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.
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The wire size depends on how much current it will conduct.
You listed no gauge wire. This is the required breakers.14 gauge - 15 amp12 gauge - 20 amp10 gauge - 30 amp8 gauge - 40 amp
#6 wire is good for 65 Amps as long as it is type THHN.
A rather thin copper or aluminum wire.
Yes, # 4 AWG copper and 100 amps is the max.