# 20.3 Resistance and resistivity

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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 $R$ is directly proportional to its length $L$ , 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, $R$ is inversely proportional to the cylinder’s cross-sectional area $A$ .

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     $\rho$ of a substance so that the resistance $R$ of an object is directly proportional to $\rho$ . Resistivity $\rho$ is an intrinsic property of a material, independent of its shape or size. The resistance $R$ of a uniform cylinder of length $L$ , of cross-sectional area $A$ , and made of a material with resistivity $\rho$ , is

$R=\frac{\mathrm{\rho L}}{A}\text{.}$

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

definition of mass of conversion
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
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effiom
how many topic are in physics
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yh I need someone to explain something im tryna solve . I'll send the question if u down for it
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linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
Saeedul
Hi
aliyu
Richard
Linear motion is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
Jason
is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimensions.
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Marga
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dynamic is the force that stimulates change or progress within the system or process
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Word : Mechanical wave Definition : The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
correct
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a wave which require material medium for its propagation
syed
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watt
Okoli
Am I correct
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it can be in kilowatt, megawatt and so
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yes
Femi
correct
Jaheim
kW
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OK that's right
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reasonable
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because it is balanced by the inward acceleration otherwise known as centripetal acceleration
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is the disturbance that carry materials as propagation from one medium to another
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