   Chapter 17, Problem 27P

Chapter
Section
Textbook Problem

Gold is the most ductile of all metals. For example, one gram of gold can be drawn into a wire 2.40 km long. The density of gold is 19.3 × 103 kg/m3, and its resistivity is 2.44 × 10−8Ω · m. What is the resistance of such a wire at 20.0°C?

To determine
The resistance of gold wire at 20°C

Explanation

Given Info: The mass of gold wire is 1.0g and the density is 19.3×103kg/m3 The length of wire is 2.40km The resistivity of gold is given by 2.44×108Ωm , The mass of gold wire is 1.0g and the density is 19.3×103kg/m3 The length of wire is 2.40km The resistivity of gold is given by 2.44×108Ωm

Explanation:

Formula which relates mass, volume and density is

V=MD

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

Formula to calculate volume from area of cross section and the length is given by,

V=AL

• A is the area of cross section of gold wire
• L is the length of gold wire

Substitute this relation in the previous equation to find A .

A=MDL

Substitute 1.00g for M , 19.3×103kg/m3 for D , and 2.40km for L in the above equation to find A .

A=(1.00g)(10-3kg1g)(19

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