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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb234898a-ca00-4740-ae3d-79576f672843%2Fbc4d581a-1ad5-41bf-96b2-4df398beda86%2Fvyerr3o_processed.jpeg&w=3840&q=75)
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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