Depends on what it is powering. The longer the run the more voltage drop you get. For example if you run 200 feet of copper 10 wire you'll lose about 4 volts. There are voltage calculators you can use. The less volts you have the more amps the wire will have. Watts/volts=amps. 10 wire is rated for 30 amps. Do the calculation. You should not go past 80% of 30 amps (24 amps).
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To answer this question the amperage of the load must be stated along with the voltage of the circuit. Without these values, line voltage drop and hence the distance, can not be calculated.
This is a voltage drop question. To answer it, the load amperage must be stated. Without the amperage of the load the question can not be answered.
At that distance you will have a voltage drop of 81.25 volts if you use the recommended #6 wire on a 240 volt, 100 amp single phase circuit. Therefore I recommend you contact you electric utility and let them figure the voltage drop and the size wire required to safely run this distance. Using too small a wire can damage the electronics at the end of the run.
For that distance I would run AWG # 3 copper and install a sub-panel.
Yes.
# 4 copper wire short distance.
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.