A long conducting rod has length L = 2.60 m and a square cross section with side d = 3.70E-3 m, as shown in the figure. The electric resistance between the two ends A and B of the rod is measured to be 0.636 2. What is the resistivity of material that makes the rod (in Ohm meters)? d B L

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**Problem Statement:**

A long conducting rod has length \( L = 2.60 \, \text{m} \) and a square cross section with side \( d = 3.70 \times 10^{-3} \, \text{m} \), as shown in the figure. The electric resistance between the two ends A and B of the rod is measured to be \( 0.636 \, \Omega \). What is the resistivity of material that makes the rod (in Ohm\(\cdot\)meters)?

**Explanation of the Diagram:**

The diagram shows a rectangular prism representing a conducting rod. The dimensions are marked as follows:
- The length of the rod \( L \) is measured horizontally.
- The cross-sectional side \( d \) is marked vertically at both ends.
- Points A and B are located at the two ends of the rod along its length.

The rod has a uniform square cross section and the resistance between points A and B is provided.

**Given Data:**
- Length of the rod, \( L = 2.60 \, \text{m} \)
- Side of the square cross section, \( d = 3.70 \times 10^{-3} \, \text{m} \)
- Resistance measured between points A and B, \( R = 0.636 \, \Omega \)

**Objective:**
Determine the resistivity (ρ) of the material that makes up the rod.

**Solution:**

To find the resistivity, use the formula for resistance in terms of resistivity:

\[ R = \rho \frac{L}{A} \]

Where:
- \( R \) = Resistance
- \( \rho \) = Resistivity
- \( L \) = Length of the conductor
- \( A \) = Cross-sectional area of the conductor

For our square cross-sectional rod:

\[ A = d^2 \]

Substitute \( A \) and re-arrange the formula to solve for \( \rho \):

\[ \rho = R \frac{A}{L} = R \frac{d^2}{L} \]

Substituting the given values:

\[ d = 3.70 \times 10^{-3} \, \text{m} \]
\[ d^2 = (3.70 \times 10^{-3} \, \text{m})^2
Transcribed Image Text:**Problem Statement:** A long conducting rod has length \( L = 2.60 \, \text{m} \) and a square cross section with side \( d = 3.70 \times 10^{-3} \, \text{m} \), as shown in the figure. The electric resistance between the two ends A and B of the rod is measured to be \( 0.636 \, \Omega \). What is the resistivity of material that makes the rod (in Ohm\(\cdot\)meters)? **Explanation of the Diagram:** The diagram shows a rectangular prism representing a conducting rod. The dimensions are marked as follows: - The length of the rod \( L \) is measured horizontally. - The cross-sectional side \( d \) is marked vertically at both ends. - Points A and B are located at the two ends of the rod along its length. The rod has a uniform square cross section and the resistance between points A and B is provided. **Given Data:** - Length of the rod, \( L = 2.60 \, \text{m} \) - Side of the square cross section, \( d = 3.70 \times 10^{-3} \, \text{m} \) - Resistance measured between points A and B, \( R = 0.636 \, \Omega \) **Objective:** Determine the resistivity (ρ) of the material that makes up the rod. **Solution:** To find the resistivity, use the formula for resistance in terms of resistivity: \[ R = \rho \frac{L}{A} \] Where: - \( R \) = Resistance - \( \rho \) = Resistivity - \( L \) = Length of the conductor - \( A \) = Cross-sectional area of the conductor For our square cross-sectional rod: \[ A = d^2 \] Substitute \( A \) and re-arrange the formula to solve for \( \rho \): \[ \rho = R \frac{A}{L} = R \frac{d^2}{L} \] Substituting the given values: \[ d = 3.70 \times 10^{-3} \, \text{m} \] \[ d^2 = (3.70 \times 10^{-3} \, \text{m})^2
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