The primary and the secondary winding of an actual transformer have some resistance which is represented by R_{1} and R_{2} respectively (shown external to the windings in the figure). The resistances of the two windings can be transferred to any one side. It is done in order to make the calculations easy.

**The resistance is transferred from one side to the other side in such a manner that percentage voltage drop remains the same on either side. We can find the equivalent resistance and reactance of transformer by the short circuit test**.

# Equivalent Resistance of Transformer Formula

Let

R_{1} = primary winding resistance

R_{2} = secondary winding resistance

K = transformation ratio

Then,

Secondary resistance referred to primary R_{2}’ can be calculated by the formula given below.**R _{2}’ = R_{2}/K^{2}**

The equivalent resistance of transformer referred to the primary is represented by R

_{01}.

Therefore,

**R**

_{01}= R_{1}+ R_{2}’ = R_{1}+ R_{2}/K^{2}## Equivalent Resistance of Transformer Referred to Secondary

The primary resistance referred to the secondary is denoted by R_{1}’ and can be calculated by the formula given below.

**R _{1}’ = K^{2}R_{1}**

The equivalent resistance of transformer referred to the secondary is represented by R

_{02}.

Therefore,

**R**

_{02}= R_{2}+ R_{1}’ = R_{2}+ K^{2}R_{1}## Equivalent Leakage Reactance of Transformer

**The flux that links with both the windings of the transformer is called mutual flux and the flux which links only with one winding of the transformer is called leakage flux. ** Due to leakage flux of the primary winding and the secondary winding, an EMF is induced in the respective winding. The primary and secondary voltage will have to overcome these induced EMFs. Thus these induced EMFs are considered as the voltage drops across the factitious reactances placed in the series with the primary and secondary windings. These reactances are called as the leakage reactances and they are shown in the figure.

As done in the case of resistances, the reactances can also be transferred to either side.

**The reactance from one side to other is transferred in such a manner that percentage voltage drop remains the same on the either side.**

## Equivalent Reactance of Transformer Referred to Primary

Let

X_{1} = primary winding reactance

X_{2} = secondary winding reactance

K = transformation ratio

Then,

Secondary reactance referred to primary X_{2}’ can be calculated by the formula given below.

**X _{2}’ = X_{2}/K^{2}**

The equivalent reactance of transformer referred to the primary is represented by X

_{01}.

Therefore,

**X**

_{01}= X_{1}+ X_{2}’ = X_{1}+ X_{2}/K^{2}## Equivalent Reactance of Transformer Referred to Secondary

The primary reactance referred to the secondary is denoted by X_{1}’ and can be calculated by the formula given below.

**X _{1}’ = K^{2}X_{1}**

The equivalent reactance of transformer referred to the secondary is represented by X

_{02}.

Therefore,

**X**

_{02}= X_{2}+ X_{1}’ = X_{2}+ K^{2}X_{1}## Impedance of Transformer

The primary impedance Z_{1} = R_{1} + jX_{1}

And secondary impedance Z_{2} = R_{2} + jX_{2}

The transfer of impedances takes place on the same lines as that of the resistances. The transfer of impedances can take place from primary to secondary and vice versa.

Z_{01} = (R_{01}^{2} + X_{01}^{2})^{1/2} impedance referred to primary side.

Z_{02} = (R_{02}^{2} + X_{02}^{2})^{1/2} impedance referred to secondary side.

## Transformer | All Posts

- Ideal Transformer
- Construction of Three Phase Transformer
- Types of Transformers
- Equivalent Resistance and Reactance of Transformer
- Equivalent Circuit of Single Phase Transformer
- Power Loss in a Transformer
- Open Circuit Test of Single Phase Transformer
- Short Circuit Test on Single Phase Transformer
- Transformer Efficiency
- Regulation of Transformer
- Autotransformer
- Instrument Transformers
- Polarity of Transformer Windings
- Significance of Vector Group of Transformer
- Buchholz Relay Construction | Working
- Why current transformer secondary should not be opened
- Dielectric Strength Test of Transformer Oil
- Transformer Moisture Removal Process

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