I am running a wire 300+ feet. I'll need to place a transformer every 100 feet that would maintain voltage/current, therefore I wouldn't get any drop so that I can maintain 110vac 20 amp. Which transformer should I use?
Edit: I'm powering a shed.
You cannot afford to fall below 110V. Ok.
Supply at your house is supposed to be 120V so we have a little room to play with.
If you use 8 AWG cable, voltage drop will be limited to 8.29V on a full 20A load, giving 111.71V. That meets your criteria. If actual pulled amperage is less, voltage drop will be proportionately less, and voltage will be higher.
If that is not good enough, you can run thicker wire. Any bigger than #8 and you should be looking at aluminum wire, e.g. a #1 Al cable will create a 1.46V drop, giving 118.54V.
Now if you power the circuit off a 240V breaker, you can do your transmission at 240V and power a 240->120V transformer. A 5 KVA transformer will more than suffice, and is often available on Craigslist for as little as $100.
Nominally you assume 2:1 on the transformer, but you can jumper the transformer for slightly more or less if transmission voltage drop warrants it.
Anyway, since your feed voltage is 240V, you have half the voltage drop and 1/4 the power loss.
14 AWG wire will suffice. At a full 20A on the 120V side (10A at 240V), it will drop 16.08 volts off 240V (8.04V on 120), giving 111.96 volts at your plug.
You can use 2 transformers back to back to kick the transmission voltage up to 480V, 575V or even 600V, and voltage drop will be considerably less still. However, we can't use wire smaller than #14, and #14 wire is getting the job done as above. So this is a bad idea given the higher hazard in the higher voltage section.
Then install an "always online" type UPS at the shed. The online UPS always fabricates AC power through its onboard inverter, so it's always making it to the spec you paid for. The supply side of this online UPS will have an input tolerance; wire thick enough wires to satisfy that, and if at all possible, use 240V for thinner, cheaper wires.
Doesn't work. You can't hold voltage steady by selecting a single transformer tap, because voltage drop is proportional to actual load. Whatever tap you select, voltage will go up and down with load, you're only affecting the range bracket. You can get transformer-based equipment that will automatically "select-a-tap" as needed to keep voltage within spec, it will step up to the next tap as voltage sags etc. But this is not perfect, there will be some sawtoothing.
Adding transformers will not "stabilize" anything, I have no idea where you got that idea, but it's wrong. Sometimes people step up the voltage to a higher level (like 480V) and back down again for a long distance run so that the current is less, because less current results in less voltage drop since voltage drop is a function of I (current) Squared / R (resistance, in this case of the wire itself).
But you can ALSO just decrease the R by using larger gauge wire, which would cost you a LOT less than adding transformers. There are on-line Voltage Drop calculators that will give you the size of wire you need. According to one that I found, to have no more than a 3% VD on a full 20A load at 120V, you would use #4 Cu wire or #2 Al.