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Question:

Homemade transformer overheating!?

I have a homemade transformer that steps down 120 VAC (outlet) to 42 VAC. But no matter the resistance I place on the secondary, the primary always overheats!

Answer:

The primary is either too small or not enough turns.
Remove any load ( resistor ) from secondary winding first. Plug in 120V power. If you feel it warm hot within 10 minutes, That means either not enough turns per volt ( wrong calculation ) or winding is partially shorted in either two windings.
It sounds like the design of the transformer is wrong, or perhaps the windings are loose. Use thicker wire for the primary to decrease the resistance
Any transformer has to have enough inductance to limit the idle current to a small value when the secondary is not loaded. How much inductance does your transformer primary have? The idle current should not be more than a few % of the max current. If you really have too little inductance (not enough turns), the core will saturate and loose impedance causing a huge current. My guess is that you used too few turns (both primary and secondary) and your idle current is way too high. Ironically that means that you need to use a smaller wire guage so that you can fit several times as many turns.

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