| Thanks Charles for clarifying my formula usage. | I can accept that formula, but my brain wants to know why. I guess what I'm | looking for is an analogy or something to help me visualize. A lot of my | learning recently has been through analogies, because I can't see EM fields | yet and I tend to be a visual learner. I also don't like the old fashioned | response of "because I said so." Just because a formula says it, I still | want to know why. :-)
Suppose I have a 20 ohm resistor connected to 240 volts. That will draw a current of 12 amps and dissipate 2880 watts of power in the form of heat.
Upstream from me is a transformer that has a 240 volt secondary and a
7200 volt primary. That transformer will present my 20 ohm load to the primary as an 18000 ohm load thus drawing 0.4 amps at 7200 volts. The power is still the same.
Note that although the transformer ratio is 30:1, the impedance ratio is 900:1.
Adding 1 ohm of wire to a circuit with a 20 ohm load is going to do two things. It will reduce the current somewhat to 11.4285714 amps. And it will divide the voltage drop of 240 volts between the 20 ohm load and the
1 ohm wire. If you visualize the load as 20 resistors of 1 ohm each, plus the added 1 ohm for the wire, you can see how the 240 volts gets split up 20 ways to the load (228.5714285 volts for the load and the remaining 11.4285714 volts for the wire).
To get the same effective drop in power on the 7200 distribution line, which is operating into a load of 18000 ohms (not 20 ohms), that would involve 900 ohms being added. For the same size wire, that would mean the circuit could be run 900 times the distance.
According to table 8 of NEC chapter 9, 1000 feet of AWG 4/0 aluminum wire has 1/10 ohm. That means I can run almost a mile of 2 conductors of wire to power that heater within an acceptable 5% voltage drop. But for 900 ohms of added wire resistance (to the 18,000 ohm load), that would be 852 miles for the same ratio of voltage drop.
There are a LOT of other factors involved in engineering power distribution. But the above, I hope, gives a clearer picture of why a higher voltage is so much better for longer distances. The key point you may have missed was that the impedance at the higher voltage is increased in proportion to the square of the voltage increase. So as the voltage goes up 30 times, the impedance goes up 30^2 times.
Of course in reality, electrical distribution does deal with much more power than my 2880 watt heater. But they use even higher voltages and larger wires over such greater distances. And they have the option to boost generator voltage or change transformer taps to tweak the voltage to compensate for varying losses due to varying loads.
If you were expecting the 7200 volts to see 20 ohms directly, then you would be seeing 360 amps and 2.592 million watts. All the magic smoke would be released in a rather spectacular boom as the resistor vaporizes and the current flows as a terrific arc. Don't do this at home ... or anywhere else.