Fundamentals of Ohm's Law

You learned this stuff in school. Maybe you use it every day, maybe you forgot it. Either way, I'll keep it very simple.

You've got VOLTAGE. Using the favored "hydraulic analogy" - it's easier to see water than electrons - this corresponds to pressure in a pipe. If you fill a pipe five feet high with water and put your finger at the bottom to stop it from flowing out, you'll feel more pressure than you would if it were only filled up to one foot.

You've got CURRENT. Current corresponds to how many electrons, or how much water, flows past a given point in a system in a certain lenghth of time. If you've got a full bathtub and (somehow) two drains, opening one drain will allow it to empty in a certain period. If you open both drains, it will empty in half the time. Likewise, let's say you have a big battery and you connect a tiny wire to the terminal, only so much current will flow through that wire before it gets hot and melts. Connect a second identical wire and the same amount of current will flow in both, or twice as much total.

RESISTANCE you've also got, but you don't want it. It's why small wires can only carry small currents, and small pipes don't let a lot of water flow quickly through them. All wires (except superconductors) have resistance. For a particular conductor (e.g., copper, silver, aluminum) each will have more and less desirable characteristics. Copper is a better conductor than aluminum, and silver is better than both. On the other hand, silver costs more than either, and aluminum, although the worst conductor of the lot, is less expensive than copper, and also carries more current per pound, even though it carries less current per given wire cross sectional area. Interestingly, the large wires that connect the Prius battery in the rear of the car to what they call the "engine room" are made of aluminum, since weight and possibly cost are more critical than size in this application.

The mathematical basis of Ohm's law can be found by a quick web search, I won't bother with it here. The important thing to remember is what's proportional to what, even if you don't feel like calculating anything.

If you have a higher resistance, it requires more voltage to get a given current through that resistance. Practically, that means that if you're trying to get a lot of current into or out of something, you need to use thick (or multiple) wires to keep the resistance low.

If you have a current going through a resistance, the voltage across that resistance increases proportionally to the amount of current being forced through it, Using a pipe analogy, you have to apply more pressure, and just as there will be a pressure drop across the pipe, there will be a voltage drop across the wire.

Finally, if you have a voltage drop across a wire, you are losing efficiency, since a voltage across a resistance corresponds to power, and the power in such cases is wasted. (An extreme case of this is the common light bulb. You are putting 115V across a resistance, the lamp filament, which gets so hot that it glows white hot and illuminates the room.) This power is measured, just like the light bulb, in watts. If they're used to heat wires, they can't be put to other uses.

Just as you use thicker extension cords for long runs or high power, you need to use heavy wire to connect the high current sources in the Prius to the inverter. Something to keep in mind if you undertake any of this.

Ohm's Law for Fundamentalists

Voltage is Good.
Current is Good.
Resistance is Evil.