Why do different countries use different mains voltage?

Just so you know, in America we have both 120 volts and 240 volts delivered to our homes. Then we can run circuits for whichever voltage we want. Usually for high powered appliances 240 volts is used and 120 volts for the usual things, like lighting, outlets, etc.

The reason one voltage is exactly half of the other voltage is because the 240 volts is center tapped at the transformer's secondary winding. It would be like if you have two five volt batteries connected together in a string fashion (in series like in a flashlight) so that you have 10 volts now. But you also can get 5 volts by connecting to the in between point where the two batteries connect to each other. It's called a split phase system and it has some advantages.

I'd rather have the 120 volt domestic power that I have. Why? For safety.

Higher voltage is cheaper but more dangerous. In North America, the residential standard is 120/240V single phase, so high power appliances operate at 240VAC while most outlets are 120VAC. Utility companies typically achieve 1% accuracy (119 -121). Wiring standards in USA and Canada are very thorough and quite safe. The 2:1 ratio between countries allows two winding transformers to be wired either way, series or parallel, but as much as 25% tolerance is required in equipment for standards acceptance.

America and other countries with American influence run 110V.

Virtually all the rest of the countries run 220 to 240V.

Pretty ridiculous situation, I reckon. It's rather like America using imperial and some strictly American imperial units (like pint and gallon), while the majority of the world work with the much simpler metric units.

For the same reason we don't all drive on the same side of the street. People just couldn't agree on what voltage is best. Doubling the voltage allows half the size wire to deliver the same watts, but is more dangerous if it leaks.

Watts is the measure of power needed, it's kind of like volts is the speed, amps is number of lanes, watts is the total cars. You can speed up the cars, then you need less lanes. You could cook something faster with 240v if you design it with the same resistance, by they typically design it to have higher resistance so is uses the same number of watts.

Voltage is a measure of electrical potential, or in other words, the amount of energy that a unit of charge can do moving from one point to another. You can also represent it as power per unit of current. Since it's power per unit of current, it does NOT mean that a 240 Volt vacuum has twice the power as a 120 Volt vacuum. So, if you have twice the voltage but half the current, you will have the same amount of power available.

But, plugging a device rated for 120 Volts AC into a 240 Volt system when it is NOT designed to do so will result in bad things happening. It's made to use carry a certain current at a certain voltage. More specifically, it's made to allow a certain amount of current through at a certain voltage. Because of the relationship between voltage, current, and resistance in a circuit, if you double the voltage without also doubling the resistance of the circuit, you double the current through the circuit as well. Some quick equations to consider:

(Eq. 1) V = IxR (Voltage (V) = Current (I) x Resistance (R))

(Eq. 2) W = VxI (Power (W) = Voltage x Current)

Since the current in the (Eq. 1) is the same as the current in (Eq. 2), we can take (1) and substitute it into (2) to get:

W = V x V / R or W = V^2 / R

So now what happens when you double the voltage? You quadruple the amount of power lost across the circuit. But the circuit is only designed to do a certain amount of work, which means that the remaining power turns into this thing called "heat"... and that's where the bad things start happening.

double the voltage means half the current for the same amount of power, so you can use smaller gauge wiring. Also, in most countries the decision of which voltage to usepay was made around 100 years ago, more or less.

Higher voltages are more efficient in getting power through the wires. It doesn't make appliances run any faster, because they are designed to run at a certain optimal speed. Also, they are designed to be operated with a certain mains voltage.

Higher voltages might be more efficient, but they are also more dangerous in terms of starting house fires and electrocuting people.

Edison picked 100 volts DC to the house as that was a compromise between higher voltage requiring thinner wire for the bulbs, which was difficult to make, and lower requiring thicker power cables. Later he changed to 120 to allow for drops in the cables.

When AC won out over DC, they decided to stay with 120 volts for compatibility reasons, the same bulbs would work.

When Europe started to electrify, they wanted to use a different voltage so they could develop their own manufacturing facilities and not just buy US equipment. They picked twice 120 or 240 volts, twice the US, for convenience in designing the equipment and in conversion hardware.

Actually the 120 was closer to 117-118 volts, which made the european standard closer to 230 volts.

The voltages are a compromise. Higher voltage means thinner wires can be used, but the dangers of shock and fire are higher.

Voltage has little to do with power in an appliance, the appliance can be designed to work with any voltage from 12 volts to 480 volts. Your list of what is to be gained by doubling the voltage is totally bogus. All that is to be gained is less copper in the wires inside the walls.