}induced in the primary winding due to flux produced by the magnetizing current I_{Î¼}. The magnitude of emf E_{1}will be less and in opposition to the applied voltage V_{1}. The reactance X_{o}due to flux Î¦, which is connected in parallel to the resistance R_{o}is such that,Here, R_{1} X_{1} and R_{2} X_{2} are the drops due to primary and secondary winding resistance and leakage reactance respectively. The current I_{2} is the counter-balance current I_{2} of secondary on the primary. Now, we can further simplify the equivalent circuit either by shifting the primary parameters to the secondary side or vice-versa, this reduces the complexity of the circuit and computation. This can be done by using the transformation ratio of the transformer.

## Equivalent Circuit of Transformer Referred to Primary Side :

The above equivalent circuit of the transformer can be modified by transferring the voltage, current, and impedance of the secondary side to the primary side as shown below figure.

#### By transferring all the parameters of the secondary side to the primary side with transformation ratio K. Then,- The primary equivalent of the secondary emf,
- The primary equivalent of secondary terminal voltage,
- The primary equivalent of the secondary current,
- Similarly, the secondary resistance, reactance, and impedance referred to as primary is given as,

The equivalent circuit can further be modified by transferring R_{o} and X_{o} (exciting circuit) towards the left end known as the approximate equivalent circuit as shown in the figure below. The error introduced by doing so is small and can be neglected. It should be noted that in this case R_{o} = V_{1}/I_{w} and X_{o} = V_{o}/I_{Î¼}.

Since no-load current I_{o} is very small, the circuit can be further simplified by neglecting I_{o} taking as I_{1}' = I_{1} shown in the below figure. Here, R_{01} (R_{1} + R_{2}') and X_{01} (X_{1} + X_{2}') are the total equivalent resistance and reactance of the transformer referred to as primary.

## Equivalent Circuit of Transformer Referred to Secondary Side :

Similarly, as the transformer equivalent circuit referred to the primary, we can also refer the primary parameters towards the secondary side by transferring the primary side to the secondary side as shown below.

#### By transferring all the parameters of the primary side to the secondary side with transformation ratio K. Then,- The secondary equivalent of the primary emf,
- The secondary equivalent of primary voltage,
- The secondary equivalent of the primary current,
- Similarly, the primary resistance, reactance, and impedance referred to as secondary is given as,

Similarly, by neglecting the no-load current I_{o} the simplified equivalent circuit referred to secondary is shown below. Here, R_{02} (R_{1}' + R_{2}) and X_{02} (X_{1}' + X_{2}) are the total equivalent resistance and reactance of the transformer referred to as secondary.