Technology, current at the time of US electrification, locked the US into 110, then 120 volt outlets. Europe's electrification came later, and proceeded in response to advanced technology. The US was too deep into the 110/120 volt infrastructure to upgrade. The US has remained in this situation ever since.
House voltage was first determined by Thomas Edison who set it for optimal performance of his equipment.
The United States distribution system actually provides a 240 volt residential service in the form of two 120 volt conductors and a neutral conductor. You can see this if you look inside your breaker panel. When a load is applied from either 120 volt conductor to the neutral (as is the case for typical receptacles, lights, and so forth) it is using 120 volts.
However, when a load is applied from one 120 volt conductor to the other, without using the neutral, the voltage being used is the sum of both 120 volt conductors (240 volts). This is the case for many water heaters, air conditioners, electric furnaces, clothes dryers, and so forth.
So equipment that is connected to strictly 240 volts is connected with only a two wire cable plus a safety ground wire. (For example 240 volt base board heaters use this.) The only time a cable with three wires plus safety ground is used is if 120/240 volts is needed in the equipment. (For example kitchen ranges or washing machines which have time clocks or programmers that require only a 120 volt feed.)
For systems outside the US, receptacles are 240 volts. Lower voltages tend to be safer, which is why in the US, you are receiving 240 volts at the home box and 120 at receptacles, instead of the thousands of volts generated by the power plant.
Power is transmitted over High Voltage cables - usually above 10K Volts. The power is then stepped down before it reaches consumers. Outlet power in the US is 120 volts, increased from 110 volts sometime around 1950.
The US system theoretically could be made as good or better than the European system with no infrastructure change, except appliances and consumer structuresthemselves (collectively costing home owners billions). US houses get 240 volts at the panel. If wall outlets all were fed with 240V you'd have the lower current and higher power advantage of the European system and it would be safer too, since each "hot" would still be only 120V from ground (not 240V) which keeps the reduced shock hazard advantage. Of course it is still possible to touch the two hots.
The origin of the 120 volt standard dates back to the feud between George Westinghouse and Thomas Edison. The first public electricity utilities were set up by Edison, whose concept was that there would be a power station (Coal fired) at the end of every street, supplying low voltage DC. Westinghouse came up with the idea of using AC, which can be transmitted over long distances from a small number of giant power stations. Edison worked to get the concept banned to protect his system by claiming that it would lead to the use of dangerously high voltages.
The result of this public debate was that the US opted for the low voltage, but using AC as Westinghouse recommended.
120v and 240v cords usually have different end configurations and will not plug into the different recepticles. However, if you changed the plug end, and the cord has the proper size rating, then yes, you could use the same cord. But, it also depends on the cord too. Most 120v cords only have three wires in them. One "hot one "neutral" and one "ground" wire. A 240v cord would have FOUR wires, two "hot" wires, one neutral wire, and one ground wire. Therefore, if you changed the voltage from 120v to 240 using a 3 wire cord, you'd not have a ground wire and that could be VERY dangerous. Note that occasionally a 240v device (e.g. some motors) will only need three wires (red,black,green, no neutral) and can be wired with a 120v cord if the cord is rated for 240v.
It depends on what voltage outputs you have on the generator. Some generators have 120V only. Some have a combination of 120V and 240V. Watts = Amps x volts. If the generator has only 120V output then you can pull, Watts/volts = 16.6 amps from the machine. If you have 240V capacity then you can pull, Watts/volts = 8.3 amps from the machine. To put it into perspective a toaster draws about 1500 watts. Check your appliances and check out what they draw. Appliances are usually rated either in amps or watts. My personal generator is 6000 watts and I can carry part of the house load on it.
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