Most modern electrical appliances have three prong wiring. Years ago most had only two prong wiring. The third prong is a ground wire, which I assume is mainly a safety consideration. Is there any other reason for the third wire, say an improvement in efficiency?
Nope. Pretty much just safety. It provides a return path for current that isn’t you.
Safety, and equipment protection in some sensitive circuits which might build up static charge. Provides a reference ground for equipment which is interconnected, and requires the same reference potential. Mostly for safety.
Tris
the grounding prong is there for safety.
safety is also achieved in some cases with a polarized two prong plug and the device constructed in a manner that leaves no exposed metal parts that could be energized if the wiring in the device failed.
there are some electronic devices that to work well need to have some of the circuitry affected by grounded elements though that is where the device works at radio frequencies, this grounding could be done through connections other than the power cable.
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the third prong completes the happy face. 
In an AC system, you’ve got two wires, and if you don’t bother to ground either one then there really isn’t a significant difference between the two of them (you could call them both “hot” wires if you wanted to, I suppose). This is actually safer than grounding one of them, because you can touch either wire and ground and not get shocked. You only get shocked if you touch both wires.
You may be thinking if it is safer not to ground them, then why do we ground them? The answer to that is Mother Nature. If we don’t ground one of the wires, then Mother Nature will tend to randomly ground one wire or the other by letting tree branches come into contact with the wires and other similar methods. Now you’ve got a grounded system whether you like it or not. It is safer to have an intentionally grounded system than a randomly grounded system, so that’s why we do it that way. There are ungrounded systems in use though. They are called “isolated” systems because they are isolated from earth ground. If you ever happen to be in a hospital, look for the red outlets. Those are isolated. Hospitals go to great lengths to keep them isolated, including yearly inspections and testing of all of those circuits. it may be safer, but trying to keep a residential power system isolated like that would be a nightmare.
So now you’ve got a grounded wire (aka the “neutral”) and an ungrounded wire (aka the “hot”). If you touch neutral and earth ground (like a water pipe) then you are mostly safe. Touch the hot and earth ground and you get zapped.
So, what do you do if you have a great big electrical thing in some kind of metal box, like say a stove or a refrigerator? If you don’t connect the metal box to anything, then as it ages, the hot wire could come loose and touch the metal case. Now if you touch the metal case and something else, you get shocked. So, you don’t want to leave the metal case disconnected from everything. In the old days (two prong outlets), they used to connect the case to the neutral. This is safer, but if your neutral corrodes, you can develop a dangerous voltage on the metal case and you can get shocked.
To make it safer, they added a third “ground” connection which is just a safety ground. The safety grounds all connect to the neutrals back at the breaker box, and they are all connected to earth ground somewhere close to that as well. That may seem kinda stupid. If you are going to just connect the wires together, why bother having the third wire?
There are two reasons for having the separate ground. The first is that if you have current flowing through the neutral, then, since it is not a superconductor, it is going to develop a small voltage, so your neutral really isn’t at true earth ground potential out where your appliance is.
The second reason is that what happens if one wire breaks? In a two wire system, if the hot breaks then the thing doesn’t work, but if the neutral breaks, then the metal case can potentially become hot and shock you. In a three wire system, if the hot breaks, the thing stops working. If the neutral breaks, then the metal case is still earth grounded, and is still safe. If the earth ground breaks, then you’ve lost your safety, but it isn’t immediately dangerous unless something else breaks.
There are other failure modes too where having a three wire system is safer, depending on what breaks.
In the two prong days, people would often get ticked off and would file down the wider prong so they could more easily shove the plug in the outlet, since they wouldn’t have to make sure they had the plug the right way around. This could be dangerous if you had something with a metal case that was intended to be connected to the neutral. A three prong plug prevents people from doing this.
So the short answer is that overall using a three wire system is just a lot safer. It adds nothing at all to efficiency. Under normal conditions, the safety ground carries no current at all.
Well I suppose that could happen. But the *primary *reason is because the transformer hanging out on the pole does not have perfect isolation. If the secondary were allowed to float, it might float up to the primary voltage, which is around 7,000 V. That would not be good. So we purposefully reference the secondary to earth ground to prevent this from happening.
You mentioned that many appliances of yesteryear would connect the neutral to chassis ground. This is true. And a broken neutral happens more often than you think. If you had such an appliance, and plugged it into the wall, there is a 50% chance the hot prong will make contact before the neutral prong as you’re inserting it into the receptacle. Though this condition may only last a few milliseconds, it is long enough to shock someone (assuming they were grounded and were touching the chassis).
Besides being a safety ground, some devices require an independent ground in order to even operate:
- Some devices require an EMI shield to be connected to earth ground.
- Some fluorescent lamp fixtures rely on current in the ground wire in order to start. If you don’t connect the metal reflector to earth ground, the light will be unreliable.