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.

 

[rwisz]

Your logic is not failing, but there are a few important points to consider when discussing the phase relationship between the voltages in the primary and secondary coils of a transformer.

Firstly, it is important to understand that the primary and secondary coils of a transformer are connected by a shared magnetic field, created by the alternating current flowing through the primary coil. This magnetic field is constantly changing and is responsible for inducing a voltage in the secondary coil.

Now, we know that in an AC circuit, the voltage and current are constantly changing in magnitude and direction. This means that at any given point in time, the voltage and current in the primary coil are not necessarily in phase with each other. However, the changing magnetic field in the transformer core is always in phase with the current in the primary coil, as you correctly stated. This is because the magnetic field is directly proportional to the current flowing through the primary coil.

Next, let's consider the secondary coil. As the changing magnetic field passes through the secondary coil, it induces a voltage in the coil. This induced voltage will have the same frequency as the voltage applied to the primary coil, but its magnitude and phase relationship may differ. In an ideal transformer with no losses, the voltage induced in the secondary coil will be directly proportional to the rate of change of the magnetic field passing through it. This rate of change is determined by the frequency and amplitude of the applied voltage, as well as the number of turns in the secondary coil.

So, to answer the question of why the voltages in the primary and secondary coils are in phase - it is because the changing magnetic field created by the primary current is directly responsible for inducing the voltage in the secondary coil. The voltage in the secondary will always be in phase with the changing magnetic field, which is in turn in phase with the primary current. This is why the voltages in the primary and secondary coils are in phase.

In summary, the phase relationship between the voltages in the primary and secondary coils of a transformer is a result of the shared magnetic field and the process of electromagnetic induction. Understanding this relationship is crucial in designing and analyzing transformer circuits for a variety of applications.