Copper has 8.5 times 10^28 free electrons per cubic meter A 65.0 cm length of 12

Question

Copper has 8.5 times 10^28 free electrons per cubic meter A 65.0 cm length of 12-gauge copper wire, that is 2.05 mm in diameter carries 4.70 A of current. You may want to review For related problem solving tips and strategies, you may want to view a Video Tutor Solution of Current density and drift velocity in a wire How much time does it take for an electron to travel the length of the wire? Repeat part A for 6-gauge copper wire (diameter 4-12 mm) of the same length that carries the same current.

Explanation / Answer

Electrons density = 8.50*10^28 el./m^3
a)
cable volume = pi/4*0.205^2*65 = 2.34 cm^3 = 2.14*10^-6 m^3
8.50*10^28 el./m^3*2.14*10^-6 m^3 = 1.82*10^23 el.
El./Coulomb = 6.24*10^18 el/(A*sec)
6.24*10^18 el/(A*sec)*4.70 A = 2.93*10^19 el/sec
1.82*10^23 el./2.93*10^19 el/sec = 6211.60 sec = 6211.60/60 = 103.52 min

b)
cable volume = 0.7854*0.412^2*65 = 2.34 cm^3 = 8.665*10^-6 m^3
8.50*10^28 el./m^3*8.665*10^-6 m^3 = 7.36*10^23 el.
El./Coulomb = 6.24*10^18 el/(A*sec)
6.24*10^18 el/(A*sec)*4.70 A = 2.93*10^19 el/sec
8.05*10^23 el./2.93*10^19 el/sec = 27474.40 sec = 27474/60 = 457.9 min

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.