Question

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 No. 14 wire is 1.6 mm. Assume one conduction electron per atom in copper. The atomic weight of copper is 63.3 and its density is 8900 kg/m3.
a. 4.89 x 10-5 m/s
b. 4.56 x 10-4 m/s
c. 5.52 x 10-4 m/s
d. 4.44 x 10-2 m/s
e. 1.65 x 10-3 m/s

Answer 1

Answer:

The drift velocity of the electrons in this case is c) 5.52 x 10-4 m/s

Explanation:

Hi

First of all, we need to find the volume occupied by 63.3g of copper, so $V=\frac{m}{\rho}= \frac{0.0633Kg}{8,900kg/m^{3}} =7.11 \times 10^{-6} m^{3}$, then if we assume each atom of copper contributes with one free electron to the material body $n=\frac{N_{A}}{V}=\frac{6.02 \times 10^{23} electrons}{7.11 \times 10^{-6} m^{3}} =8.46 \times 10^{28} electrons/m^{3}$.

Finally, we apply $v_{d}=\frac{I}{nqA}$, where A is area so, $A=\pi (\frac{d}{2})^{2}= \pi (\frac{0.0016m}{2})^{2}=2 \times 10^{-6} m^{2}$, thus $v_{d}=\frac{I}{nqA}=\frac{15C/s}{(8.46 \times 10^{28} m^{-3})(1.60 \times 10^{-19} C)(2 \times 10^{-6} m^{2})}=5.50 \times 10^{-4} m/s$.

As we can see c. 5.52 x 10-4 m/s is the nearest one.