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In general, instantaneous power into the primary does not equal the power delivered by the secondary: some goes to change the internal energy stored in the transformer. That internal energy is not just that from the self-inductances $L_1$ and $L_2$. The mutual inductance $M$ terms arise because the primary and secondary magnetic circuits are coupled, ...

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To add to Floris's reply, just to elaborate in a very basic manner in what way the flux linkage (analogous of displacement x in Force Current analogy) and magnetic flux differ. Consider the scenario where a magnetic field is present, and we have an open circuit that has been closed using a metalic rod. As the picture shows: We know that the induced EMF ...

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I think there is something wrong with your mapping. Looking at http://lpsa.swarthmore.edu/Analogs/ElectricalMechanicalAnalogs.html , I see the following table: This is inconsistent with the mapping you are showing. I can understand this table - I can't understand yours. I think an error crept in - which would reasonably explain your confusion. Looking ...

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