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Grounding boxes in home wiring are totally safe for you?

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msuffidy:
I always assumed grounded metal boxes would save you because all the electrons would go down the wire. So I was watching a video about what is ground and it eventually got into the topic of using grounding boxes as safety for persons. It seems to me that it relies on the idea that a wire is supposed to have some degree of resistance as part of the proof. In the video, it sort of suggests the wire segment before the box is a resistor, thus the potential at the box is lower than mains. I am a bit worried about how treating the wire as a resistor has such drastic implications. I am a bit confused about how it actually works in reality, but suspect in that case the potential at the box is in fact lower than the mains potential. I drew this diagram trying to understand it without the idea the wire had resistance and came up with treating the box path as a parallel near 0 ohms resistor. Here is the video:

msuffidy:

1) The length of the wire from the station is much higher than the grounding side thus the potential is lower at the box
2) The amperage of the near zero resistance ground path may reach the amperage limits of the supply wire and deplete the usually accepted 2nd (human) path supply.
3) You may be briefly shocked but the simultaneous ground path will ensure the trip of the circuit breaker.

Actually, theoretically in this scenario this would only happen if you were touching the box when something live hit the inside of the box, or a breaker failed to trip. In the case of the stuck breaker you would probably also be worried about an electrical fire in the wall.

evb149:
https://en.wikipedia.org/wiki/Ground_(electricity)

There's a lot of "history" involved with the design of AC electric mains wiring design and electrical codes for buildings.

A "ground" doesn't have to be perfect, it just has to be a "good enough" to be considered adequate for representing the local
environment potential of the nearby earth & ground connected wiring & plumbing & structural elements in a particular location.

Protective ground functions roughly like this.  A conduit or electrical box may need to be grounded which is to say it is connected to the local ground potential through a dedicated earthing / grounding wire and to the ground such as plumbing, via a grounding rod, etc.
The connection of the protectively grounded item (chassis, outlet box, conduit, ...) typically has to be good enough that it can pass a fault
current that is sufficiently large so that the fuse / circuit breaker feeding the live conductor which the ground fault current is coming from will be tripped.  So if you have a 20A rated circuit / live conductor, you generally expect to have a 20A rated grounding conductor and path so that if the live conductor shorts to the protectively grounded chassis / box etc. that the live circuit will pass >= 20A while the grounded elements (chassis etc.) remain at low voltage relative to the local ground potential (where the protectively grounded item is actually indirectly connected) and there will be no fire in the wiring until the over current protection breaker / fuse trips and protects the circuit from over current related heating etc.

A plumbing analogy would be something like that a tub having a water inlet pipe and a water outlet drain pipe can be used to receive water by opening the inlet valve and permitting water to flow into the tub.  But the drain pipe has the same flow capacity or more as the inlet pipe so simply leaving the water valve open can't cause the level of water in the tub to rise much / quickly since water is draining out as fast as it comes in.  So as long as the ground circuit is "solidly" grounded by conductors of comparable or better ampacity / conductance level as the source of the fault current the grounded object's potential will be safe enough for the short time it will take for the large fault current to trip a fuse / breaker.

Yes you could say well for X time the "grounded object"'s potential rises by ohm's law above the earth ground potential to some extent but they consider the likely fault scenarios and risks and specify what they consider to be "good enough" earth bonding / grounding practices and wire gauges and ampacities and so on to say that it is protective enough in the case of the anticipated fault cases.

Different practices apply depending on the relevant electrical codes, the magnitude of the mains voltage and current involved, whether it is medical, residential, industrial, etc. etc. so there will be varying worst case grounded item potentials during faults.

In some cases one has GFCI type circuits which have an even more sensitive ground leakage detector and circuit breaker that will trip in a few milliseconds after even a few milliamps of ground fault current flow.

Berni:

Yes earth wires have a resistance to them like any other wire, so an earthed metal housing will still rise in voltage if live shorts to it. But due to the low resistances of wires and high voltages involved this will send a massive current down the earth wire(100 to 1000A). So within the next milliseconds the GFCI will trip and the fuse for that live wire will trip. This stops the current and the metal housing is at earth potential again.

If you ware holding the metal box and something else (like a metal pipe) when such a hard short happened you would likely get a brief jolt, but you would not be dead.

But if you did that with no earth connection to the box you would effectively holding a box at 110/220V and the current would flow trough your body until you let go of it. Hopefully you have a GFCI to trip and save you there and you might end up dead

msuffidy:
I have been shocked by this and that over the years, but not at the ozzy 240. Just our 120 in Canada. I finished a basement once and did some stuff with the breakers still on without turning them off and either got straight up shocked or like rotated a wall light and it made a big spark. Around 2003 when I was renting, I got a shock when touching some appliances and found out one ot the outlets had something backwards, neutral and hot and fixed it myself. I am going to try to be more careful in the future.