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A copper wire of radius a = 0.161 mm has an aluminum jacket of outer radius b = 0.218 mm. There is a current i = 1.58 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 × 10-8-m and 2.75 × 10-8-m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 11.8 V between the ends maintains the current, what is the length in meters of the composite wire?

A copper wire of radius a = 0.161 mm has an aluminum jacket of outer radius b = 0.218 mm. There is a current i = 1.58 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 × 10-8-m and 2.75 × 10-8-m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 11.8 V between the ends maintains the current, what is the length in meters of the composite wire?

College Physics
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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A copper wire of radius \( a = 0.161 \, \text{mm} \) has an aluminum jacket of outer radius \( b = 0.218 \, \text{mm} \). There is a current \( i = 1.58 \, \text{A} \) in the composite wire. Take the resistivity for copper and aluminum to be \( 1.69 \times 10^{-8} \, \Omega \cdot \text{m} \) and \( 2.75 \times 10^{-8} \, \Omega \cdot \text{m} \). Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference \( V = 11.8 \, \text{V} \) between the ends maintains the current, what is the length in meters of the composite wire?
Transcribed Image Text:A copper wire of radius \( a = 0.161 \, \text{mm} \) has an aluminum jacket of outer radius \( b = 0.218 \, \text{mm} \). There is a current \( i = 1.58 \, \text{A} \) in the composite wire. Take the resistivity for copper and aluminum to be \( 1.69 \times 10^{-8} \, \Omega \cdot \text{m} \) and \( 2.75 \times 10^{-8} \, \Omega \cdot \text{m} \). Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference \( V = 11.8 \, \text{V} \) between the ends maintains the current, what is the length in meters of the composite wire?
Expert Solution
Step 1

Given:

Radius of copper wire, a=0.161 mm=0.161×10-3 m

outer radius of jacket, b=0.218 mm=0.218×10-3 m

Current in the composite wire, i=1.58 A

Resistivity of copper, ρCu=1.69×10-8 Ω m

Resistivity of aluminum, ρAl=2.75×10-8 Ω m

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