The equations are as follows:
1) Power = V x I.
So, if at some moment in time a town requires 1 Million Watts to run it's TV sets and street lights, you can choose to supply it with 1,000,000 Volts at 1A, or 1V at 1,000,000Amps, or more usefully, some compromise like 250V at 4,000 amps.
2) The voltage drop across a resistor is I x R.
3) Combining (1) and (2) the power dissipated by a resister is I x (I x R)., or I squared R.
If you look upon the power line as a big resistor, then you can see from (3) that the power loss is proportional to the square of current. Yet, as in (1) you can freely choose either volts or amps, at no extra cost to the generator, allowing you to vastly reduce the power-loss just by tilting the voltage/current balance towards volts rather than amps.
I remember, as a youth, being quite impressed and excited by this method of, to my simple mind, apparently tricking the laws of nature. I got even more excited when as a student I learned that complex number theory could be used to explain what happens inside inductors and capacitors which, thus making a useless mathematical impossibility (square root of -1) suddenly very useful. Ah, these were the days. I wish I could get so easily enthused nowadays. I wish I could even remember what the heck complex numbers are
- 7LM