Ohms law is simple, voltage is current times resistance, then power is current times voltage, P=IE
Transmitting power over distance is where the higher voltage makes sense.
End load in POWER or WATTS is same.
The resistance of the wires between end points is same.
Since power is current times voltage, one could estimate that for any given load at some voltage the current would be some value.
Given voltage is current times resistance. That current traveling in the wire will have some voltage drop based on the resistance of the wire.
Most transmission lines are ac as transformers easily bost/reduce the voltage, we will assume transformers as no loss for power, they all use some, but for this discussion, it does not matter.
So far, we have not used any actual numbers as this is just theroy.
The load at one end of the transmission line will draw current through the line causing a voltage drop across the line due to the current required to get the needed load in watts.
Now add a transformer to each end of the transmission line that is 1000 to 1 ratio.
The load remains the same. But the current through the line is now only 1/1000 of what it was before.
The resistance is still the same, so the voltage drop across the wire is less.
The transformer can also have different ratio at one end to compensate for the voltage loss of the wire.
Your wires will be cooler at 240 vac.
Motor will be same as there are 2 windings, in series for 240, in parallel for 120.
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