It's really hard to deal with it in pure theory.
Let's try a practical example.
Let's suppose I've built an off-grid house with a perfectly functional home-power system. Batteries, most lighting and auxiliary loads are DC, inverter runs a few things as needed. Battery voltage is 12 volts.
500 metres away, I have a 480 VA (basically 480 watt) windmill, whose furling makes it run at basically one speed. It isn't hard to wind it so you get 60-ish Hz out of it, single-phase. I'm stuck with the location because that's where the nape of the hill is. How do I wind the generator? What voltage?
My system voltage is 12 volts. So let's just wind the generator for 12V, giving 40 amps. Now, I need to get my 12V @ 40A from the windmill to the house 500 metres. What wire will I use????
The minimum Code allowed wire for 40A is 8 AWG (8.37mm2). That stuff is 2.061 milliohms per metre, so my 1000m round trip is 2.06 ohms. E=IR voltage drop is 82.4 - well that doesn't work!
Let's go up a wire size to 6 AWG (13.3 mm2). 1.3mohm/m, or 1.3 ohms at 1000m, or 52 volt - No, that won't work either.
Let's go to the biggest - 0000 or 4/0 AWG (107 mm2). That is 0.161 mohm/m, or 0.161 ohms for our 1000m run. 6.4 volt or 53% voltage drop, *wow, we are losing half of it, and we are paying $10/metre for the wire (actually for 300kcmil aluminum at $1.59/ft; we wouldn't use copper at this size).
Let's go for the biggest wire made. 2500 kcmil AAC "Lupine" the size of your wrist, at $18/metre each way. 0.023 ohms/km. So 0.91 volt or 7.6% voltage drop (finally! A reasonable number!) but that's still considered not a good number in practice.
well, this ain't good.
But look. This XHHW wire we're using actually says "600V" on it. How about if we bump the voltage and step it down at the house? 600V transformers are weirdobtanium, so let's try 480V since it's common. 480 VA, at 480V, happens at 1 amp. Now let's go back and hit that voltage drop calculator.
14 AWG copper wire (2.08 mm2) @$0.23/metre is the smallest THWN/XHHW wire available. Let's try it. Resistance is 8.282 milliohms per metre or 8.282 ohms for us. Horrible! Oh snap, we're in trouble. This is not working out, but let's press on just for academic sake to see how bad it is. Let's see, 8.282 ohms x 1A = 8.282 volt or 1.7% voltage drop. Wait.... that's perfectly acceptable, why did that work???
But that seems weird, like something went wrong there. Let's try it one more time with the smallest available aluminum wire, 6 AWG.
6 AWG aluminum (17.16 mm2) @$0.55/metre. Resistance is 2.16 milliohms/metre or 2.16 ohms (uh oh!) for our run. Giving 2.16 volt or 0.45% voltage drop. That really, really works.
All we did was change voltage from 12 to 480.
Ohm's Law, meet Watt's Law.
Here's the thing. Ohm's Law is
E = I R
Voltage (drop) = Current x Resistance
So voltage drop is proportional to current. Above, we're flowing 1 amp instead of 40 amps, so voltage drop is obviously 1/40 as much. But there's more.
Watt's Law says
P = E I
Power = Voltage x Current
Remember, in our application, power was constant: 480 W / VA. When we raised the voltage, this caused a proportionate reduction in current for the same power. We dropped current by a factor of 40.
So back to Ohm's Law, voltage drop (in absolute volts) fell by a factor of 40. However another thing was happening. Voltage increased by a factor of 40. That means that the bite that voltage drop was taking also shrunk by a factor of 40. Relative voltage drop compared to system voltage, dropped by 40 squared.
Ka-zinga! You can see the power of this increase in voltage (for a given static power requirement).
Try it again in a very practical, typical application.
1500 feet away, you want to power a set of driveway post lights. They draw 240 watts. You can power them either with 120V or 240V (the lights will happily handle either). 3.5% voltage drop is acceptable.
Sidle up to your friendly neighborhood voltage drop calculator and see what makes sense. You'll also be pricing the options here selecting /2 UF-B w/safety ground.
- Run 120V. Current draw is 2 amps.
- Run 240V. Current draw is 1 amp.
Which would you rather pay for?