Final answer:
To find the time it takes for electrons to travel through a wire, calculate the drift velocity and use it to calculate the time using the given formulas.
Step-by-step explanation:
The time it takes for the electrons to travel through a wire can be calculated using the formula: time = length / velocity. In this case, we need to calculate the velocity of the electrons in the wire.
The velocity can be calculated using the formula: velocity = drift velocity x current density. The drift velocity can be calculated using the formula: drift velocity = current / (n x A x e), where n is the number of free electrons per cubic meter, A is the cross-sectional area of the wire, and e is the fundamental charge of an electron.
Using the given values for the 12-gauge copper wire, we can calculate the drift velocity and then use it to calculate the time it takes for the electrons to travel through the wire. Repeat the process for the 6-gauge copper wire using its given values.