Electrical devices use power, and their relation is P = U * I, where P is the power delivered, U is the voltage, and I is the current. Cables have resistance (not much, but it's non-zero at room temperatures) as U = I * R. U is the voltage that you loose, I is agay the current, and R is the resistance of the cable. It's constant, and decreases with diameter of the cable.
Power loss is proportional to the square of the current (P = I^2 * R -- Ohm's law, arrived at empirically). That's the key to AC superiority for a commercial electrical power distribution grid. The result was arrived at through analysis.
Sorry, I know this is a very old comment but as an electronic engineer I need to respond to this.
P=I^2*R is most definitely NOT the key to AC superiority. P=I^2*R applies to both AC and DC. AC was chosen because of how simple it is to transform from/to different voltage levels. DC would have been more efficient as far as power loss goes, but in order to transform DC from one voltage to another one must use a switching transformer (it basically converts DC to AC, transforms it, then converts AC back to DC) and those cost a lot more than an AC transformer, so AC it was.
The reason why AC is less efficient is firstly due to reactive losses. Power lines are basically gigantic antennae. If you are oscillating a 10 kilometre long power cable at 50 Hz with 300kV, some of that energy is bound to induce current in surrounding objects and also emit electromagnetic waves. Another AC related loss is the skin effect, which causes current to flow more densely on the outside of the cable and less densely in the centre, increasing the effective resistance of the cable and thus increasing power loss. DC does not suffer from this phenomenon.
Needless to say, another issue with an AC power grid is how every generator needs to be synchronized properly. You can't have one power plant provide its power with a 180° phase shift - that would short circuit the entire grid. A DC power grid would not suffer from this either.
And lastly, it is important to note that AC-AC transformers are inefficient. Typically they are in the range 70%-80% efficient, whereas DC-DC transformers these days are typically over 88%, some even close to 98%.
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