500 MCM (thousand circular mils) is equivalent to approximately 3/0 AWG (3 aught) in the American Wire Gauge (AWG) system. MCM is often used for larger conductors, particularly in industrial applications, while AWG is more common for smaller wires. The exact conversion may vary slightly depending on the specific context or wire type, but 3/0 AWG is the standard equivalent for 500 MCM.
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AWG 10.
10 AWG can be solid. 8 AWG and larger should be stranded. 2008 NEC 310.3 2011 NEC 310.106(C)
AWG # 10
6 AWG.
Normally it is a 20 amp using AWG 12/2 gauge wire. But it really depends on what size wire is on that circuit. If it is white AWG 14 gauge then use a 15 amp breaker. If it is yellow AWG 12 gauge then use a 20 amp breaker.