# Mutual Induction in Transformer

So in a transformer, when an alternating current flows through the primary, thanks to the Ampere's law, a changing magnetic field is produced around it. This induces an alternating current in the secondary. So far so good. Now my question is, does this induced AC not create a changing magnetic field in the secondary, which in turn induces current in the primary (just like the primary did to the secondary)? And thus, won't we have a self-sustaining circuit where the primary and the secondary took turns to induce each other?

• Your question appears to be based on that fact that current is induced. It isn't; voltage is induced and if there is a load then current flows. There rest of your question contradicts the reality of the situation without any hint as to why you think this way. VTC. – Andy aka Jul 19 '17 at 7:26

So in a transformer, when an alternating current flows through the primary, thanks to the Ampere's law, a changing magnetic field is produced around it.

A primary current flows. This induces a changing magnetic field H around it. The changing H field in the core induces a changing B field in the core.

This induces an alternating current in the secondary. So far so good.

No. The changing B field induces an alternating voltage in the secondary. It also induces an alternating voltage in the primary of the right magnitude to more or less cancel out the primary applied voltage. The small difference between the applied voltage and the primary induced voltage allows sufficient current to flow in the primary resistance to create enough field for this all to be in balance.

If there's a load connected to the secondary, then the secondary voltage pushes a current through the load, which of course completes its circuit through the secondary.

Now my question is, does this induced AC not create a changing magnetic field in the secondary ...

Don't forget they are wound round the same core. Any current that flows in the secondary creates an H field that adds to the primary's H field. The phase of the secondary current is always to reduce the H field. The reduced H field generates a reduced B field in the core.

... which in turn induces current in the primary (just like the primary did to the secondary)?

more or less correct. The reduced B field doesn't cancel as much of the primary input voltage, so the larger difference between the applied voltage and the primary induced voltage allows (demands) a higher primary current. The net result of the secondary current flow is to cause an increased primary current to be drawn.

And thus, won't we have a self-sustaining circuit where the primary and the secondary took turns to induce each other?

As I said, the phase is such to reduce the field. The net result of the two-way interaction is that as the secondary supplies more power to its load, the transformer draws more power from its supply to match it.

The feedback is negative, not positive. Given a finite Rsource providing current into the primary, as the secondary begins to drive a load the additional secondary current does feedback to the primary and reduces the voltage across the primary, which increases the voltage across the Rsource.

simulate this circuit – Schematic created using CircuitLab

Now my question is, does this induced AC not create a changing magnetic field in the secondary, which in turn induces current in the primary (just like the primary did to the secondary)?

Not in that sense, think of inductors as water pump spinning with some mass. A single inductor is like one water pump, if I stop the flow of water the pump still continues to spin and still creates flow (and pressure if there is resistance). A transformer is like two pumps connected together with a shaft, one will spin the other. If I put more resistance one one pump, the other pump will slow down from the resistance of the other side.

The magnetic field is shared, if your modeling it, it is its own variable that is shared between the two, but it is related to the current of both, so it can be simplified out. If your dealing with nonlinear transformers, you can't simplify it out. Here is the simplified version of an ideal transformer:

$$V_1 = L_1\frac{di}{dt}+M_s*I_1$$ $$V_2 = L_2\frac{di}{dt}+M_s*I_2$$

And thus, won't we have a self-sustaining circuit where the primary and the secondary took turns to induce each other?

No, not in the real world, because you will always have a load and leakage. Any load is going to dissipate current, even if it is a small ammount. And as far as magnetic fields around the tranformer, they leak magnetic flux and waste magnetic energy. If there is material in the transformer, like ferrite, it will also burn up magnetic energy as heat.