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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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.
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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