A #6 copper conductor with an insulation factor of 75 or 90 degrees C both have an amp rating of 65 amps. If the #6 conductor is connected to a breaker having a 90 degree C rating then the conductor can carry an amperage of 75 amps
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10 amps
ref: http://www.okonite.com/engineering/nec-ampacity-tables.html generally see the latest NEC (National Electrical Code) standard but from the tables with assumed temperatures, the rating for 14ga copper is 15 amps (120V).
If you mean 2/0 copper wire it is rated 175 amps. # 2 wire is 115 amps. If you are referring to 2.0 metric it is rated 15 amps.
# 4 copper wire short distance.
Sorry, there is no such wire size as "30 gauge" in the AWG (American Wire Gauge) system. For the ampacity rating of all standard conductor sizes, go to Table 310-16 of the National Electric Code. If you mean what wire size will carry 30 amps then a #10 copper wire insulation rating of 90 degree C is rated at 30 amps.