Typically you don't want more than a 10% drop in voltage. If it were a 120 VAC circuit that would be a drop of 12 volts. At 20 Amps that is a resistance of .6 ohms. That is about 380 feet.
Allowing for a 10% drop in voltage would allow you to run 20 amps on 12 gauge copper to 151 feet.
Also, the NEC suggests, but does not require, that voltage drop be limited to 3% on branch circuits. In the field this is treated by most electricians as an absolute requirement, not a suggestion. This allows you to run a 20 amp load to only 45 feet on 12 gauge wire. Notice that voltage drop is calculated based on connected load, not the rating of the circuit. A 20 amp load would be connected to a 25 amp or 30 amp circuit, requiring larger wire and allowing for longer distance.
In a home a 30 amp circuit would most likely be 240v and would require #10 gauge conductors. Using these numbers to calculate a 3% voltage drop allows you to run this circuit 145 feet. At 120v on #10 gauge wire a 20 amp load can be run just over 72 feet.
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It depends on the application, but for Single-Phase dwelling service and feeders 3 AWG copper is good for 110 amps. That really equates to 100 amps since you can't get a 110 amp circuit breaker.
A 10 AWG wire is typically only rated for 30 amps, but conditions such as length of run, whether the wire is to be used in a "plenum", temperature and other factors may affect the type of wire that you must use for a specific application. If you have any questions, contact a qualified electrician or your local building inspector.
It depends on the load applied. With a load of 10 amps you would loose 5 volts at 100 feet. I would not run it over 50'. This is one of the reasons I never wire any home with AWG#14 wire even though you can use it in bedrooms. I prefer to use AWG #12.
10 AWG.
You will need AWG #3 if it is a short run.