Copper has 8.5 x 1028 free electrons per cubic meter. A 94.5-cm length of 12-gau
ID: 1789550 • Letter: C
Question
Copper has 8.5 x 1028 free electrons per cubic meter. A 94.5-cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.60 A of current. (a) How much time does it take for an electron to travel the length of the wire? min (b) Repeat part (a) for 6-gauge copper wire (diameter 4.12 mm) of the same length that carries the same current. min (c) Generally speaking, how does changing the diameter of a wire that carries a given amount of current affect the drift velocity of the electrons in the wire? This answer has not been graded yet.Explanation / Answer
Electrons density = 8.50 x 10^28 electrons/m^3
a)
cable volume = (pi/4)*(0.205 cm)^2*94.5 cm = 3.80 cm^3 = 3.80 x 10^-6 m^3
no of electrons = (8.50 x 10^28 el./m^3) x (3.80 x 10^-6 m^3)
no of electrons = 3.23 x 10^23 electrons.
El/Coulomb = 6.24 x 10^18 el/(A*sec)
(6.24 x 10^18 el / (A*sec) x 4.60 A = 2.87 x 10^19 el/sec
t = 3.23 x 10^23 electrons. / 2.87 x 10^19 electrons / sec
t = 11254.3554 s
t = 11254.3554 s / 60
t = 187.57259 min
b)
cable volume = (pi/4)*(0.412 cm)^2*94.5 cm = 12.598 cm^3 = 12.5989 x 10^-6 m^3
no of electrons = (8.50 x 10^28 el./m^3) x (12.598 x 10^-6 m^3)
no of electrons = 10.7 x 10^23 electrons.
El/Coulomb = 6.24 x 10^18 el/(A*sec)
(6.24 x 10^18 el / (A*sec) x 4.60 A = 2.87 x 10^19 el/sec
t = 10.7 x 10^23 electrons. / 2.87 x 10^19 electrons / sec
t = 37282.2299 s
t = 37282.2299 s / 60
t = 621.37 min
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