A real transformer differs from the ideal model because its windings have resistance, some flux does not link both windings, and the magnetic core requires magnetizing current and dissipates power.

These effects can be represented by an equivalent circuit around an ideal transformer.

Winding resistance

Primary and secondary resistances represent copper loss and produce voltage drops proportional to winding current.

Leakage reactance

Flux that links only one winding behaves like an additional inductance in series with that winding. In sinusoidal steady state this becomes a leakage reactance.

Leakage reactance mainly affects voltage drop and reactive behavior; it is not itself a mechanism of real power dissipation.

Magnetizing branch

The core needs current to establish alternating magnetic flux. A shunt magnetizing reactance models this current, while a parallel resistance represents core loss.

Referring quantities across the transformer

If

$$a=\frac{N_1}{N_2},$$

an impedance on the secondary can be referred to the primary as

$$Z_2'=a^2Z_2.$$

This removes the ideal-transformer element from many calculations and lets the complete circuit be analyzed on one voltage level.

The equivalent circuit separates real physical imperfections into electrical elements that can be handled with ordinary phasor circuit analysis.