The number of free electrons moving through the cross-sectional area of the wire can be calculated using the formula:
Number of electrons = (current * time) / (charge of one electron)
Given that the current is 5 Amps and the velocity of the electrons is 7.5 x 10^-5 m/s, we can calculate the number of electrons per unit volume by dividing the current by the charge of one electron. This gives us 5 / (1.6 x 10^-19) = 3.125 x 10^19 electrons per second.
To find the number of electrons per unit volume, we multiply this value by the cross-sectional area of the wire, which is given as 0.7 cm^2 or 7 x 10^-5 m^2. This gives us (3.125 x 10^19) * (7 x 10^-5) = 2.1875 x 10^15 electrons per second per unit volume.
To convert this to the number of electrons per unit volume per unit time, we multiply by the time, which is 1 second. Therefore, the number of electrons per unit volume is 2.1875 x 10^15 electrons per unit volume.
The answer choice that matches this value is 2.7 x 10^27 electrons per unit volume, so it is the correct answer.