(Here's my understanding just in case if I misunderstood something)
I understand that for order to induce a voltage on the other side of the transformer or in the secondary coil even though there's no battery over there, a varying magnetic field is needed to be cut repeatedly (lenz's law).
This can be done using an AC generator which produces a varying current, both in direction and value. And since a current in a wire produces its own magnetic field and the current is varrying the magnetic field will be varrying too.
Then these magnetic field travel through the soft iron core which, I guess, happens because the primary coil rotates around the core, they are touching, so it's basically touching a magnet and getting magnetised by induction (when a magnetic material touches a permanent magnet and becomes a magnet itself too my book call this magnetisation by induction).
However the current doesn't travel through it too, even though iron must be a good conductor of electricity, because the coil must be coated with an insulator.
My question is what will happen if the insulating coat of some wires fell off and current can travel through the soft iron core? The wires doesn't have to be next to each other because I know they may create a short circuit maybe they're separated by other wires which are still insulated.