Why transformer voltages in phase?

[teroenza]

Homework Statement

Why are the voltages of the primary and secondary coils of a transformer in phase? The transformer is a simple one with two coils, and an iron core. A.C. voltage applied to the primary, no load on the secondary.

Homework Equations

The Attempt at a Solution

Voltage in the primary is 90 degrees ahead of the current. The flux in the core changes with the current and is this "in phase" with the current (unsure of the correct terminology). The core acts a a "flux pipe" and transfers the flux through the secondary. Flux through secondary induces an EMF/voltage in the secondary. Voltage of secondary in phase with flux in phase with current of primary. So voltage in secondary would be 90 degrees behind that of the voltage in the primary.
Can someone point out where my logic is failing?
Thanks

 

[fizika_kz]

The Voltage of secondary coil is not in phase with the flux, because it is a time derivative of the flux, isn't it?

 

[teroenza]

So if current in the primary varies as a sine wave, so does flux, and then because induced emf is time derivative of the flux, the induced emf varies as a cosine wave (derivative of sine). Because the current in the primary was 90 behind the primary's voltage to begin with, primary voltage varies as a cosine and is thus in phase with voltage in the secondary?

 

[Redbelly98]

So if current in the primary varies as a sine wave, so does flux, and then because induced emf is time derivative of the flux, the induced emf varies as a cosine wave (derivative of sine). Because the current in the primary was 90 behind the primary's voltage to begin with, primary voltage varies as a cosine and is thus in phase with voltage in the secondary?

Yes.