# Inductors in Transformers

Why is it the flux change which induces the ac current of primary coil equal to the flux change that primary coil induces on the secondary coil? Is it possible to prove this?

slide from video SlidePlayer: Transformer taking the ratio of two equations

• If rate of flux change in secondary was the same as in primary, both would have the same amplitude of voltage, so no transformation would happen. The flux and rate of flux of secondary is actually different from the primary in a transformer. This is because of different number of wire turns in their windings. – Ján Lalinský Sep 15 at 13:32
• In my textbook the equation is derived under assumption that both have equivalent flux change but different turns,however flux for one singular coil is equivalent in each and I am asking why that is so. – DDD4C4U Sep 15 at 13:51
• @JánLalinský For an ideal transformer (no flux leakage) the magnetic flux is the same in the primary and secondary. – Bob D Sep 15 at 15:37
• Flux per single turn is the same, because the core does not leak much, but net flux for secondary depends also on the number of turns in the secondary. – Ján Lalinský Sep 16 at 14:54

Why is it the flux change which induces the ac current of primary coil equal to the flux change that primary coil induces on the secondary coil?

Because you're only studying or modeling an ideal transformer.

In a real transformer, flux through the secondary is somewhat less than the flux through the primary. Some of the flux produced by the current through the primary coil goes outside the core, where it doesn't produce any effect in the secondary. We call this the leakage flux.

Its effect is as if there is an additional inductance in series with the primary, which we call the leakage inductance of the transformer.

A common model for a non-ideal inductor including this effect is this:

Here, $$X_{l_1}$$ is the primary leakage inductance and $$X_{l_2}$$ is the secondary leakage inductance.

$$R_C$$ and $$X_M$$ represent additional non-idealities: core losses and magnetizing reactance.

It's also common, for practical circuit design, to transform the secondary leakage inductance across the transformer and represent both leakage inductances with a single parasitic element on the primary side of the ideal transformer.

For well designed transformers, the leakage inductances can be as low as 1-2% of the coupled inductances.