# Equivalent Circuit of a Transformer

The equivalent circuit diagram of any device can be quite helpful in predetermination of the behavior of the device under the various condition of operation. It is simply the circuit representation of the equation describing the performance of the device.

**Contents:**

- Equivalent Circuit When all the Quantities are Referred to Primary side
- Equivalent Circuit When all the Quantities are Referred to Secondary side

The simplified equivalent circuit of a transformer is drawn by representing all the parameters of the transformer either on the secondary side or on the primary side. The equivalent circuit diagram of the transformer is shown below

Let the equivalent circuit of a transformer having the transformation ratio K = E_{2}/E_{1}

The induced emf E_{1} is equal to the primary applied voltage V_{1} less primary voltage drop.This voltage causes current I_{0 }no load current in the primary winding of the transformer. The value of no-load current is very small, and thus, it is neglected. Hence, I_{1} = I_{1}’. The no load current is further divided into two components called magnetizing current (I_{m}) and working current (I_{w}).

These two components of no-load current are due to the current drawn by a noninductive resistance R_{0 }and pure reactance X_{0} having voltage E_{1} or (V_{1 }– primary voltage drop).

The secondary current I_{2 } is

The terminal voltage V_{2} across the load is equal to the induced emf E_{2 }in the secondary winding less voltage drop in the secondary winding.

## Equivalent Circuit When all the Quantities are Referred to Primary side

In this case to draw the equivalent circuit of the transformer all the quantities are to be referred to the primary as shown in the figure below

The following are the values of resistance and reactance given below

Secondary resistance referred to primary side is given as

The equivalent resistance referred to primary side is given as

Secondary reactance referred to primary side is given as

The equivalent reactance referred to primary side is given as

## Equivalent Circuit When all the Quantities are Referred to Secondary side

The equivalent circuit diagram of the transformer is shown below when all the quantities are referred to the secondary side.

The following are the values of resistance and reactance given below

Primary resistance referred to secondary side is given as

The equivalent resistance referred to secondary side is given as

Primary reactance referred to secondary side is given as

The equivalent reactance referred to secondary side is given as

No load current I_{0} is hardly 3 to 5% of full load rated current, the parallel branch consisting of resistance R_{0} and reactance X_{0} can be omitted without introducing any appreciable error in the behavior of the transformer under the loaded condition.

Further simplification of the equivalent circuit of the transformer can be done by neglecting the parallel branch consisting R_{0} and X_{0}. The simplified circuit diagram of the transformer is shown below