26.12 (a) A 34.6-m length of copper wire at 20.0°C has a radius of 0.28 mm. If a potential difference of 7.50 V isapplied across the length of the wire, determine the current in the wire.(b) If the wire is heated to 31.0°C while the 7.50-V potential difference is maintained, what is the resultingcurrent in the wire?Step 1(a) From the table below, the resistivity of copper at 20.0°C is Pcucoefficient of resistivity Cuhave R =pL/A. Therefore, the resistance Ro of the copper wire at To=Ro=PcuA=PCu²πr²-81.7 x 10 m with temperature3.9 x 10-3 (°C)-¹. From the general relation between resistance and resistivity, we20.0°C is given by the following.(1.7 x1.7 x 10-8 mJU 0.28m)( 34.634.6 m0.28 x 10-3 m2=2.382.39| Ω. Step 2When a 7.50-V potential difference is applied across the length of this wire at 20.0°C, the resulting current IoisIoI ==AVRoIIAVR7.50Step 3=(b) At T = 31.0°C, the res tance is given by Rresistivity. The current in the copper wire becomes2.392.397.5 V2.39| ΩAVRo[1 + acu(T - To)]A.3.137.53.14 A.Ro[1 + a(TTO)], where a is the temperature coefficient ofv)Ω 1 + (3.9 x 10-³ (°C)-¹)(31.0Your response differs from the correct answer by more than 100%.°

Answered: Image /qna-images/answer/a4f1720c-4ea2-44f0-81b9-1e7962cd02db.jpg

(b) At T = 31.0°C, the resistance is given by R = Ro[1 + a(T-To)], where a is the temperature coefficient of resistivity. The current in the copper wire becomes AV Ro[1 + acu(T-To)] I = = AV R = 2.39 M)1 + (3.9 × 10-³ (°C)-¹)( 31.0 Your response differs from the correct answer by more than 100%. °C 7.5 A.

(b) At T = 31.0°C, the resistance is given by R = Ro[1 + a(T-To)], where a is the temperature coefficient of resistivity. The current in the copper wire becomes AV Ro[1 + acu(T-To)] I = = AV R = 2.39 M)1 + (3.9 × 10-³ (°C)-¹)( 31.0 Your response differs from the correct answer by more than 100%. °C 7.5 A.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter28: Current And Resistance

Section28.3: Current Density

Problem 28.3CE

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