#6 wire is good for 65 Amps as long as it is type THHN.
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Yes, there is a difference between single phase and three phase circuits.
single phase variac can give 0-270 voltage in ac forms. So it is used to know the voltage in any circuit.
Sure. In a two-wire circuit, both wires carry equal currents.
A 3 phase system needs only to use 3 or 4 conductors, as against 6 conductors if it were 3, single phase conductors The amount of copper used in a 3 phase is much less than what would be needed in a single phase system carrying the same current, this reduction in copper allows for weight reduction and cost savings. The power losses in a 3 phase system are much less than in a single phase system.
In a pure resistive circuit the voltage and current are in phase. In an inductive circuit they are fro zero to 180 degrees out of phase. If they are in phase the Power Factor is 1 and 180 degrees the PF is zero. The exact amount of the phase difference depends on the specific circuit.