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

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Chapter1: Units, Trigonometry. And Vectors
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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
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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