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Learning objectives

By the end of this section, you will be able to:

  • 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.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 1.E.2.1 The student is able to choose and justify the selection of data needed to determine resistivity for a given material. (S.P. 4.1)
  • 4.E.4.2 The student is able to design a plan for the collection of data to determine the effect of changing the geometry and/or materials on the resistance or capacitance of a circuit element and relate results to the basic properties of resistors and capacitors. (S.P. 4.1, 4.2)
  • 4.E.4.3 The student is able to analyze data to determine the effect of changing the geometry and/or materials on the resistance or capacitance of a circuit element and relate results to the basic properties of resistors and capacitors. (S.P. 5.1)

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.

Questions & Answers

Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
room?
Abrar
What is position?
Amoah Reply
What is law of gravition
sushil Reply
Practice Key Terms 2

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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