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The transformer in question is a step up transformer, which converts 240 VAC @ 3.75 Amps to about 2100 VAC @ 0.4-0.5 Amps. (50 Hz)

I want to test whether it works, it is salvaged anyways. If the secondary coil is shorted, would that cause any problems? I know that the impendance of the primary coil is enough to keep it from being shorted, since it's AC.

But what about the secondary coil, would it be damaged? Would it just output 0.4-0.5 Amps as it is designed in a short circuit, or would it spike (like in DC)?

(I've also heard that it is common to short the secondary, as leaving it open would be dangerous, I would like to know if the secondary would be damaged)

For lower voltage transformers, I've seen videos like this, however I'm not sure whether it would be wise to do that on a 2200 V transformer: https://youtu.be/mE_K7sG_wEQ (2:22)

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Depends upon magnitude of primary voltage. If you short circuit secondary and apply nominal voltage (240V) across primary, then at secondary side you will have 2100V and secondary current will only be limited by secondary impedance. That 0.4 or 0.5A you said sounds like rated current to me, in short circuited case, secondary current is going to probably much larger than this and you'd probably fry your transformer.

What you want to check? If you just want to check transformation ratio, just apply 240V at primary, with the secondary open-circuited, and measure secondary voltage. The current in transformer depends upon the load connected across secondary and you want to be sure that load doesn't draws more current than rated.

Short circuit test is often performed to find out copper losses, equivalent impedance and equivalent resistance. If you want to find efficiency then you may perform SC test, usual method is to short circuit one winding (preferably LV winding) via ammeter and applying low primary voltage (using variac) - just enough so that rated current flows.

Also, transformer secondaries are NEVER short circuited (with nominal voltage acroos their primaries) except in case of special transformers called "Current Transformers (CTs)". It is necessary that CT secondary is never left open. More discussion on CT is perhaps out of the scope of this question and CT will probably be described better in some other dedicated source.

But yeah, never short circuit your transformer with nominal applied voltage.

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    \$\begingroup\$ I just tested it with the secondary safely disconnected without any problems. Thanks for the advice. \$\endgroup\$ – imagentab Aug 14 '17 at 4:40

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