#### 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 in turn 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 which produces flux and magnetizes the core with losses in the core.
- The core losses ( hysteresis loss and eddy-current loss ) is 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 Ï†, 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.

_{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 Ï†, which is connected in parallel to the resistance R_{o}is such that,