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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

Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
anas Reply
Hi
saeid
hi
Yimam
What is thê principle behind movement of thê taps control
Oluwakayode Reply
what is atomic mass
thomas Reply
this is the mass of an atom of an element in ratio with the mass of carbon-atom
Chukwuka
show me how to get the accuracies of the values of the resistors for the two circuits i.e for series and parallel sides
Jesuovie Reply
Explain why it is difficult to have an ideal machine in real life situations.
Isaac Reply
tell me
Promise
what's the s . i unit for couple?
Promise
its s.i unit is Nm
Covenant
Force×perpendicular distance N×m=Nm
Oluwakayode
İt iş diffucult to have idêal machine because of FRİCTİON definitely reduce thê efficiency
Oluwakayode
if the classica theory of specific heat is valid,what would be the thermal energy of one kmol of copper at the debye temperature (for copper is 340k)
Zaharadeen Reply
can i get all formulas of physics
BPH Reply
yes
haider
what affects fluid
Doreen Reply
pressure
Oluwakayode
Dimension for force MLT-2
Promise Reply
what is the dimensions of Force?
Osueke Reply
how do you calculate the 5% uncertainty of 4cm?
melia Reply
4cm/100×5= 0.2cm
haider
how do you calculate the 5% absolute uncertainty of a 200g mass?
melia Reply
= 200g±(5%)10g
haider
use the 10g as the uncertainty?
melia
which topic u discussing about?
haider
topic of question?
haider
the relationship between the applied force and the deflection
melia
sorry wrong question i meant the 5% uncertainty of 4cm?
melia
its 0.2 cm or 2mm
haider
thank you
melia
Hello group...
Chioma
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haider
well hello there
sean
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Noks
hii
Chibueze
10g
Olokuntoye
0.2m
Olokuntoye
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thomas
the meaning of phrase in physics
Chovwe Reply
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Chovwe
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
Gabriel Reply
how does a model differ from a theory
Friday Reply
To use the vocabulary of model theory and meta-logic, a theory is a set of sentences which can be derived from a formal model using some rule of inference (usually just modus ponens). So, for example, Number Theory is the set of sentences true about numbers. But the model is a structure together wit
Jesilda
with an iterpretation.
Jesilda
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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