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It all depends on where you are going to use your inductor. In applications like AM Radio Ferrite core is a must. Ferrite improves the Q-factor (Quality factor) of the coil.
Air-core can also work in some cases.
Let me know your application
If you find it difficult to get the ferrite rod use other oscillators which do-not use inductors. One such is astable oscillator. Have a look at ths stun gun project at https://www.electro-tech-online.com/threads/simple-lie-detector.40/.
Instead of audio transformer mentioned in the project you can use normal iron core transformers and obtain high voltage to drive tube lights. One thing to be noted here is that if the frequency of the oscillator is high, the losses in iron-core transformer will be high as compared to ferrite core which will drain you battery faster (not very fast but backup time will be less)
A mains transformer will work fine connected backwards -BUT-
The little oscillator driving the transformer will only be capable of a few-hundred mA, trying to use a transformer with a 10A secondary will provide such a low impedance as to completely short the output.
You need to choose logically - a small transformer as used to power old cassette recorders or tiny radios would be best - a 9v secondary capable of 100mA ? or 50mA ?
Experiment to find something that works (240v to 3v tx backwards with 9v in could give 600v out ??? [yes you are pushing the insulation beyond its design] )
Don't expect the full voltage out - you will have losses.
Don't expect more power out than you put in (100mA to a 24/1 ratio transformer will give 4mA out ???)
Mechie, How about a Push-Pull Transistor Configuration for Centre-Tap transformer or Simple Transistor as a Switch for 2-terminal transformer? It won't short the output of oscillator and will effeciently drive the transformer upto many Amperes. And if MOSFETs are used it will work out at its best giving very high input impedance without loading the oscillator.
What do you think.