[mikethedruid]

As I told you, the two sides of an IF transformer are BOTH TUNED LC TANK CIRCUITS. One tunes them to peak at the desired frequency, on both sides. Tuning can be accomplished in an LC tank circuit by varying either the inductance, or the capacitance. In your case the capacitance is fixed, and the inductance is varied. This still tunes the tank circuit.

In a resonant tank circuit both the capacitance and the inductance affect the frequency at which the circuit "peaks" Inductance is affected by the diameter of the coil, the number of turns, the length of the winding, and the magnetic properties of the coil core. The gauge of the wire is of little importance except in that it can affect the length of the winding, and must be heavy enough to handle any current which will pass through it without overheating. The slug which moves in and out of the coil tunes the inductance, increasing or decreasing it by varying the magnetic properties of the core.

I STRONGLY suggest you invest in a copy of Audel's Radioman's Guide. Get an old one from before the mid 1960s. You can find them cheaply enough on Amazon or even eBay sometimes. READ IT CAREFULLY. You will find the answers to these, and many other questions you may have along the way.

Alternately, if you don't mind reading from a screen, or investing in several reams of paper and a lot of ink cartridges to print it out, you can download the entire old National Radio Institute course for radio repair men here:

https://worldradiohistory.com/Archive-Co...o_1930.htm
It is a series of PDFs, 49 in all, and will give you an even more thorough grounding in electronics than Audel's