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The whole safety of your electrical installation relies on neutral and earth being separate
Yes an no - Our system relies on earth being the fault path and that is why neutral is at the same potential (theoretically). When a class 1 appliance's case goes live, traditionally a large fault current would flow to earth and blow a fuse/mcb and therefore protect you and me.
You are correct though in terms of an RCD and the imbalance in current flow when a N-E fault is in effect when something it turned on, I was incorrectly over simplifying it.
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Your example literally describes earth and neutral being separate. Having the same potential doesn’t mean they’re the same thing. One returns current in normal use, the other in fault condition.
If they weren’t separated, it would be a TNC system (terra neutral combined) which is highly uncommon.
Either way. I’m an electrician, and I have no idea what the point your making actually is, or why you think neutral and earth are the same.
They're often tied to each other at the incoming supply. You just get two cables coming in - a live and a neutral. But critically they're separated before your meter. TNCS literally stands for terra neutral combined separated, IE your earth and neutral are combined in supply but separated into separate conductors for the consumer side. They aren't the same thing because of how they're used.
The whole safety of your electrical installation relies on neutral and earth being separate, lol. RCDs don't work otherwise.