# Resistance and Reactance of the Transformer

The Resistance of the transformer is defined as the internal resistance of both primary and secondary windings. In an actual transformer, the primary and the secondary windings have some resistance represented by R_{1} and R_{2} and the reactances by X_{1} and X_{2}. Let K be the transformation ratio. To make the calculations easy the resistances and reactances can be transferred to either side, that means either all the primary terms are referred to the secondary side, or all the secondary terms are referred to the primary side.

The resistive and the reactive drops in the primary and secondary side are represented as follows

- Resistive drop in the secondary side = I
_{2}R_{2} - Reactive drop in the secondary side = I
_{2}X_{2} - Resistive drop in the primary side = I
_{1}R_{1} - Reactive drop in the primary side = I
_{1}X_{1}

## Primary Side Referred to Secondary Side

Since the transformation ratio is K, primary resistive and reactive drop as referred to secondary side will be K times, i.e., K I_{1}R_{1 }and K I_{1}X_{1 }respectively. If I_{1} is substituted equal to KI_{2} then we have primary resistive, and reactive drop referred to secondary side equal to K^{2}I_{2}R_{1} and K^{2}I_{2}X_{1} respectively.

The Total resistive drop in a transformer

Total reactive drop in a transformer

The term

represent the equivalent resistance and reactance of the transformer referred to the secondary side.

From the phasor diagram shown above the equation can be formed as

Where V_{2} is the secondary terminal voltage and I_{2} is secondary current lagging behind the terminal voltage V_{2 }by an angle ϕ.

Since the term

is very small and is neglected as compared to the term

Where V_{1} is the applied voltage to the primary winding

If the load on the secondary side of the transformer is purely resistive then ϕ = 0 and the equation (1) becomes

If the load on the secondary side of the transformer is capacitive then ϕ should be taken as negative, and the equation (1) becomes