But a Variac seems safer as you can control the voltage you're working with.
As in : "hey!!! I set it to 12V !!! I'm safe !!!!
Well, you are still directly connected to mains.
Any wiring problem somewhere such as:
> wrongly wired outlet or extension
> losing neutral connection (wiring problems, bad switch somewhere, you name it) and now you are "at 12V" ... superimposed with 120 or 230V .
while none of these problems is a problem if the transformer is a real insulated windings one.
To put in perspective: using a Variac is technically not more dangerous than straight working with mains, but is psychologically dangerous, you feel safe ... which may be not true.
Just as a trailer, I'm posting this method as used to find proper primary phase in a 2x110V primary transformer, in this case in an old Brazilian Giannini amp, their version of blackface Fender ... obviously still very popular today
I'll draw a new one for your power and output transformers, but the basic idea is the same: you can apply full line voltage (for safety through a limiting bulb) to a unknown PT primary ... and also to an OT primary
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