At what value of primary current will maximum efficiency occur in a transformer?

Would be very grateful if somebody could answer this question for me.

Thanks

 

Probably the point just below where the transformer goes into saturation is the point of maximum efficiency. More current is drawn when a transformer goes into saturation, but the output remains un-changed.
The additional current is converted into heat which is to be avoided.

Cheers, Dpw [ Everything has limitations...and I hate limitations.]

 

I have many "western" name-brand wall-warts that are very efficient because they are cold without a load. When loaded they barely get warm.
But I have a wall-wart that is made in (I am not allowed to say the country) and it is very hot without a load and its voltage without a load is very high. It is very inefficient. It is cheap. Its core is too small and its wire is also too small.