   Chapter 17, Problem 21P

Chapter
Section
Textbook Problem

The resistivity of copper is 1.70 × 10−8 Ω · m. (a) Find the resistance of a copper wire with a radius of 1.29 mm and a length of 1.00 m. (b) Calculate the volume of copper in the wire. (c) Suppose that volume of copper is formed into a new wire with a length of 2.00 m. Find the new resistance of the wire.

(a)

To determine
The resistance of the copper wire.

Explanation

Given Info: The resistivity of copper is 1.70×108Ωm The wire has radius 1.29mm and length 1.00m

Explanation:

Formula to calculate the resistance of wire is,

R=ρlA

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

Area of circular cross section of wire is given by

A=πr2

• r is the radius of the wire

Substitute equation for area in the above equation to rewrite R .

R=ρlπr2

Substitute 1.70×108Ωm for ρ , 1.00m for l , 3

(b)

To determine
The volume of the copper wire.

(c)

To determine
The resistance of the copper wire.

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