A copper wire of radius a = 0.204 mm has an aluminum jacket of outer radius b = 0.296 mm. There is a current i =2.61 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 x 10-80-m and 2.75 x 10 8Q-m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 16.5 V between the ends maintains the current, what is the length in meters of the composite wire? (a) Number i Units A (b) Number i Units A (c) Number i Units m
A copper wire of radius a = 0.204 mm has an aluminum jacket of outer radius b = 0.296 mm. There is a current i =2.61 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 x 10-80-m and 2.75 x 10 8Q-m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 16.5 V between the ends maintains the current, what is the length in meters of the composite wire? (a) Number i Units A (b) Number i Units A (c) Number i Units m
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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![**Physics Problem: Electrical Resistivity in Composite Wires**
A copper wire of radius \( a = 0.204 \, \text{mm} \) has an aluminum jacket of outer radius \( b = 0.296 \, \text{mm} \). There is a current \( i = 2.61 \, \text{A} \) in the composite wire. Take the resistivity for copper and aluminum to be \( 1.69 \times 10^{-8} \, \Omega \cdot \text{m} \) and \( 2.75 \times 10^{-8} \, \Omega \cdot \text{m} \), respectively. Calculate the current in:
(a) The copper.
(b) The aluminum.
(c) If a potential difference \( V = 16.5 \, \text{V} \) between the ends maintains the current, what is the length in meters of the composite wire?
**Solution:**
### Part (a)
**Number:**
[ ............................. ] **Units:** [A]
### Part (b)
**Number:**
[ ............................. ] **Units:** [A]
### Part (c)
**Number:**
[ ............................. ] **Units:** [m]
*Notes:*
1. **Calculating the Current in Copper (a):**
- The formula for calculating the current in Copper using resistivity and dimensions.
2. **Calculating the Current in Aluminum (b):**
- Similarly, the formula for calculating the current in Aluminum with its respective resistivity and dimensions would be used.
3. **Finding the Length of the Composite Wire (c):**
- Using the supplied potential difference and resulting current, the length of the composite wire can be calculated.
**Explanation:**
- The problem involves determining the distribution of electrical current in a composite wire made of copper and aluminum.
- The resistivity (\( \rho \)) of materials and the geometrical dimensions play crucial roles.
- The potential difference is provided to find the overall length that supports the stated current.
**Diagrams/Graphs:**
- Not applicable. The question is text-based and involves calculations.
**Learning Outcomes:**
- Understanding of how resistivity affects the flow of current through different materials.
- Application of Ohm's law and resistivity relations in coaxial structures.
- Analysis of series and parallel combinations in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8b65224-21df-49da-a8da-84f6a1af571d%2F3e2f6044-cba4-475d-b6b7-9c4f7c210e11%2Fq0zllobi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Electrical Resistivity in Composite Wires**
A copper wire of radius \( a = 0.204 \, \text{mm} \) has an aluminum jacket of outer radius \( b = 0.296 \, \text{mm} \). There is a current \( i = 2.61 \, \text{A} \) in the composite wire. Take the resistivity for copper and aluminum to be \( 1.69 \times 10^{-8} \, \Omega \cdot \text{m} \) and \( 2.75 \times 10^{-8} \, \Omega \cdot \text{m} \), respectively. Calculate the current in:
(a) The copper.
(b) The aluminum.
(c) If a potential difference \( V = 16.5 \, \text{V} \) between the ends maintains the current, what is the length in meters of the composite wire?
**Solution:**
### Part (a)
**Number:**
[ ............................. ] **Units:** [A]
### Part (b)
**Number:**
[ ............................. ] **Units:** [A]
### Part (c)
**Number:**
[ ............................. ] **Units:** [m]
*Notes:*
1. **Calculating the Current in Copper (a):**
- The formula for calculating the current in Copper using resistivity and dimensions.
2. **Calculating the Current in Aluminum (b):**
- Similarly, the formula for calculating the current in Aluminum with its respective resistivity and dimensions would be used.
3. **Finding the Length of the Composite Wire (c):**
- Using the supplied potential difference and resulting current, the length of the composite wire can be calculated.
**Explanation:**
- The problem involves determining the distribution of electrical current in a composite wire made of copper and aluminum.
- The resistivity (\( \rho \)) of materials and the geometrical dimensions play crucial roles.
- The potential difference is provided to find the overall length that supports the stated current.
**Diagrams/Graphs:**
- Not applicable. The question is text-based and involves calculations.
**Learning Outcomes:**
- Understanding of how resistivity affects the flow of current through different materials.
- Application of Ohm's law and resistivity relations in coaxial structures.
- Analysis of series and parallel combinations in
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