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Transformers' Problem



Here is the problem:
An ac voltage of Vp is applied across the primary coil, and if the secondary coil of a transformer is connected across a load, most texts, if ever mentioned, have concluded that there will be be an increase in current in the primary coil.
The reason:
The induced current in the secondary produces a changing magnetic flux, which induces a current which will reduce the back e.m.f. (i.e. in the same direction as the applied current due to Vp). As Vp is fixed (fixed freq.), an increase in current in the primary would therefore imply an increase in the rate of change of magnetic flux, hence greater induced current in the secondary. Moreover, the back e.m.f. in the primary is also increased! The greater induced current in the secondary now again reduces the back e.m.f., increases current, increases back e.m.f. and the cycle repeats itself.
One text (I think Tom Duncan, 4th edition) mentioned that the situation would stablise when Vs = back e.m.f., why?
I think there's some confusions here. Can someone offer a clearer perspective?
 
Regards,
Chow