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

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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} {} .

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Problems&Exercises

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

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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.

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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"} {}

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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).

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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"} {}

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(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?

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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

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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"} {} ?

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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?

1.03

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(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"} {} ?

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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"} {} ?

0.06%

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

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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"} {}

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(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.)

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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

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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?

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Questions & Answers

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below me
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
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what is a conductor
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hello
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why below you
Timothy
no....I said below me ...... nothing below .....ok?
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corona charge can verify
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remains the temperature
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dude.....next time Google it
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the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
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Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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