Please refer to the attached pdf file. I am curious why the phasor of I'1 and I2 are 180 degree apart from each other? To my understanding, I2 creates flux "phi2" in Fig. 2.27(b). Then I'1 creates flux " phi' " to oppose the change of "phi2".
So, both I'1 and phi' will have terms like d{phi2}/dt. They should be 90 degrees apart from I2 and phi2, aren't they?

Sincerely,
blackmelon

 

There are some errors in the file, typo and drawing.

The current in the primary winding creates a flux in the iron core that travels thru the core to induce current I2 in the secondary. This current in the secondary also creates a flux in the core, but it is in the opposite direction. The paper asserts that this counter mmf opposes and reduces the original flux and lowers the emf, such that additional current must flow in the primary to restore emf. This additional current I' creates a flux in the core in the original direction, which is in the opposite direction of the flux from I2, hence 180° represents the direction of the flux in the core.

 

There are some errors in the file, typo and drawing.

The current in the primary winding creates a flux in the iron core that travels thru the core to induce current I2 in the secondary. This current in the secondary also creates a flux in the core, but it is in the opposite direction. The paper asserts that this counter mmf opposes and reduces the original flux and lowers the emf, such that additional current must flow in the primary to restore emf. This additional current I' creates a flux in the core in the original direction, which is in the opposite direction of the flux from I2, hence 180° represents the direction of the flux in the core.

I agree. The direction of that flux should be in the other direction. Thank you very much for spending time reviewing the file for me.