About transformers: very little primary current if the secondary is unloaded

Question

This extract is from a popular electronics book:

... a transformer of turns ratio \$n\$ increases the impedance by \$n^2\$. There is very little primary current if the secondary is unloaded.

I'm thinking about the emboldened part. Please see if the following argument is correct: If the secondary is unloaded, its current is zero, so the secondary can be neglected (as if it doesn't exist at all), and the transformer can be modeled as a single inductor with inductance of \$L\$. And according to the relations

$$X_L=2\pi\nu L$$

and

$$V=X_L I,$$

\$L\$ must be large if primary current is 'very little'.

Answer 1

Yes, you are correct. A transformer always has a "magnetizing current" (reactive) that is determined by its own inductance, whether or not it is loaded.

Loading the secondary imposes a second "resistive" (in-phase) current that varies with the load.

It sounds as if the book you quoted is referring to this in-phase component only, and ignoring the magnetizing current.