NEC 310.16 conductor ampacities
NEC 240.4(D)
For residential installations the smallest wire to be used is 14 AWG (15 amps rating)
and for commercial installations the smallest wire to be used is 12 AWG (20 amp rating)
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Yes, a #10 wire will carry 30 amps for 30 feet. If the load is rated as continuous then the wire will have to be derated to 80% capacity which will leave you with 24 workable amps. If the load demands currents higher that 24 amps then you will have to go to the next wire size up which is a #8 which is rated at 45 amps.
AWG 10.
# 4 copper wire short distance.
A 3/0 aluminum conductor will limit the voltage drop to 3% or less when supplying 150 amps for 150 feet on a 240 volt system. This size will allow the conductor to be loaded to 120 amps. 150 x 80% = 120 Conductors are only allowed to be loaded to 80% or their rated capacity. If you need the full 150 amps then you would need to use a wire with a rating of 190 amps. 190 x 80% = 152 amps A 4/0 aluminum conductor will limit the voltage drop to 3% or less when supplying 190 amps for 150 feet on a 240 volt system.
The V stands for volts and A is amps. If for example you have a 12kVA device and are running off a voltage of 120 volts then Amps = 12000/120 = 100. You then use the calculated amps in a wire size table to get the correct size.