A BIG spool of copper wire has a resistance of 8 2 as measured from end of the wire to the other. If the wire has a diameter of 3.0 mm and if copper has a resistivity of 1.68x10-8 m, find the length of the wire in meters.

A BIG spool of copper wire has a resistance of 8 2 as measured from end of the wire to the other. If the wire has a diameter of 3.0 mm and if copper has a resistivity of 1.68x10-8 m, find the length of the wire in meters.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter28: Current And Resistance

Section: Chapter Questions

Problem 67PQ

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Concept explainers

Temperature Variance of Resistance

Electrical resistance or simply resistance is the property of a material that opposes the free flow of electrons through it. The total amount of resistance to the flow of charges (or current) is affected by many factors like the length of the conducting material, its cross-sectional area, resistivity, and temperature.

Question

19 please need help, keep in mind the 7 basic units and watch the sig figs. Please write in standard form need to see all the numbers in solution thank you so much

A BIG spool of copper wire has a resistance of 8 2 as measured from end of the wire
to the other. If the wire has a diameter of 3.0 mm and if copper has a resistivity of
1.68x10-8 m, find the length of the wire in meters.
Your Answer:

Expert Solution

Concept

Given: Diameter of wire $d = 3 m m$ , Radius of wire $r = \frac{d}{2} = \frac{3 m m}{2} = 1.5 m m = 1.5 \times 10^{- 3} m$ , Resistivity of wire $ρ = 1.68 \times 10^{- 8} Ω m$ , Resistance of wire $R = 8 Ω$ .

Required: Length of the wire $(L)$ .

Resistance of a wire of length L and area of cross section A is given by, $R = \frac{ρ L}{A}$ , where $ρ$ is resistivity of wire.

$R = \frac{ρ L}{A} = \frac{ρ L}{π r^{2}}$

$L = \frac{π r^{2} R}{ρ}$

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