The attached diagram is the equivalent circuit of a practical transformer. Why is the coupling shown only between primary winding and secondary winding of ideal transformer?
Suppose secondary is open. So 'i_s' is zero.Hence 'i_p' should also be zero (ideal transformer). If both primary winding and secondary winding currents are zero, then as per the model,no mutual flux is produced by ideal primary and secondary windings, and hence no EMF should be induced in both. (Note that in the model, coupling is only between primary and secondary of ideal transformer.) But 'v_p' is in parallel with 'Lm' and hence 'v_p' will not be zero. Similarly we know that 'v_s' is also not zero under open circuit conditions.
To explain this behavior, shouldn't both primary and secondary windings of ideal transformer have magnetic coupling with magnetizing inductance'Lm'? (Since model should have the same behavior as the actual device.)
Please note that I understand 'Lm' is not a physical inductor but it is only for representing the behavior of actual transformer.