   Chapter 17, Problem 14P

Chapter
Section
Textbook Problem

Suppose you wish to fabricate a uniform wire out of 1.00 g of copper. If the wire is to have a resistance R = 0.500 Ω, and if all the copper is to be used, what will be (a) the length and (b) the diameter of the wire?

(a)

To determine
The length of copper wire.

Explanation

Given Info: The mass of copper wire is 1.00g and Copper wire has resistance 0.500Ω , The mass of copper wire is 1.00g Copper wire has resistance 0.500Ω

Explanation:

Formula to calculate volume is,

V=MD

• V is the volume of copper wire,
• M is the mass of copper wire,
• D is the density of copper,

Substitute 1.00g for M and 8.92×103kgm3 for d in the above equation to find V

V=(1.00g)(10-3kg1g)(8.92×103kgm3)=1.12×107m3

Volume of copper wire is 1.12×107m3

Formula to calculate resistivity is

ρ=RAL

• ρ is the resistivity of copper,
• R is the resistance of copper
• A is the area of cross section of copper wire,
• L is the length of copper wire,

Substitute 1.7×108Ωm for ρ and 0

(b)

To determine
The diameter of copper wire.

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