An aluminum wire 1.291 mm in diameter (16-gauge) carries a current of 4.5 amps. Overall Hint Review Section 9.2 Model of Conduction in Metals for relevant descriptions. Additional hints specific to each question are below. a. What is the number density of charge carriers (electrons) in the wire? Hint for (a) It is generally true that in conductors, each atom contributes one free electron (charge carrier; it has to do with where "Fermi surface" is). So the number density of conductor atoms can be taken to be the number density of charge carriers (electrons). The density of aluminum is 2700 kg/m³ and the mass of a single aluminum atom is 4.48 x 10-26 kg. 1 The number density of electrons in the wire is (Use "E" notation to enter your answer in scientific notation. For example, to enter 3.14 x 10¹2, enter "3.14E12".) b. What is the magnitude of the drift velocity of the electrons? Hint for (b) From Section' 9.2, use Equation 9.4, va = I/nqA. All the necessary information to calculate this numerically is given or just calculated in (a). The drift velocity of the electrons is vd = m/s. c. What would be the drift velocity if the same gauge copper were used instead of aluminum? Hint for (c) Repeat above calculations, starting with number density calculation for copper. Each copper atom still contributes one free electron; the density of copper is 8960 kg/m³ and the mass of a single copper atom is 1.0552 x 10-25 kg. Watch how, in a better conductor, it takes less drift velocity for the same amount of current. For the same gauge copper wire, the drift velocity would be va Submit Question m/s. There is a disconnect between how small drift velocities are and how quickly electrical signals travel through wires (nearly at the speed of light). For the moment, treat the two as completely unrelated to each other.
An aluminum wire 1.291 mm in diameter (16-gauge) carries a current of 4.5 amps. Overall Hint Review Section 9.2 Model of Conduction in Metals for relevant descriptions. Additional hints specific to each question are below. a. What is the number density of charge carriers (electrons) in the wire? Hint for (a) It is generally true that in conductors, each atom contributes one free electron (charge carrier; it has to do with where "Fermi surface" is). So the number density of conductor atoms can be taken to be the number density of charge carriers (electrons). The density of aluminum is 2700 kg/m³ and the mass of a single aluminum atom is 4.48 x 10-26 kg. 1 The number density of electrons in the wire is (Use "E" notation to enter your answer in scientific notation. For example, to enter 3.14 x 10¹2, enter "3.14E12".) b. What is the magnitude of the drift velocity of the electrons? Hint for (b) From Section' 9.2, use Equation 9.4, va = I/nqA. All the necessary information to calculate this numerically is given or just calculated in (a). The drift velocity of the electrons is vd = m/s. c. What would be the drift velocity if the same gauge copper were used instead of aluminum? Hint for (c) Repeat above calculations, starting with number density calculation for copper. Each copper atom still contributes one free electron; the density of copper is 8960 kg/m³ and the mass of a single copper atom is 1.0552 x 10-25 kg. Watch how, in a better conductor, it takes less drift velocity for the same amount of current. For the same gauge copper wire, the drift velocity would be va Submit Question m/s. There is a disconnect between how small drift velocities are and how quickly electrical signals travel through wires (nearly at the speed of light). For the moment, treat the two as completely unrelated to each other.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:An aluminum wire 1.291 mm in diameter (16-gauge) carries a current of 4.5 amps.
Overall Hint
Review Section 9.2 Model of Conduction in Metals for relevant descriptions. Additional hints specific to
each question are below.
3
a. What is the number density of charge carriers (electrons) in the wire?
Hint for (a)
It is generally true that in conductors, each atom contributes one free electron (charge carrier; it has
to do with where "Fermi surface" is). So the number density of conductor atoms can be taken to be
the number density of charge carriers (electrons). The density of aluminum is 2700 kg/m³ and the
mass of a single aluminum atom is 4.48 x 10-26 kg.
The number density of electrons in the wire is
m3
(Use "E" notation to enter your answer in scientific notation. For example, to enter 3.14 × 10¹2,
enter "3.14E12".)
b. What is the magnitude of the drift velocity of the electrons?
Hint for (b)
From Section 9.2, use Equation 9.4, va = I/nqA. All the necessary information to calculate this
numerically is given or just calculated in (a).
The drift velocity of the electrons is vd =
c. What would be the drift velocity if the same gauge copper were used instead of aluminum?
Hint for (c)
Repeat above calculations, starting with number density calculation for copper. Each copper atom
still contributes one free electron; the density of copper is 8960 kg/m³ and the mass of a single
copper atom is 1.0552 x 10-25 kg. Watch how, in a better conductor, it takes less drift velocity for
the same amount of current.
F
For the same gauge copper wire, the drift velocity would be va =
с
There is a disconnect between how small drift velocities are and how quickly electrical signals travel
through wires (nearly at the speed of light). For the moment, treat the two as completely unrelated to
each other.
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