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Does the resistance of an object depend on the path current takes through it? Consider, for example, a rectangular bar—is its resistance the same along its length as across its width? (See [link] .)

Part a of the figure shows a voltage V applied along the length of a rectangular bar using a battery. The current is shown to emerge from the positive terminal, pass along the length of the rectangular bar, and enter the negative terminal of the battery. The resistance of the rectangular bar along the length is shown as R and the current is shown as I. Part b of the figure shows a voltage V applied along the width of the same rectangular bar using a battery. The current is shown to emerge from the positive terminal, pass along the width of the rectangular bar, and enter the negative terminal of the battery. The resistance of the rectangular bar along the width is shown as R prime, and the current is shown as I prime.
Does current taking two different paths through the same object encounter different resistance?

If aluminum and copper wires of the same length have the same resistance, which has the larger diameter? Why?

Explain why R = R 0 ( 1 + α Δ T ) size 12{R = R rSub { size 8{0} } \( "1 "+ αΔT \) } {} for the temperature variation of the resistance R size 12{R} {} of an object is not as accurate as ρ = ρ 0 ( 1 + α Δ T ) size 12{ρ = ρ rSub { size 8{0} } \( "1 "+ αΔT \) } {} , which gives the temperature variation of resistivity ρ size 12{ρ} {} .


What is the resistance of a 20.0-m-long piece of 12-gauge copper wire having a 2.053-mm diameter?

0.104 Ω

The diameter of 0-gauge copper wire is 8.252 mm. Find the resistance of a 1.00-km length of such wire used for power transmission.

If the 0.100-mm diameter tungsten filament in a light bulb is to have a resistance of 0.200 Ω at 20 . C size 12{"20" "." 0°"C"} {} , how long should it be?

2 . 8 × 10 2 m size 12{2 "." "82"´"10" rSup { size 8{-2} } " m"} {}

Find the ratio of the diameter of aluminum to copper wire, if they have the same resistance per unit length (as they might in household wiring).

What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when 1.00 × 10 3 V is applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)

1 . 10 × 10 3 A size 12{1 "." "10"´"10" rSup { size 8{-3} } " A"} {}

(a) To what temperature must you raise a copper wire, originally at 20.0ºC , to double its resistance, neglecting any changes in dimensions? (b) Does this happen in household wiring under ordinary circumstances?

A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.00% from its value at 20 . C size 12{"20" "." 0°"C"} {} . Over what temperature range can it be used?

C to 45ºC

Of what material is a resistor made if its resistance is 40.0% greater at 100º C size 12{"100"°"C"} {} than at 20 . C size 12{"20" "." 0°"C"} {} ?

An electronic device designed to operate at any temperature in the range from –10 . C to 55 . C size 12{"10" "." 0°"C to 55" "." 0°"C"} {} contains pure carbon resistors. By what factor does their resistance increase over this range?


(a) Of what material is a wire made, if it is 25.0 m long with a 0.100 mm diameter and has a resistance of 77 . 7 Ω size 12{"77" "." 7 %OMEGA } {} at 20 . C size 12{"20" "." 0°"C"} {} ? (b) What is its resistance at 150º C size 12{"150"°"C"} {} ?

Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease in the resistance of a constantan wire starting at 20 . C size 12{"20" "." 0°"C"} {} ?


A wire is drawn through a die, stretching it to four times its original length. By what factor does its resistance increase?

A copper wire has a resistance of 0 . 500 Ω size 12{0 "." "500 " %OMEGA } {} at 20 . C size 12{"20" "." 0°"C"} {} , and an iron wire has a resistance of 0 . 525 Ω size 12{0 "." "525 " %OMEGA } {} at the same temperature. At what temperature are their resistances equal?

17º C size 12{-"17"°"C"} {}

(a) Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has α = 0 . 0600 / ºC size 12{α"=-"0 "." "0600"/°"C"} {} ) when it is at the same temperature as the patient. What is a patient’s temperature if the thermistor’s resistance at that temperature is 82.0% of its value at 37 . C size 12{"37" "." 0°"C"} {} (normal body temperature)? (b) The negative value for α size 12{α} {} may not be maintained for very low temperatures. Discuss why and whether this is the case here. (Hint: Resistance can’t become negative.)

Integrated Concepts

(a) Redo [link] taking into account the thermal expansion of the tungsten filament. You may assume a thermal expansion coefficient of 12 × 10 6 / ºC size 12{"12"´"10" rSup { size 8{-6} } /°"C"} {} . (b) By what percentage does your answer differ from that in the example?

(a) 4 . 7 Ω size 12{4 "." 7 %OMEGA } {} (total)

(b) 3.0% decrease

Unreasonable Results

(a) To what temperature must you raise a resistor made of constantan to double its resistance, assuming a constant temperature coefficient of resistivity? (b) To cut it in half? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable, or which premises are inconsistent?

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
How we can toraidal magnetic field
Aditya Reply
How we can create polaidal magnetic field
Mykayuh Reply
Because I'm writing a report and I would like to be really precise for the references
Gre Reply
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
Gre Reply
Practice Key Terms 2

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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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