# Magnetizing Inductance Vs. Mutual Inductance

1.) In the transformer equivalent circuit model, is the Magnetizing Reactance/Inductance the same as the transformers Mutual Reactance/Inductance?

2.) Does the secondary have a magnetizing reactance? and is this the same thing as the primary magnetizing reactance, or are they lumped into one quantity called Xm?

• Is there none that can answer this seemingly simple question? Nov 1 '14 at 2:34

I've seen the terms mutual and magnetizing inductance used interchangeably, but I don't believe them to be the same. Mutual inductance can be derived if you consider a simple magnetic circuit with two separately excited coils (such as the one shown here: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html). The flux linkage in coil 2 that is produced by the current flowing in coil 1 is related to mutual inductance ($$\\lambda_{21} = L_{21}*i_1\$$, where $$\"L_{21}"\$$ is the mutual inductance term). You can derive the same relationship for the flux linking coil 1 due to the current in coil 2 ($$\\lambda_{12} = L_{12}*i_2\$$). In theory, $$\L_{12} = L_{21}\$$ = the mutual inductance.

Magnetizing inductance is associated with the flux that actually links the core of the transformer (as opposed to leakage flux, which does not). If you're familiar with the 'open circuit test' for a transformer that's used to measure Xm, think about how the test is performed. The secondary is left open while rated voltage is applied to the primary. This test actually measures primary side leakage and magnetizing reactance, but the former is typically assumed to be much smaller, and is therefore neglected. This is more closely related to the self-inductance of one side (in this case the primary) of the transformer.

The Magnetizing inductance / reactance can be referred to either the primary or the secondary of the transformer. For example, if you use the open circuit test as described above, you would include it in the primary of your model. You can then use the turns ratio to refer it to the secondary.

Here's a picture that might help: -

It's basically two coupled inductors aka a transformer. L1 is the primary and L2 is the secondary. With L2 open circuit, L1 always measures the same irrespective of the L2's distance.

Mutual inductance of two coils that are 100% coupled (like a perfect transformer) is: -

Given that primary magnetizing inductance is L1, M can equal L1 when L1 = L2. Pretty pictures taken from here

(1) They aren't the same. Only when turns ratio=1. (2) In the transformer model, there only have one magnetizing inductance, usually "put on" the primary side. When you derive the secondary voltage(combine the magnetizing inductance and leakage inductance of both side), you will find the voltage of secondary is derived from the magnetizing voltage in the primary.

Since there is no current flowing on the HV side, there should be no mutual inductance, and the Magnetizing inductance should simply be equal to the self inductance of the LV coil (neglecting leakage inductance of course), not mutual inductance.