CD is correct.
Each MMF is approximately equal but Opposite. Thus the Opposing Red Arrows.
Note: The average Textbook does not ever consider any Opposing Magnetic Field from the Secondary Coil. You can see:
Did you notice the error in the second image, above? Try applying the Right Hand Grip Rule:
Oddly, and only partially correct, the above image does show two Fluxes, Φσ1 and Φσ2 however, only marked as Leakage Flux. This is still not correct! It is inaccurate!
If the average Transformer is around 90% efficient, most of them are around this figure, and we are dealing with a step down Transformer, lets say 24 : 1, 240 Volts Input, 10 Volts Output. 240 Volts / 400 Turns on the Input, that's 1.66 Volts per turn. 17 Turns gives 10 Volts. Our Input is pulling One Ampere with a Load attached to the Secondary. Some figures:
- Impedance ( Z ): 1+j239.998 in Ohms. ( Ω )
- Inductive Reactance ( XL ): 239.998 in Ohms. ( Ω )
- Capacitive Reactance ( XC ): 239.997916693793 in Ohms. ( Ω )
- Phase Angle ( θ ): 89.7612689669011 degrees. ( θ )
Our power on the input calculates as follows:
Power ( P ) = Volts ( V ) ⋅ Amperes ( I ) ⋅ cos( θ ) = 240 ⋅ 1 ⋅ cos( 89.76 ) = 1.0 watts.
At 1 Watt on the Input, a 90% efficient Transformer will give you 0.9 Watts on the Output.
Magnetomotive force ( MMF ) = Fm = N ⋅ I = Ampere-Turns ( At ).
For illustration purposes I am going to consider DC Power. We are going to put aside Phase Angle for the moment. Assuming Unity Coupling:
- 400 Turns ⋅ 1 Amperes = 400 Ampere-Turns.
- 17 Turns ⋅ 24 Amperes = 408 Ampere-Turns.
We have a big problem here! Yes we have not considered Losses! Also, 17 turns is rounded up from Volts per Turn: 400 / 240 = 1.6666666666666666666666666666667 ( Turns Per Volt ) ⋅ 10 ( Volts ) = 16.666666666666666666666666666667 ( Turns ).
On the Output at 10 Volts we should get 24 Amperes without Losses and all Transformers have losses! So we have a 90% efficient Transformer! What is 10% off 400? 40 right? So more accurate estimation would be:
- 400 Turns ⋅ 1 Ampere = 400 Ampere-Turns.
- 17 Turns ⋅ 21.6 Amperes = 367.2 Ampere-Turns.
But, is this the correct way to look at this?
What is work? The Current or MMF is the work Component, and we have a Phase angle to think about. But Watts is not the Magnetising Force, MMF is! MMF does not consider where the Voltage is, it is only Turns multiplied by Amperes.
You can see, it is easy for confusion and therefore inaccuracy's to creep in!
367.2 Ampere-Turns / 400 Ampere-Turns = 0.918 or 91.8% of the work is producing Output, nearly 10% is lost to Hysteresis and Heat losses.
PrimaryMMF = Primary Turns ( N ) ⋅ Primary Current ( I ) and SecondaryMMF = Secondary Turns ( N ) ⋅ Secondary Current ( I ) so together we must conclude:
MMFPrimary ≅ -MMFSecondary
As you can see, there are Two Fluxes in a Transformer Core at any time the Secondary is Loaded! It is assumed the Secondary Current Opposes the Primary Current and most of the Time this is correct. Importantly, none of the equations predict the Current Direction, again, they only predict E.M.F.