adding or subtracting some small amount of voltage from each variac
output as they are combined to create a voltage source. So if variac
one outputs 220V while number 2 outputs 222V, the combining
transformers will add one volt to variac 1, and subtract a volt from
variac 2, giving 221V output. Making up for the voltage difference
between units will then cause them to source relatively equal currents
to the load, and prevent one variac output from driving the other
output (which also will equalize the voltage outputs, in a less
efficient way). This implies that the voltage across each of the
balancing "chokes" (id call them transformers) is not equal when they
are actually doing something useful. Hence, you need an independent
core and windings for the system to work as intended.