Transformer magnetizing inductance

I am learning about transformers and in the equivalent circuit the magnetizing inductance of the excitation branch is supposed to represent the current needed to "set up" the flux in the core due to finite permeability of iron. However, this does not explain to me why flux needs to be "set up" to begin with. The voltage induced is not a function of the magnitude of the flux but rather the rate of change of flux. The flux could at one instant be zero and changing quickly and the same voltage would be induced in a winding as if the magnitude were larger with the same rate of change. This seems to be one of the biggest problems when analyzing "magnetic circuits" to me as there is a clear discrepancy in the duality with respect to maxwell's equations. The rate of change of magnetic flux would seem to be the "magnetic current" especially for energy conservation and duality for Faraday's law with Ampere's law. Can someone explain why there needs to be flux "set up" in the core and for that matter what the magnetizing inductance does.

• Perhaps what you're misunderstanding is that the flux Φ itself is the "magnetic current", not dΦ/dt. – Hearth Oct 23 '18 at 22:04
• I understand that's how it was defined but the voltage induce would be equal to the rate of change of magnetic flux not the magnitude of the flux. This can be compared to amperes law where the magnetic field is proportional the rate of change of electric charge not the magnitude of the electric field itself. I don't see why a magnetic flux needs to be set up to begin with just like a build-up of electric charge does not create a magnetic field. – Colin Hicks Oct 23 '18 at 22:14
• I'm not sure I understand what you're not understanding, honestly. The flux needs to be "set up" because it has to get there somehow, it's not just magically there. – Hearth Oct 23 '18 at 22:31
• Since an answer would entail the behavior of the core itself, could you please refer to specific core types. Iron,soft ferrite, high density ferrite, Permalloy (nickle-iron), etc – Sparky256 Oct 23 '18 at 22:31
• I don't understand why a given magnitude of B field needs to be maintained in the core. The magnetizing inductance will generate a given level of B field as far as I understand, but why does there need to be a given magnitude of B field. If the B field at one instant was 0 but increasing at a given rate of change that would induce a voltage. It seems to me that "setting up" is unnecessary as the rate of change is whats important. Intuitively the "set up" flux is like the "DC" value of the changing flux that doesn't matter. – Colin Hicks Oct 23 '18 at 22:35

Transformers are feedback systems, with summation of input and feedback FLUX occurring within the core.

When the secondary load current changes, the flux summation changes, the voltage induced in the PRIMARY changes, and the voltage changes across the impedance between the external power source and the primary. This change of voltage across the impedance causes a change in current drawn from the external power source.

simulate this circuit – Schematic created using CircuitLab

Let we look what the rate of change is. A magnetic flux of a given transformer is: $$\Phi=\Phi_{max}sin(\omega t)$$

Rate of change is given as differential over time:

$$\dfrac{d\Phi}{dt}=\Phi_{max}\ \omega\ cos(\omega t)$$

And the induced voltage is: $$u_i=-N\dfrac{d\Phi}{dt}$$

You can clearly see that rate of change as you are refering at is not magnitude invariant. It is clearly seen (second equation) that an induced voltage will vary with magnitude of flux ($$\\Phi_{max} \$$) but also with frequency ($$\\omega\$$) and finally with number of turns (N).