200703-1543 EDT
There have been many statements in this thread that show total ignorance on the part of the responder with respect to magnetic circuit theory, and ferro-magnetic characteristics.
For some magnetic material curves see "Electric and Magnetic Fields", Stephen S, Attwood, U of M, 1949, John Wiley and Sons, Chapter 13.
Back in the 1870s when Edison was developing an efficient dynamo he discovered ferro-magnetic core saturation.
Ordinary transformer iron has a moderately soft saturation characteristic as compared to a square loop material. Thus, as voltage to the primary is increased at a constant frequency the magnetizing current to an unloaded transformer is nonlinear with respect to excitation voltage, and rises faster than excitation voltage, but does not abruptly jump at some voltage.
Magnetizing current reaches its peak at a voltage zero crossing, and flux density is a maximum at the zero crossing.
Following is measured data from a Signal Transformer A41-175-24. Meaning a nominal 120 V input. 175 VA, and 24 V output at full load. Input current from the load at full load would be 175/120 = 1.46 A. Room temperature primary resistance is about 1,7 ohms. Assume this goes up by 30%, then primary power dissipation from the secondary load is about 1.46*1.46*2,2 = 4.68 W. Add about 0.15 to 1.46 for the magnetizing current effect, and we get 5.7 W. Multiply by 4 and the result is about 20 W, or an efficiency of about 175/195 = 90%.
Measurements to unloaded transformer ---
Input voltage from Variac dial, input current from RMS meter.
Input V, Out V, Out V/Out V at 120 input, Input V/120, Input I, Input I normalized to that at 120
20 .... 4.08 .... 0.15 ..... 0.17 .... 0.006 .... 0.03
40 .... 8.64 .... 0.31 .... 0.33 .... 0.014 .... 0.06
60 .... 13,8 .... 0.49 .... 0.50 .... 0.028 .... 0.12
80 .... 18.8 .... 0.67 .... 0.67 .... 0.045 .... 0.19
100 .. 23.7 .... 0.85 .... 0.83 .... 0.100 .... 0.42
120 .. 28.0 .... 1.00 .... 1.00 .... 0.240 .... 1.00
140 .. 32.2 .... 1.17 .... 1.17 .... 0.500 .... 2.08
This is enough for you to chew on now. Ordinary power transformers have substantial saturation effects, but not extremely sharp.
.
.
l