   Chapter 17, Problem 5P

Chapter
Section
Textbook Problem

A certain laboratory experiment requires an aluminum wire of length of 32.0 m and a resistance of 2.50 Ω at 20.0°C. What diameter wire must be used?

To determine
The diameter of aluminum wire.

Explanation

Given Info: The length of aluminum wire with length 32.0m has resistance 2.50Ω at 20.0C and resistivity of aluminum wire is 2.82×108Ωm from table 17.1.

Explanation:

Formula to calculate diameter of aluminum wire is

R=ρLA

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

Formula to calculate circular area of cross section of wire is,

A=πd24

• A is the area of cross section,
• d is the diameter of the wire,

Substitute the relation for area of cross section in above equation to rewrite R

R=ρL(πd24)d=2ρLπR

Substitute 2.82×108Ωm for ρ , 32

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