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Resistivity $\rho $ ( $\Omega \cdot \text{m}$ ) 

Conductors  

$$1\text{.}\text{59}\times {\text{10}}^{8}$$ 

$$1\text{.}\text{72}\times {\text{10}}^{8}$$ 

$$2\text{.}\text{44}\times {\text{10}}^{8}$$ 

$$2\text{.}\text{65}\times {\text{10}}^{8}$$ 

$$5\text{.}6\times {\text{10}}^{8}$$ 

$$9\text{.}\text{71}\times {\text{10}}^{8}$$ 

$$\text{10}\text{.}6\times {\text{10}}^{8}$$ 

$$\text{20}\times {\text{10}}^{8}$$ 

$$\text{22}\times {\text{10}}^{8}$$ 

$$\text{44}\times {\text{10}}^{8}$$ 

$$\text{49}\times {\text{10}}^{8}$$ 

$$\text{96}\times {\text{10}}^{8}$$ 

$$\text{100}\times {\text{10}}^{8}$$ 
Semiconductors Values depend strongly on amounts and types of impurities  

$$\text{3.5}\times {\text{10}}^{5}$$ 

$$(3.5\text{60})\times {\text{10}}^{5}$$ 

$$\text{600}\times {\text{10}}^{3}$$ 

$$(1\text{600})\times {\text{10}}^{3}$$ 

$$\text{2300}$$ 

$$\text{0.1\u20132300}$$ 
Insulators  

$$5\times {\text{10}}^{\text{14}}$$ 

$${\text{10}}^{9}{\text{10}}^{\text{14}}$$ 

$${\text{>10}}^{\text{13}}$$ 

$${\text{10}}^{\text{11}}{\text{10}}^{\text{15}}$$ 

$$\text{75}\times {\text{10}}^{\text{16}}$$ 

$${\text{10}}^{\text{13}}{\text{10}}^{\text{16}}$$ 

$${\text{10}}^{\text{15}}$$ 

$${\text{>10}}^{\text{13}}$$ 

${10}^{8}{10}^{14}$ 
A car headlight filament is made of tungsten and has a cold resistance of $0\text{.}\text{350}\phantom{\rule{0.25em}{0ex}}\Omega $ . If the filament is a cylinder 4.00 cm long (it may be coiled to save space), what is its diameter?
Strategy
We can rearrange the equation $R=\frac{\mathrm{\rho L}}{A}$ to find the crosssectional area $A$ of the filament from the given information. Then its diameter can be found by assuming it has a circular crosssection.
Solution
The crosssectional area, found by rearranging the expression for the resistance of a cylinder given in $R=\frac{\mathrm{\rho L}}{A}$ , is
Substituting the given values, and taking $\rho $ from [link] , yields
The area of a circle is related to its diameter $D$ by
Solving for the diameter $D$ , and substituting the value found for $A$ , gives
Discussion
The diameter is just under a tenth of a millimeter. It is quoted to only two digits, because $\rho $ is known to only two digits.
The resistivity of all materials depends on temperature. Some even become superconductors (zero resistivity) at very low temperatures. (See [link] .) Conversely, the resistivity of conductors increases with increasing temperature. Since the atoms vibrate more rapidly and over larger distances at higher temperatures, the electrons moving through a metal make more collisions, effectively making the resistivity higher. Over relatively small temperature changes (about $\text{100\xba}\text{C}$ or less), resistivity $\rho $ varies with temperature change $\mathrm{\Delta}T$ as expressed in the following equation
where ${\rho}_{0}$ is the original resistivity and $\alpha $ is the temperature coefficient of resistivity . (See the values of $\alpha $ in [link] below.) For larger temperature changes, $\alpha $ may vary or a nonlinear equation may be needed to find $\rho $ . Note that $\alpha $ is positive for metals, meaning their resistivity increases with temperature. Some alloys have been developed specifically to have a small temperature dependence. Manganin (which is made of copper, manganese and nickel), for example, has $\alpha $ close to zero (to three digits on the scale in [link] ), and so its resistivity varies only slightly with temperature. This is useful for making a temperatureindependent resistance standard, for example.
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