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> When the circuit is broken, it's current limited.

When the circuit is broken .. by definition, there isn't any current flowing!

You need a loop somehow from one of the terminals of the transformer through you to the other terminal in order to get a current flow.

(There might be some transient effect caused by the inductance of the system within one half-cycle, which may give you an arc as you smash the heater, but that can't continue and is unlikely to pass through you)



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