<< Chapter < Page Chapter >> Page >

The resistance of an object also depends on temperature, since R 0 size 12{R rSub { size 8{0} } } {} is directly proportional to ρ size 12{ρ} {} . For a cylinder we know R = ρL / A size 12{R=ρL/A} {} , and so, if L size 12{L} {} and A size 12{A} {} do not change greatly with temperature, R size 12{R} {} will have the same temperature dependence as ρ size 12{ρ} {} . (Examination of the coefficients of linear expansion shows them to be about two orders of magnitude less than typical temperature coefficients of resistivity, and so the effect of temperature on L size 12{L} {} and A size 12{A} {} is about two orders of magnitude less than on ρ size 12{ρ} {} .) Thus,

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

is the temperature dependence of the resistance of an object, where R 0 size 12{R rSub { size 8{0} } } {} is the original resistance and R size 12{R} {} is the resistance after a temperature change Δ T size 12{DT} {} . Numerous thermometers are based on the effect of temperature on resistance. (See [link] .) One of the most common is the thermistor, a semiconductor crystal with a strong temperature dependence, the resistance of which is measured to obtain its temperature. The device is small, so that it quickly comes into thermal equilibrium with the part of a person it touches.

A photograph showing two digital thermometers used for measuring body temperature.
These familiar thermometers are based on the automated measurement of a thermistor’s temperature-dependent resistance. (credit: Biol, Wikimedia Commons)

Calculating resistance: hot-filament resistance

Although caution must be used in applying ρ = ρ 0 ( 1 + α Δ T ) size 12{ρ = ρ rSub { size 8{0} } \( "1 "+ αΔT \) } {} and R = R 0 ( 1 + α Δ T ) size 12{R = R rSub { size 8{0} } \( "1 "+ αΔT \) } {} for temperature changes greater than 100º C size 12{"100"°"C"} {} , for tungsten the equations work reasonably well for very large temperature changes. What, then, is the resistance of the tungsten filament in the previous example if its temperature is increased from room temperature ( 20ºC ) to a typical operating temperature of 2850º C size 12{"2850"°"C"} {} ?

Strategy

This is a straightforward application of R = R 0 ( 1 + α Δ T ) size 12{R = R rSub { size 8{0} } \( "1 "+ αΔT \) } {} , since the original resistance of the filament was given to be R 0 = 0 . 350 Ω size 12{R rSub { size 8{0} } =0 "." "350"` %OMEGA } {} , and the temperature change is Δ T = 2830º C size 12{ΔT="2830"°"C"} {} .

Solution

The hot resistance R size 12{R} {} is obtained by entering known values into the above equation:

R = R 0 ( 1 + α Δ T ) = ( 0 . 350 Ω ) [ 1 + ( 4.5 × 10 –3 / ºC ) ( 2830º C ) ] = 4.8 Ω.

Discussion

This value is consistent with the headlight resistance example in Ohm’s Law: Resistance and Simple Circuits .

Got questions? Get instant answers now!

Phet explorations: resistance in a wire

Learn about the physics of resistance in a wire. Change its resistivity, length, and area to see how they affect the wire's resistance. The sizes of the symbols in the equation change along with the diagram of a wire.

Resistance in a Wire

Section summary

  • The resistance R size 12{R} {} of a cylinder of length L size 12{L} {} and cross-sectional area A size 12{A} {} is R = ρL A size 12{R = { {ρL} over {A} } } {} , where ρ size 12{ρ} {} is the resistivity of the material.
  • Values of ρ size 12{ρ} {} in [link] show that materials fall into three groups— conductors, semiconductors, and insulators .
  • Temperature affects resistivity; for relatively small temperature changes Δ T size 12{DT} {} , resistivity is 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 is the temperature coefficient of resistivity.
  • [link] gives values for α size 12{α} {} , the temperature coefficient of resistivity.
  • The resistance R size 12{R} {} of an object also varies with temperature: R = R 0 ( 1 + α Δ T ) size 12{R = R rSub { size 8{0} } \( "1 "+ ΔαT \) } {} , where R 0 size 12{R rSub { size 8{0} } } {} is the original resistance, and R is the resistance after the temperature change.

Conceptual questions

In which of the three semiconducting materials listed in [link] do impurities supply free charges? (Hint: Examine the range of resistivity for each and determine whether the pure semiconductor has the higher or lower conductivity.)

Got questions? Get instant answers now!

Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
Theophilus Reply
what's lochia albra
Kizito
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 2

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. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask