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Making connections: take-home investigation—filament observations

Find a lightbulb with a filament. Look carefully at the filament and describe its structure. To what points is the filament connected?

We can obtain an expression for the relationship between current and drift velocity by considering the number of free charges in a segment of wire, as illustrated in [link] . The number of free charges per unit volume is given the symbol n size 12{n} {} and depends on the material. The shaded segment has a volume Ax size 12{ ital "Ax"} {} , so that the number of free charges in it is nAx size 12{ ital "nAx"} {} . The charge Δ Q size 12{DQ} {} in this segment is thus qnAx size 12{ ital "qnAx"} {} , where q size 12{q} {} is the amount of charge on each carrier. (Recall that for electrons, q size 12{q} {} is 1 . 60 × 10 19 C size 12{ - 1 "." "60" times "10" rSup { size 8{ - "19"} } "C"} {} .) Current is charge moved per unit time; thus, if all the original charges move out of this segment in time Δ t size 12{Dt} {} , the current is

I = Δ Q Δ t = qnAx Δ t . size 12{I = { {ΔQ} over {Δt} } = { { ital "qnAx"} over {Δt} } "."} {}

Note that x / Δ t size 12{x/Δt} {} is the magnitude of the drift velocity, v d , since the charges move an average distance x size 12{x} {} in a time Δ t size 12{Dt} {} . Rearranging terms gives

I = nqAv d , size 12{I= ital "nqAv" rSub { size 8{"d"} } } {}

where I size 12{I } {} is the current through a wire of cross-sectional area A size 12{A} {} made of a material with a free charge density n size 12{n} {} . The carriers of the current each have charge q size 12{q} {} and move with a drift velocity of magnitude v d size 12{v rSub { size 8{d} } } {} .

Charges are shown moving through a section of a conducting wire. The charges have a drift velocity v sub d along the length of the wire, shown by an arrow pointing to the right. The volume of a segment of the wire is equal to A times x, where x equals the product of the drift velocity, v sub d, and time t. A cross section of the wire is marked as A, and the length of the section is x.
All the charges in the shaded volume of this wire move out in a time t size 12{t} {} , having a drift velocity of magnitude v d = x / t size 12{v rSub { size 8{d} } =x/t} {} . See text for further discussion.

Note that simple drift velocity is not the entire story. The speed of an electron is much greater than its drift velocity. In addition, not all of the electrons in a conductor can move freely, and those that do might move somewhat faster or slower than the drift velocity. So what do we mean by free electrons? Atoms in a metallic conductor are packed in the form of a lattice structure. Some electrons are far enough away from the atomic nuclei that they do not experience the attraction of the nuclei as much as the inner electrons do. These are the free electrons. They are not bound to a single atom but can instead move freely among the atoms in a “sea” of electrons. These free electrons respond by accelerating when an electric field is applied. Of course as they move they collide with the atoms in the lattice and other electrons, generating thermal energy, and the conductor gets warmer. In an insulator, the organization of the atoms and the structure do not allow for such free electrons.

Calculating drift velocity in a common wire

Calculate the drift velocity of electrons in a 12-gauge copper wire (which has a diameter of 2.053 mm) carrying a 20.0-A current, given that there is one free electron per copper atom. (Household wiring often contains 12-gauge copper wire, and the maximum current allowed in such wire is usually 20 A.) The density of copper is 8 . 80 × 10 3 kg/m 3 size 12{8 "." "80" times "10" rSup { size 8{3} } `"kg/m" rSup { size 8{3} } } {} .

Strategy

We can calculate the drift velocity using the equation I = nqAv d . The current I = 20.0 A is given, and q = 1.60 × 10 19 C is the charge of an electron. We can calculate the area of a cross-section of the wire using the formula A = π r 2 , where r is one-half the given diameter, 2.053 mm. We are given the density of copper, 8.80 × 10 3 kg/m 3 , and the periodic table shows that the atomic mass of copper is 63.54 g/mol. We can use these two quantities along with Avogadro’s number, 6.02 × 10 23 atoms/mol , to determine n , the number of free electrons per cubic meter.

Solution

First, calculate the density of free electrons in copper. There is one free electron per copper atom. Therefore, is the same as the number of copper atoms per m 3 . We can now find n as follows:

n = 1 e atom × 6 . 02 × 10 23 atoms mol × 1 mol 63 . 54 g × 1000 g kg × 8.80 × 10 3 kg 1 m 3 = 8 . 342 × 10 28 e /m 3 .

The cross-sectional area of the wire is

A = π r 2 = π 2.053 × 10 −3 m 2 2 = 3.310 × 10 –6 m 2 .

Rearranging I = n q A v d to isolate drift velocity gives

v d = I nqA = 20.0 A ( 8 . 342 × 10 28 /m 3 ) ( –1 . 60 × 10 –19 C ) ( 3 . 310 × 10 –6 m 2 ) = –4 . 53 × 10 –4 m/s.

Discussion

The minus sign indicates that the negative charges are moving in the direction opposite to conventional current. The small value for drift velocity (on the order of 10 4 m/s size 12{"10" rSup { size 8{ - 4} } `"m/s"} {} ) confirms that the signal moves on the order of 10 12 size 12{"10" rSup { size 8{"12"} } } {} times faster (about 10 8 m/s size 12{"10" rSup { size 8{8} } `"m/s"} {} ) than the charges that carry it.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Beverly Reply
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Source:  OpenStax, General physics ii phy2202ca. OpenStax CNX. Jul 05, 2013 Download for free at http://legacy.cnx.org/content/col11538/1.2
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