The length and diameter of an aluminum wire is twice the length and diameter of a copper wire, respectively. Find the ratio of the resistances of the two wires.

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Chapter1: Units, Trigonometry. And Vectors
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The length and diameter of an aluminum wire is twice the length and diameter of a copper wire, respectively. Find the ratio of the resistances of the two wires.

Material of the Wire
The effect of the kind of material on the resistance of the wire is determined by its resistivity.
Resistivity p is the reciprocal of conductivity. Conductors have small resistivities, while insulators have
large resistivities. Semiconductors have intermediate values of resistivity. Table 3-2 lists the values of
resistivity for some materials. Note that resistivity is dependent on temperature.
Table 3-2
Resistivities of Some Materials at 20°C
Material
ρ (Ω.m)
Material
p (요.m)
Conductors
Semiconductors
Aluminum
2.75x10-8
Pure carbon
2.75x10-5
Copper
1.72x10-8
Pure germanium
0.60
Gold
2.44x10-8
Pure silicon
2300
Iron
9.7×10-8
Insulators
Lead
22x10-8
Amber
5x1014
Nichrome
100x10-8
Glass
1010–1014
Platinum
10.6x10-8
Mica
1011-1015
Silver
1.62x10-8
Rubber (hard)
1013-1016
Steel
20x10-8
Teflon
1016
Tungsten
5.25x10-8
Wood (maple)
3x1010
Transcribed Image Text:Material of the Wire The effect of the kind of material on the resistance of the wire is determined by its resistivity. Resistivity p is the reciprocal of conductivity. Conductors have small resistivities, while insulators have large resistivities. Semiconductors have intermediate values of resistivity. Table 3-2 lists the values of resistivity for some materials. Note that resistivity is dependent on temperature. Table 3-2 Resistivities of Some Materials at 20°C Material ρ (Ω.m) Material p (요.m) Conductors Semiconductors Aluminum 2.75x10-8 Pure carbon 2.75x10-5 Copper 1.72x10-8 Pure germanium 0.60 Gold 2.44x10-8 Pure silicon 2300 Iron 9.7×10-8 Insulators Lead 22x10-8 Amber 5x1014 Nichrome 100x10-8 Glass 1010–1014 Platinum 10.6x10-8 Mica 1011-1015 Silver 1.62x10-8 Rubber (hard) 1013-1016 Steel 20x10-8 Teflon 1016 Tungsten 5.25x10-8 Wood (maple) 3x1010
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