Copper has 8.5 times 10^28 free per cubic meter. A 75.0 cm length of 12-gauge co

Question

Copper has 8.5 times 10^28 free per cubic meter. A 75.0 cm length of 12-gauge copper wire, that is 2.05 mm in diameter, caries 4.95 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 wire How much time does it take for an electron to travel the length of the wire? T = ____ Repeat part A for 6 gauge copper wire (diameter 4.12 mm) of the same length that carries the same current t = ____

Explanation / Answer

Electrons density = 8.50*10^28 el./m^3
a)
cable volume = 0.7854*0.205^2*75 = 2.48 cm^3 = 2.48*10^-6 m^3
8.50*10^28 el./m^3*2.48*10^-6 m^3 = 2.1*10^23 el.
El./Coulomb = 6.24*10^18 el/(A*sec)
6.24*10^18 el/(A*sec)*4.95 A = 3.09*10^19 el/sec
2.1*10^23 el./3.09*10^19 el/sec = 6796 sec = 6796/60 = 113.3 min

b)
cable volume = 0.7854*0.412^2*75 = 9.999 cm^3 = 9.99*10^-6 m^3
8.50*10^28 el./m^3*9.99*10^-6 m^3 = 8.5*10^23 el.
El./Coulomb = 6.24*10^18 el/(A*sec)
6.24*10^18 el/(A*sec)*4.55 A = 3.09*10^19 el/sec
8.5*10^23 el./3.09*10^19 el/sec = 27508 sec = 27508/60 = 458.5 min

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