Three resistors are made out of three different materials an have different (but uniform) cross sections. Resistor 1 has : circular cross section of radius 2.90 mm. Resistor 2 has a square cross section with a side length of 2.22 mm. The th resistor's cross section is a right triangle with two sides of lenoth 5.50 mm. All of the resistors are 0.913 cm in lenoth
Three resistors are made out of three different materials an have different (but uniform) cross sections. Resistor 1 has : circular cross section of radius 2.90 mm. Resistor 2 has a square cross section with a side length of 2.22 mm. The th resistor's cross section is a right triangle with two sides of lenoth 5.50 mm. All of the resistors are 0.913 cm in lenoth
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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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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![**Resistor Analysis and Calculation**
Three resistors are made from three different materials and feature distinct cross-sectional shapes. Each resistor has a uniform cross section and a length of 0.913 cm. Below are the details for each:
- **Resistor 1**:
- Shape: Circle
- Radius: 2.90 mm
- Material: Material 1
- Resistivity: 0.00367 Ω·m
- **Resistor 2**:
- Shape: Square
- Side Length: 2.22 mm
- Material: Material 2
- Resistivity: 0.488 Ω·m
- **Resistor 3**:
- Shape: Right Triangle
- Side Lengths: 5.50 mm each
- Material: Material 3
- Resistivity: 7.99 × 10⁻⁵ Ω·m
**Resistivity Table:**
| Material | Resistivity (Ω·m) |
|------------|-------------------|
| Material 1 | 0.00367 |
| Material 2 | 0.488 |
| Material 3 | 7.99 × 10⁻⁵ |
**Cross-Section Diagrams:**
1. **Circle (Resistor 1)**: A blue circle representing the circular cross-section.
2. **Square (Resistor 2)**: A green square denoting the square cross-section.
3. **Right Triangle (Resistor 3)**: A yellow right triangle outlining the triangular cross-section.
**Formulas:**
The resistance \( R \) is given by:
\[ R = \frac{\rho \cdot L}{A} \]
where:
- \( \rho \) = Resistivity of the material,
- \( L \) = Length of the resistor,
- \( A \) = Cross-sectional area.
For the calculations:
- The area of the circular cross-section (Resistor 1) is calculated using \( A = \pi r^2 \).
- The area of the square cross-section (Resistor 2) is \( A = \text{side length}^2 \).
- The area of the triangular cross-section (Resistor 3) is \( A = \frac{1}{2} \times \text{side}^2 \).
**Resistance Calcul](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86752c1b-283e-4521-8dc6-ff7e4cb88ac7%2F7d02d606-006d-4e63-9667-8322973b71d2%2F3mg3swc_processed.png&w=3840&q=75)
Transcribed Image Text:**Resistor Analysis and Calculation**
Three resistors are made from three different materials and feature distinct cross-sectional shapes. Each resistor has a uniform cross section and a length of 0.913 cm. Below are the details for each:
- **Resistor 1**:
- Shape: Circle
- Radius: 2.90 mm
- Material: Material 1
- Resistivity: 0.00367 Ω·m
- **Resistor 2**:
- Shape: Square
- Side Length: 2.22 mm
- Material: Material 2
- Resistivity: 0.488 Ω·m
- **Resistor 3**:
- Shape: Right Triangle
- Side Lengths: 5.50 mm each
- Material: Material 3
- Resistivity: 7.99 × 10⁻⁵ Ω·m
**Resistivity Table:**
| Material | Resistivity (Ω·m) |
|------------|-------------------|
| Material 1 | 0.00367 |
| Material 2 | 0.488 |
| Material 3 | 7.99 × 10⁻⁵ |
**Cross-Section Diagrams:**
1. **Circle (Resistor 1)**: A blue circle representing the circular cross-section.
2. **Square (Resistor 2)**: A green square denoting the square cross-section.
3. **Right Triangle (Resistor 3)**: A yellow right triangle outlining the triangular cross-section.
**Formulas:**
The resistance \( R \) is given by:
\[ R = \frac{\rho \cdot L}{A} \]
where:
- \( \rho \) = Resistivity of the material,
- \( L \) = Length of the resistor,
- \( A \) = Cross-sectional area.
For the calculations:
- The area of the circular cross-section (Resistor 1) is calculated using \( A = \pi r^2 \).
- The area of the square cross-section (Resistor 2) is \( A = \text{side length}^2 \).
- The area of the triangular cross-section (Resistor 3) is \( A = \frac{1}{2} \times \text{side}^2 \).
**Resistance Calcul
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