The diameter of a 12-gauge copper wire is 0.081 in.The maximum safe current it can carry (in order to prevent fire danger in building construction)is 20 A.At this current,what is the drift velocity of the electrons? The number of electron carriers in 1.0 cm³ of copper is 8.5 × 10²² and e = 1.60 × 10^-19 C. A)0.044 mm/s B)0.44 mm/s C)0.44 cm/s D)0.44 m/s E)4.4 cm/s

Question

Quizplus · Accepted Answer

The cross-sectional area of the wire can be found using the formula for the area of a circle, A = πr^2, where r is half of the diameter. Plugging in the given diameter, we get:
A = π(0.081/2)^2 = 0.00514 cm^2

Using the current and the area, we can find the current density using the formula J = I/A:
J = 20 A/0.00514 cm^2 = 3895 A/cm^2

The current density is related to the drift velocity of the electrons by the formula J = nev_d, where n is the number of electrons per unit volume, e is the charge of an electron, and v_d is the drift velocity. We can solve for v_d:
v_d = J/ne

Plugging in the given values, we get:
v_d = (3895 A/cm^2)/(8.5 × 10^22 cm^-3 × 1.60 × 10^-19 C) = 0.44 cm/s

Therefore, the drift velocity of the electrons in the wire at maximum safe current is 0.44 cm/s. The best choice is B.

The Diameter of a 12-Gauge Copper Wire Is 0