# Equivalent circuit of the transformer

Why are the core resistance and core inductance in the equivalent circuit of the transformer shown in parallel while the winding resistance and leakage reactance are in series?

Why are core resistance and core inductance not also shown in series?

Maybe you should forget about transformers and just think about a simple inductor and its equivalent circuit: -

So, what you find for a simple inductor is this: -

Image from here. This models high-frequency capacitive coupling so we can remove this: -

Then, it's a simple matter of adding a little bit of leakage inductance in series with $$\R_{DC}\$$. Call that leakage inductance the wire inductance that connects the AC to the inductor if you want.

• That's a very nice advice. But then I would like to know why R0 and X0 are in parallel rather than being in series.
– Alex
Commented Dec 12, 2021 at 20:19
• X0 is the magnetization inductance and that's where most of the AC voltage resides when supplied with AC voltage. It is the chief component in an inductor so it should, by design have the greatest voltage present. R0 is in parallel with it because it represents losses that increase when the supplied AC voltage increases. If you put a small value DC voltage across the inductor, X0 and X1 become short circuit and, all you can measure is R1 (RDC) so it remains always a series component to everything just as the wire feeds to the transformer have a DC resistance in series with the feed. Commented Dec 12, 2021 at 20:25
• Thanks alot. Really thanks
– Alex
Commented Dec 12, 2021 at 20:33
• @Alex - think of what happens at other frequencies such as DC and infinite frequency. At DC the R0 does not affect the impedance, so it can't be in series. Similarly at very high frequencies X0 is the dominant impedance so it needs to be across the perfect inductive element, so it has to be in parallel. Commented Dec 12, 2021 at 20:35
• @Alex who mentioned R(a.c.)? - I didn't - that's another subject entirely. Maybe you meant reactance to a.c. current and not resistance? Commented Dec 12, 2021 at 20:38

The behavior of the magnetizing branch under AC excitation can be represented either by a parallel circuit (R and L in parallel, in the classic model) or by a series circuit (with R and L in series). I've seen some transformers consultants using this type of circuit, although it really isn't the most common. So it would not be surprising to see it somewhere. However, the parallel circuit has more coherent response to DC signals.

Another additional detail is that for power transformers, it is common for the magnetization branch impedance angle to be close to 45°, that is, the inductive component is not always the main one.