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  • Explain the concept of resistivity.
  • Use resistivity to calculate the resistance of specified configurations of material.
  • Use the thermal coefficient of resistivity to calculate the change of resistance with temperature.

Material and shape dependence of resistance

The resistance of an object depends on its shape and the material of which it is composed. The cylindrical resistor in [link] is easy to analyze, and, by so doing, we can gain insight into the resistance of more complicated shapes. As you might expect, the cylinder’s electric resistance R size 12{R} {} is directly proportional to its length L size 12{L} {} , similar to the resistance of a pipe to fluid flow. The longer the cylinder, the more collisions charges will make with its atoms. The greater the diameter of the cylinder, the more current it can carry (again similar to the flow of fluid through a pipe). In fact, R size 12{R} {} is inversely proportional to the cylinder’s cross-sectional area A size 12{A} {} .

A cylindrical conductor of length L and cross section A is shown. The resistivity of the cylindrical section is represented as rho. The resistance of this cross section R is equal to rho L divided by A. The section of length L of cylindrical conductor is shown equivalent to a resistor represented by symbol R.
A uniform cylinder of length L size 12{L} {} and cross-sectional area A size 12{A} {} . Its resistance to the flow of current is similar to the resistance posed by a pipe to fluid flow. The longer the cylinder, the greater its resistance. The larger its cross-sectional area A size 12{A} {} , the smaller its resistance.

For a given shape, the resistance depends on the material of which the object is composed. Different materials offer different resistance to the flow of charge. We define the resistivity     ρ size 12{ρ} {} of a substance so that the resistance R size 12{R} {} of an object is directly proportional to ρ size 12{ρ} {} . Resistivity ρ size 12{ρ} {} is an intrinsic property of a material, independent of its shape or size. The resistance R size 12{R} {} of a uniform cylinder of length L size 12{L} {} , of cross-sectional area A size 12{A} {} , and made of a material with resistivity ρ size 12{ρ} {} , is

R = ρL A . size 12{R = { {ρL} over {A} } "."} {}

[link] gives representative values of ρ size 12{ρ} {} . The materials listed in the table are separated into categories of conductors, semiconductors, and insulators, based on broad groupings of resistivities. Conductors have the smallest resistivities, and insulators have the largest; semiconductors have intermediate resistivities. Conductors have varying but large free charge densities, whereas most charges in insulators are bound to atoms and are not free to move. Semiconductors are intermediate, having far fewer free charges than conductors, but having properties that make the number of free charges depend strongly on the type and amount of impurities in the semiconductor. These unique properties of semiconductors are put to use in modern electronics, as will be explored in later chapters.

Resistivities ρ size 12{ρ} {} Of various materials at 20º C
Material Resistivity ρ size 12{ρ} {} ( Ω m size 12{ %OMEGA cdot m} {} )
Conductors
Silver 1 . 59 × 10 8 size 12{1 "." "59" times "10" rSup { size 8{ - 8} } } {}
Copper 1 . 72 × 10 8 size 12{1 "." "72" times "10" rSup { size 8{ - 8} } } {}
Gold 2 . 44 × 10 8 size 12{2 "." "44" times "10" rSup { size 8{ - 8} } } {}
Aluminum 2 . 65 × 10 8 size 12{2 "." "65" times "10" rSup { size 8{ - 8} } } {}
Tungsten 5 . 6 × 10 8 size 12{5 "." 6 times "10" rSup { size 8{ - 8} } } {}
Iron 9 . 71 × 10 8 size 12{9 "." "71" times "10" rSup { size 8{ - 8} } } {}
Platinum 10 . 6 × 10 8 size 12{"10" "." 6 times "10" rSup { size 8{ - 8} } } {}
Steel 20 × 10 8 size 12{"20" times "10" rSup { size 8{ - 8} } } {}
Lead 22 × 10 8 size 12{"22" times "10" rSup { size 8{ - 8} } } {}
Manganin (Cu, Mn, Ni alloy) 44 × 10 8 size 12{"44" times "10" rSup { size 8{ - 8} } } {}
Constantan (Cu, Ni alloy) 49 × 10 8 size 12{"49" times "10" rSup { size 8{ - 8} } } {}
Mercury 96 × 10 8 size 12{"96" times "10" rSup { size 8{ - 8} } } {}
Nichrome (Ni, Fe, Cr alloy) 100 × 10 8 size 12{"100" times "10" rSup { size 8{ - 8} } } {}
Semiconductors Values depend strongly on amounts and types of impurities
Carbon (pure) 3.5 × 10 5
Carbon ( 3.5 60 ) × 10 5
Germanium (pure) 600 × 10 3
Germanium ( 1 600 ) × 10 3 size 12{ \( 1 - "600" \) times "10" rSup { size 8{ - 3} } } {}
Silicon (pure) 2300
Silicon 0.1–2300
Insulators
Amber 5 × 10 14 size 12{5 times "10" rSup { size 8{"14"} } } {}
Glass 10 9 10 14 size 12{"10" rSup { size 8{9} } - "10" rSup { size 8{"14"} } } {}
Lucite >10 13 size 12{>"10" rSup { size 8{"13"} } } {}
Mica 10 11 10 15 size 12{"10" rSup { size 8{"11"} } - "10" rSup { size 8{"15"} } } {}
Quartz (fused) 75 × 10 16 size 12{"75" times "10" rSup { size 8{"16"} } } {}
Rubber (hard) 10 13 10 16 size 12{"10" rSup { size 8{"13"} } - "10" rSup { size 8{"16"} } } {}
Sulfur 10 15 size 12{"10" rSup { size 8{"15"} } } {}
Teflon >10 13 size 12{>"10" rSup { size 8{"13"} } } {}
Wood 10 8 10 11 size 12{"10" rSup { size 8{8} } - "10" rSup { size 8{"11"} } } {}

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
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
Google
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
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
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
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 ?
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Physics of the world around us. OpenStax CNX. May 21, 2015 Download for free at http://legacy.cnx.org/content/col11797/1.1
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