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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

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) 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 internal energy produced in copper wire

Explanation

Given Info: The 12-gauge copper wire has diameter 0.205cm carries current 20.0A . The rate of internal energy is calculated for 1.00m length of copper wire.

Explanation:

Formula to calculate the resistance of copper wire is,

Rcu=ρcuLA

  • Rcu is the resistance of copper wire,
  • ρcu is the resistivity of copper,
  • A is the area of cross section of copper wire,
  • L is the length of copper wire,

Area of circular cross section of wire is given by

A=πd42

  • d is the diameter of the wire

Substitute πd2/4 for A in the above equation to rewrite R .

Rcu=4ρcuLπd2

Substitute 1.7×108Ωm for ρcu , 1.00m for l , 3.14 for π  and 0.205cm for d to find Rcu

Rcu=4(1.7×108Ωm)(1

(b)

To determine
The rate of internal energy produced in 12-gauge aluminum wire.

(c)

To determine
Whether a 12 gauge aluminum wire is safe as 12-gauge copper wire.

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