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Residential building codes typically require the use of 12-gauge copper wire (diameter 0.205 cm) for wiring receptacles. Such circuits carry currents as large as 20.0 A. If a wire of smaller diameter (with a higher gauge number) carried that much current, the wire could rise to a high temperature and cause a fire. (a) Calculate the rate at which internal energy is produced in 1.00 m of 12-gauge copper wire carrying 20.0 A. (b) What If? Repeat the calculation for a 12-gauge aluminum wire. (c) Explain whether a 12-gauge aluminum wire would be as safe as a copper wire.

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Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

Solutions

Chapter
Section
BuyFindarrow_forward

Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
Chapter 26, Problem 28P
Textbook Problem
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Residential building codes typically require the use of 12-gauge copper wire (diameter 0.205 cm) for wiring receptacles. Such circuits carry currents as large as 20.0 A. If a wire of smaller diameter (with a higher gauge number) carried that much current, the wire could rise to a high temperature and cause a fire. (a) Calculate the rate at which internal energy is produced in 1.00 m of 12-gauge copper wire carrying 20.0 A. (b) What If? Repeat the calculation for a 12-gauge aluminum wire. (c) Explain whether a 12-gauge aluminum wire would be as safe as a copper wire.

(a)

To determine
The rate of production of internal energy.

Explanation of Solution

Given Info: The current is 20.0A and the length of the wire is 1m . The diameter of the wire is 0.205cm .

The formula for the area of wire is,

A=π(d2)2

Here,

d is the diameter of the wire.

Substitute 0.205cm for d in above equation to find A .

A=π(0.205cm×(102m1cm)2)2=6.6×106m2

Thus, the area of wire is 6.6×106m2 .

The formula for the resistance is,

R=ρlA (1)

Here,

ρ is the resistivity.

l is the length of the tube.

A is the area.

Substitute 6.6×106m2 for A , 1.7×108Ωm for ρ and 1m for l in equation (1) to find the value of R

(b)

To determine
The rate of production of internal energy.

(c)

To determine
The wire which will be safe.

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Chapter 26 Solutions

Physics for Scientists and Engineers
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