Building codes usually limit the current carried by a No. 14 copper wire to 15 A. Many household circuits are wired with this size wire. What is the drift velocity of the electrons in this case? The diameter of this wire is 1.6 mm. Assume one conduction electron per atom in copper. The atomic weight of copper is 63.3 g/mol and its density is 8900 kg/m³. Avogadro's number is 6.022 × 10²³ molecules/mol and e = 1.60 × 10^-19 C. A) 5.51 × 10^-4 m/s B) 4.56 × 10^-4m/s C) 1.65 × 10^-3 m/s D) 4.44 × 10^-2 m/s E) 4.89 × 10^-5 m/s

Question

Quizplus · Accepted Answer

The current carried by the wire is 15 A. Using the formula for current density, J = I/A, the current density is found to be approximately 1.48 × 10^7 A/m^2. The next step is to find the number density of electrons in the wire using the density of copper, the atomic weight of copper and Avogadro's number. The number density is found to be approximately 8.49 × 10^28 electrons/m^3. Using the formula for current density, J = n×e×vd×A, the drift velocity is found to be approximately 5.51 × 10^-4 m/s. Therefore, the best choice is A.

Building Codes Usually Limit the Current Carried by a No