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Lets say we have a transformer with two primary coils. The coils are positioned end to end such that unlike poles are adjacent (NS or SN). The current in one of the coils has a phase shift of 90 degrees. Because of superposition principle the magnetic field produced by the primaries would be the vector sum of the two primaries. This is the magnetic field which would induce current in the secondary coil.

My question is:- How would the primary coils be effected by the cemf from the secondary coil ?

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"Because of superposition principle the magnetic field produced by the primaries would be the vector sum of the two primaries." But you will also have a current in the secondary, assuming that some 'load' is connected to the secondary. So the overall flux density in the core at any instant is the sum of the flux densities produced by all three coils (assuming that the transformer core can be treated as having a constant permeability). The induced emf in any of the three coils is the rate of change of flux in the core, multiplied by the number of turns on that coil.

So the emfs in the primaries are affected by the current in the secondary. The nature of the effect depends, among other things, on the secondary load (for example is it resistive or reactive). I expect the rms primary current to increase if a resistive load is connected across the secondary, though having two primaries (with unknown numbers of turns), carrying currents 90° out of phase, makes it all rather complicated.

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