Two ideal & identical coils connected in series on the same core have equal current flowing in opposite directions. The inductances are opposing so the total inductance is zero.

If we place another coil on the core to act as a primary coil we now have a transformer, or do we?
Since the inductances are canceling each other wouldn't the voltage across the secondary coil be 0?

 

If we place another coil on the core to act as a primary coil we now have a transformer, or do we?

Presumably you already have a primary coil?
It is not really clear what you are describing, if you already have a primary, any other single coil will be directly influenced by the primary and the series windings would not be considered?
Max.

 

No results in a third coil because the magnetic flux in the core is zero.

 

Except the 3rd coil would not be described as a primary?
How do the two series coils obtain the current flowing in 'opposite directions'?
An incomplete description.
Max.

 

Sorry, maybe a picture will better explain.

Assuming the coupling is 100% and both secondary coils have equal inductances. Since the current is flowing in opposite directions in each secondary coil the inductances cancel out. My question is, would the voltages also cancel each other out meaning no current would flow through the secondary circuit?

 

Still no current because the secondary coils oppose each other.

 

Ok, that's what I thought, I was just confusing myself.

Thank you #12

 

That is clearer, then no no current would flow in the resistor as the resultant voltage would be 0v.
BTW it is customary to place a black dot at the 'start' of each winding to indicate relative polarity or phasing.
It was 'place another coil to act as primary' that did not make sense.
Max.

 

And, by the way, if you swap the source and the load, so the source is driving two primaries connected out of phase, and the secondary is a single coil driving the resistor, there still will be no voltage across the resistor and no current through it.

ak

 

And, by the way, if you swap the source and the load, so the source is driving two primaries connected out of phase, and the secondary is a single coil driving the resistor, there still will be no voltage across the resistor and no current through it.

True. But the primary current will be limited only by the winding resistance and likely fry the transformer or blow a breaker.