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. [Table of resistivities](a) Calculate the rate at which internal energy is produced in 2.45 m of 12-gauge copper wire carrying a current of 20.0 A.Input box: 101.00 (marked with a red X)Hint: If you know the resistance of a wire, how do you calculate the rate at which internal energy is produced for a given current? (in watts)(b) Repeat the calculation for a 12-gauge aluminum wire.Input box: ______ WExplain whether a 12-gauge aluminum wire would be as safe as a copper wire.[Large empty text box for explanation]

Given That: The length of copper and aluminium wire is: l=2.45m The current in the wire is I=20A…

Answered: Lesidential building codes typically…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

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. [Table of resistivities]

(a) Calculate the rate at which internal energy is produced in 2.45 m of 12-gauge copper wire carrying a current of 20.0 A.

Input box: 101.00 (marked with a red X)

Hint: If you know the resistance of a wire, how do you calculate the rate at which internal energy is produced for a given current? (in watts)

(b) Repeat the calculation for a 12-gauge aluminum wire.

Input box: ______ W

Explain whether a 12-gauge aluminum wire would be as safe as a copper wire.

[Large empty text box for explanation]

Expert Solution

Step 1

Given That:

The length of copper and aluminium wire is:

l=2.45m

The current in the wire is I=20A
The diameter of the 12 gauge wire is d=2.05 $\times 10^{- 3}$ m

Resistivity of Copper Wire is $ρ_{c} = 1.68 \times 10^{- 8} Ω . m$

Resistivity of Aluminium wire is $ρ_{a} = 2.56 \times 10^{- 8} Ω . m$

a) The Equation to calculate the resistance of copper wire is

$R_{C u} = \frac{4 ρ_{c} l}{π d^{2}} s u b s t i t u t i n g t h e v a l u e s i n t h e a b o v e e q u a t i o n . R_{C u} = \frac{4 (1.68 \times 10^{- 8}) (2.45)}{π {(2.05 \times 10^{- 3})}^{2}} R_{C u} = 1.24766 \times 10^{- 2} Ω T h e e q u a t i o n t o c a l c u l a t e t h e r a t e o f i n t e r n a l e n e r g y p r o d u c e d i s E_{c} = I^{2} R_{C u} S u b s t i t u t i n g t h e v a l u e s E_{c} = {(2)}^{2} (1.24766 \times 10^{- 2}) E_{c} = 4.9906 \times 10^{- 2} W$