1. Home
  2. Physics 101
  3. Electric current, resistance,
  4. Resistance and resistivity

14.3 Resistance and resistivity  (Page 39/6)

<< Chapter < Page
  Physics 101     Page 1 / 6
Chapter >> Page >
  • 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

what is chemistry
Terhemba Reply
what is the difference between ph and poh?
Abagaro Reply
chemical bond that results from the attractive force between shared electrons and nonmetals nucleus is what?
Abagaro
what is chemistry
Ayok
what is chemistry
ISIYAKA Reply
what is oxidation
Chidiebube Reply
calculate molarity of NaOH solution when 25.0ml of NaOH titrated with 27.2ml of 0.2m H2SO4
Gasin Reply
what's Thermochemistry
rhoda Reply
the study of the heat energy which is associated with chemical reactions
Kaddija
How was CH4 and o2 was able to produce (Co2)and (H2o
Edafe Reply
explain please
Victory
First twenty elements with their valences
Martine Reply
what is chemistry
asue Reply
what is atom
asue
what is the best way to define periodic table for jamb
Damilola Reply
what is the change of matter from one state to another
Elijah Reply
what is isolation of organic compounds
IKyernum Reply
what is atomic radius
ThankGod Reply
Read Chapter 6, section 5
Dr
Read Chapter 6, section 5
Kareem
Atomic radius is the radius of the atom and is also called the orbital radius
Kareem
atomic radius is the distance between the nucleus of an atom and its valence shell
Amos
Read Chapter 6, section 5
paulino
Bohr's model of the theory atom
Ayom Reply
is there a question?
Dr
when a gas is compressed why it becomes hot?
ATOMIC
It has no oxygen then
Goldyei
read the chapter on thermochemistry...the sections on "PV" work and the First Law of Thermodynamics should help..
Dr
Which element react with water
Mukthar Reply
Mgo
Ibeh
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 2

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics 101' conversation and receive update notifications?

Ask