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The Related Link shows a transformer inside a metal cabinet, supplied with 120VAC protected by a fuse and the standard neutral connection back to the supply. There is a ground connection from the supply to ground, but there is no ground connection shown for the metal cabinet.

The question asks, if the (fused) hot side of the transformer shorts to the metal cabinet, will the fuse blow?

The answer depends on whether or not the metal cabinet is grounded.

If it is not grounded, as implied in the diagram, then the fuse will not blow, because there is no circuit formed to do so. Additionally, AND MORE CRITICALLY, this would energize the metal cabinet, creating an electrocution hazard.

However, it must be noted that per the NEC (US) and most probably any other country's electrical code, such a metal cabinet MUST be grounded.

IF, AND ONLY IF, the metal cabinet is grounded, then the fuse will blow, due to the additional fact that neutral and ground are connected together at the distribution panel (again, by code), and again, at the service entrance, and this will form a high current circuit sufficient to blow the fuse and prevent an electrocution hazard.

FYI - If I encountered such an ungrounded condition in a metal cabinet, I would do everything in my power to cause the installing electrician to lose his or her license. Additionally, if this caused an electrocution (whether fatal or not) I would sue said electrician for everything they were worth, and I would probably win, even though that would not bring back the person that died. This type of malfeasance should not and cannot be tolerated.

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Q: Will the fuse blow as shown in the link in this equipment?
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