# 4.1 Current  (Page 4/8)

 Page 4 / 8

## 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 $n$ and depends on the material. The shaded segment has a volume $\text{Ax}$ , so that the number of free charges in it is $\text{nAx}$ . The charge $\Delta Q$ in this segment is thus $\text{qnAx}$ , where $q$ is the amount of charge on each carrier. (Recall that for electrons, $q$ is $-1\text{.}\text{60}×{\text{10}}^{-\text{19}}\phantom{\rule{0.25em}{0ex}}\text{C}$ .) Current is charge moved per unit time; thus, if all the original charges move out of this segment in time $\Delta t$ , the current is

$I=\frac{\Delta Q}{\Delta t}=\frac{\text{qnAx}}{\Delta t}\text{}.$

Note that $x/\Delta t$ is the magnitude of the drift velocity, ${v}_{\text{d}}$ , since the charges move an average distance $x$ in a time $\Delta t$ . Rearranging terms gives

$I={\mathrm{nqAv}}_{\text{d}},$

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

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 $8\text{.}\text{80}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}$ .

Strategy

We can calculate the drift velocity using the equation $I={\mathrm{nqAv}}_{\text{d}}$ . The current $I=20.0 A$ is given, and $q=\phantom{\rule{0.25em}{0ex}}–1.60×{10}^{–19}\text{C}$ is the charge of an electron. We can calculate the area of a cross-section of the wire using the formula $A=\pi {r}^{2},$ where $r$ is one-half the given diameter, 2.053 mm. We are given the density of copper, $8.80×{10}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3},$ 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, $6.02×{10}^{23}\phantom{\rule{0.25em}{0ex}}\text{atoms/mol},$ 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:

$\begin{array}{lll}n& =& \frac{\text{1}\phantom{\rule{0.25em}{0ex}}{e}^{-}}{\text{atom}}×\frac{6\text{.}\text{02}×{\text{10}}^{\text{23}}\phantom{\rule{0.25em}{0ex}}\text{atoms}}{\text{mol}}×\frac{1 mol}{\text{63}\text{.}\text{54 g}}×\frac{\text{1000 g}}{\text{kg}}×\frac{\text{8.80}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{kg}}{{\text{1 m}}^{3}}\\ & =& \text{8}\text{.}\text{342}×{\text{10}}^{\text{28}}\phantom{\rule{0.25em}{0ex}}{e}^{-}{\text{/m}}^{3}\text{.}\end{array}$

The cross-sectional area of the wire is

$\begin{array}{lll}A& =& \pi {r}^{2}\\ & =& \pi {\left(\frac{2.053×{\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\text{m}}{2}\right)}^{2}\\ & =& \text{3.310}×{\text{10}}^{\text{–6}}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}\text{.}\end{array}$

Rearranging $I=nqA{v}_{\text{d}}$ to isolate drift velocity gives

$\begin{array}{c}{v}_{\text{d}}=\frac{I}{\mathit{\text{nqA}}}\\ =\frac{\text{20.0 A}}{\left(8\text{.}\text{342}×{\text{10}}^{\text{28}}{\text{/m}}^{3}\right)\left(\text{–1}\text{.}\text{60}×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}\text{C}\right)\left(3\text{.}\text{310}×{\text{10}}^{\text{–6}}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}\right)}\\ =\text{–4}\text{.}\text{53}×{\text{10}}^{\text{–4}}\phantom{\rule{0.25em}{0ex}}\text{m/s.}\end{array}$

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 ${\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ ) confirms that the signal moves on the order of ${\text{10}}^{\text{12}}$ times faster (about ${\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ ) than the charges that carry it.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!