If the frame of the appliance isn’t grounded, a bare wire can shock you.
Connecting the neutral to the frame will protect you from that, while introducing a different problem. If there is a break in the neutral cord or wall wiring, then the frame will also have high voltage and shock you.
With a neutral, and a separate ground, bonded to the frame, it will take two independent faults to shock you.
They are absolutely not connected to the same thing.
Neutral reconnects to the other end of the power source to create a circuit, you need a full circuit for any power to flow.
Ground connects to the ground, the purpose of the ground is to connect to the outside or other parts of the device that shouldn’t normally have current flowing through them, that way if a wire breaks and current does flow through it follows the ground wire to ground, as the path of least resistance, rather than flowing through the poor bugger holding the device
Electricity always wants to get back to its source. The “neutral” wire is how it gets there in normal operation. However, if something breaks and electrifies the casing of something metal, and you touch it while touching the actual ground, it *could* try to go through you. Which is bad. By providing an actual “ground” wire, you provide a quick, low resistance path back to that neutral line, which will almost certainly trip the breaker and/or GFCI.
As for why they are separate wires at the plug when they pretty much always get connected at the panel there are a few reasons. Primarily, if you just used the neutral as this safety line, the casing would always be part of the circuit, which presents a slight possibility of shocking you if it has a voltage relative to something else you touch. Other faults can make this very dangerous. You wouldn’t want to grab on to a wire sticking out of the neutral slot on a socket would you, even if theoretically safe?
The other reason is that it allows GFCIs to work (those outlets that you have to reset in your bathroom sometimes). They are able to detect if the amount of power going “out” through the hot wire is different than the amount coming “back” through the neutral wire. If it is different, this means power is going somewhere it isn’t supposed to be, usually through that ground wire, and it will trip, shutting off power. If the neutral was used as the safety, the GFCI would have no way to know.
There may be some other nuance to this, but I believe that’s the gist of it. I always had this same question so it took me a while to understand as well. Also, as I understand it, the grounding rod actually in the ground connected to your panel has more to do with lightning protection than anything to do with the “ground” on your plug. Though I believe it is still connected and can be something of a backup to that.
One last fun fact – any metal piping in your house is also probably wired to the “ground” in your panel to provide yet another relatively safe path back for any rogue electricity, again, hopefully just tripping the breaker for the source.
Edited for clarity.
Bathroom sinks have a drain and a overflow drain, even though they both are connected to the same pipe. You don’t intentionally use overflow drain, but it’s better than having water find its own path.
If anything happens to the neutral wire, the ground wire can still carry current instead of having electricity find its own path.
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