1. Home
  2. College physics for ap® courses
  3. Electric current, resistance,
  4. Resistance and resistivity

20.3 Resistance and resistivity  (Page 2/6)

<< Chapter < Page
  College physics for ap® courses     Page 2 / 6
Chapter >> Page >
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 14

Calculating resistor diameter: a headlight filament

A car headlight filament is made of tungsten and has a cold resistance of 0 . 350 Ω size 12{0 "." "350" %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 = ρL A size 12{R = { {ρL} over {A} } } {} to find the cross-sectional area A size 12{A} {} of the filament from the given information. Then its diameter can be found by assuming it has a circular cross-section.

Solution

The cross-sectional area, found by rearranging the expression for the resistance of a cylinder given in R = ρL A size 12{R = { {ρL} over {A} } } {} , is

A = ρL R . size 12{A = { {ρL} over {R} } "."} {}

Substituting the given values, and taking ρ size 12{ρ} {} from [link] , yields

A = ( 5.6 × 10 –8 Ω ⋅ m ) ( 4.00 × 10 –2 m ) 0.350 Ω = 6.40 × 10 –9 m 2 .

The area of a circle is related to its diameter D size 12{D} {} by

A = πD 2 4 . size 12{A = { {πD rSup { size 8{2} } } over {4} } "."} {}

Solving for the diameter D size 12{D} {} , and substituting the value found for A size 12{A} {} , gives

D = 2 A p 1 2 = 2 6.40 × 10 –9 m 2 3.14 1 2 = 9.0 × 10 –5 m . alignl { stack { size 12{D =" 2" left ( { {A} over {p} } right ) rSup { size 8{ { {1} over {2} } } } =" 2" left ( { {6 "." "40"´"10" rSup { size 8{ +- 9} } " m" rSup { size 8{2} } } over {3 "." "14"} } right ) rSup { size 8{ { {1} over {2} } } } } {} #=" 9" "." 0´"10" rSup { size 8{ +- 5} } " m" "." {} } } {}

Discussion

The diameter is just under a tenth of a millimeter. It is quoted to only two digits, because ρ size 12{ρ} {} is known to only two digits.

Got questions? Get instant answers now!

Temperature variation of resistance

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 100º C size 12{"100"°C} {} or less), resistivity ρ size 12{ρ} {} varies with temperature change Δ T size 12{DT} {} as expressed in the following equation

ρ = ρ 0 ( 1 + α Δ T ) , size 12{ρ = ρ rSub { size 8{0} } \( "1 "+ αΔT \) ","} {}

where ρ 0 size 12{ρ rSub { size 8{0} } } {} is the original resistivity and α size 12{α} {} is the temperature coefficient of resistivity    . (See the values of α size 12{α} {} in [link] below.) For larger temperature changes, α size 12{α} {} may vary or a nonlinear equation may be needed to find ρ size 12{ρ} {} . Note that α size 12{α} {} 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 α size 12{α} {} 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 temperature-independent resistance standard, for example.

A graph for variation of resistance R with temperature T for a mercury sample is shown. The temperature T is plotted along the x axis and is measured in Kelvin, and the resistance R is plotted along the y axis and is measured in ohms. The curve starts at x equals zero and y equals zero, and coincides with the X axis until the value of temperature is four point two Kelvin, known as the critical temperature T sub c. At temperature T sub c, the curve shows a vertical rise, represented by a dotted line, until the resistance is about zero point one one ohms. After this temperature the resistance shows a nearly linear increase with temperature T.
The resistance of a sample of mercury is zero at very low temperatures—it is a superconductor up to about 4.2 K. Above that critical temperature, its resistance makes a sudden jump and then increases nearly linearly with temperature.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 2

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask