Why was 120V chosen as the standard voltage of homes in the US and not some other voltage?

The voltage level that any AC (Alternating Current) power line must have depends on the distance that the line must travel. Power generation plants often use voltages in the hundreds of thousands, 115,000 to 165,000 volts to move power over long distances. For lines of up to 20 miles long around a city, 2400 volts works well to reduce the voltage loss in the wires. In the United States, the electricity utility powerlines going to residential streets and roads are operated from 2300 to 2400 volts. With a 2400 volt supply, it is very convenient and easy to design and build pole transformers that have a 10-to-1 step-down ratio, thus providing 240 volts to the houses. The transformers also have a center tap to provide 120 volts from each 240-volt leg to the center point. This center point tap also provides a convenient point for a grounding connection. The actual measured voltage in your house receptacle circuits will normally be 120 to 125 volts. All appliances are rated for the minimum operating voltage (110-115), thus there is much confusion about the actual level of the supply voltages.
Different voltage levels are used in different countries around the world. The reason to use higher voltage is that it is more economical. The current is less, so the wires can be smaller. On the other hand, the reason to use lower voltage in homes is safety: the lower the voltage, the safer it is.

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Well, in a way we do use 240. If you have 10 amps drawing on one leg of your 240/120 service, and 10 amps on the other leg, the I2R (Eye Squared Are is how that is pronounced) losses are one fourth what they would be if you had 20 amps on just the one leg. But I think that the Europeans use 480/240, so their I2R losses are 1/16th of our 120 volt losses (if you had the 20 amps on just one leg.)
Why not use 120?? We could use 220 or so like the Europeans only their alternating mains frequency (cycles per second) is 50Hz not 60Hz like ours. You could think 240 volts is too much in your house for simple stuff as you would get a worse beating/shock if you were working on stuff on your own. There are a whole ton of complicated other reasons having to do with transformers and transmission lines and the math involved. I recommend a book from Barnes and Nobles and a Hazelnut latte !!

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The original voltage was actually about 90 volts direct current (VDC) which was Edison's plan. Tesla proposed that the electrical grid be alternating current (AC) and competed with Edison for the first generating plant to be built in the State of New York at Niagara Falls. Edison proposed a DC system and Tesla an AC system. As history tells us Tesla won the competition and because of that we had the industrial revolution. Had Edison won we would still be in the dark ages because of the inefficiency of transmitting DC over long distances. As Edison was promoting the electrical light bulb around the country almost every town had to have its own generating station because DC would lose so much in the transmission that it became unusable after only several miles.
Tesla also had invented the poly phase alternating current generators that provided for the ability to generate the voltages necessary for long distance transmission. Tesla kept the voltage about the same as what Edison started but raised it to the 110 volts alternating current (VAC) because of the higher related voltages of 220 VAC and 440 VAC which were integral to the poly phase generators of higher efficiency.
All AC voltages distributed to homes actually come to the buildings at 440-480 VAC. Within the meter box at every home the 440-480 VAC is broken down to 220-240 VAC and then to 110-120 VAC for use in lighting, wall plugs, and small appliances. All major appliances like electric ranges, clothes dryer, air conditioning, water heaters use the 220 VAC.
There is a good discussion of this subject at http:/flyingmoose.org/truthfic/tesla.htm and good reading about the contributions of Tesla in "The Prodigal Genius: The Life of Nikola Tesla."

The standard voltage available in most parts of the country now varies from 110 VAC to 120 VAC+ volts usually around 117-118 VAC.
Correction
The last previous section has such great informational errors as to render the contributions worse than wrong. It conveys untruth and creates misconceptions about electricity and the process of distribution.
There is no 480 at residential meter enclosures.
Neither does the meter do anything more than record the consumption of power.
Period.
Correction
Common distribution voltage run up to 16000 volts. 12000 is very common but there is still a lot of activity adding on to legacy distribution grids at lower voltage. A 2400 volt primary is very low for a distribution transformer.
Correction
In actuality power transmission is not 20 miles and the voltage is more then 110kV. In fact interstate transmission is in the range of close to 500kV. At a substation it is reduced to 16kV for local area distribution. Transmission for the whole of the grid in the USA is all tied together . Why? For economy and reliability. For example in the Summer some states do not use air conditioning but in Las Vegas CA they do, so they actually buy the power from those northern states in the Summer because it is cost effective and ensures there can be less generation plants. Even then reserve spin power must be sustained for peak demands. Because power plants cannot produce almost instant acceleration to meet new demands, like car engines can do, in many cities and other peak demand areas, specialist "peakers" work to ensure that the the integrity of the grid is always maintained. 240 v is standard for the USA but only one phase is used and the transformer center tap is earthed to ground making it safer. The 60 cycles per second produced by power generation is not as stable as some people think: it sometimes has to vary throughout the day as loading changes but averages 60Hz over a complete day.
Addendum
120 V has an advantage over higher voltage such as the 230 V voltage that it is considered generally safer as it is less powerful. On the other hand, it costs more to transmit power to the end user using 120 V as copper lines must be thicker, hence lower voltages are generally used by wealthy countries.
Wrong again the transformer on a pole has en deed 240 v ac but only one phase is run to the houses the neutral or center tap is grounded.