I am sorry to have to say this, but that statement is wrong.
The magnetic flux density depends on current AND the number of turns.
Less turns and higher current gives the same flux density.
This is why 'ampere-turns' are used in calculating flux density, not simply
'amps'.
http://mysite.du.edu/~jcalvert/tech/transfor.htm
The magnetic core doesn't care which winding induces the magnetic field.
At what phase? With no load, it is NOT in phase. It DOES cause IR losses in
the primary, however.
1.5 amps at 120 volts = 180 W
1.5 amps at 120 volts at 89.57 degrees (or a power factor of 0.993) gives
1.35 watts.
Slightly over 1% loss. That is a bit high for modern power transformers
under no load, but a normal loss under max rated load.
Shouldn't. The iron core losses are PART of the total losses seen.
No. You should only, at worst (approximately) double the losses (assuming
two identical transformers).
Let us assume that the secondary of T1 is 12 vac.
To deliver 500VA at 12 volts, the secondary is going need to see a 0.288
ohm load and will deliver 41.7 amps to the load. The DC resistance of the
winding will be much lower than the load resistance, on the order of 0.03
ohms for an inefficient transformer.
The identical but reversed 2nd transformer 'expects' that higher voltage
and exactly compensates for it.
Wrong. If the output of the second transformer is carrying 1 amp, the
primary of the first transformer will carry 1 amp plus the iron and copper
losses of the two transformers. A poor efficiency is about 95% so with two
transformers, back to back, you might expect 10% losses resulting in 1.10
amps.
A low voltage, high current secondary is commonly wound with heavier wire
so it can stand more current and presents a much lower dc resistance.
When it is driven, as when the windings are reversed, it will run just
fine.
Wrong. Only the current to supply the 'no load losses' needs to be supplied
'continuously'.
Under the 500VA load, the primary will present a 28.8 ohm load to the
110VAC line, drawing 4.2 amps of current while the back to back 12 volt
windings will be carrying 42 amps of current.
The no load losses will be quite low because the primary presents an
essentially pure inductive load rather than a resistive load to the ac
line. Only the core losses, on the order of .25 to .5% of the rating will
need to be supplied.
http://findarticles.com/p/articles/mi_m0BPR/is_10_21/ai_n6259812/
Under no load, the 12 volt windings would see a 'parasitic current' on the
order of 0.02 Amps and the 110 V primary would see a current on the order
of 0.1 Amp and present a 'resistive component' of the load of 115 ohms to
the supply lines.
The combo should be able to supply close to the rated VA of
_a_single_transformer.
You will have ~twice the losses and both transformers will reach the
temperature that one would have reached.
So, de-rate the pair of 500VA back to back transformers to 450VA to give
yourself plenty of safety margin and don't seal them into an airtight box
together, and you should be just fine.
Best Regards