What is the resistance of a 150 ﻿m aluminum wire of radius 1.5 ﻿mm ?

To find the resistance \( R \) of the aluminum wire, we can use the formula:

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

Where:
- \( R \) is the resistance.
- \( \rho \) is the resistivity of aluminum (approximately \( 2.82 \times 10^{-8} \, \Omega \cdot \text{m} \)).
- \( L \) is the length of the wire (150 meters).
- \( A \) is the cross-sectional area of the wire (since the wire is cylindrical, the cross-sectional area is \( A = \pi r^2 \)).

Given:
- \( r = 1.5 \, \text{mm} = 0.0015 \, \text{m} \),
- \( L = 150 \, \text{m} \).

### Step 1: Calculate the cross-sectional area \( A \)
\[
A = \pi r^2 = \pi (0.0015)^2 \, \text{m}^2 = \pi \times 2.25 \times 10^{-6} \, \text{m}^2
\]

### Step 2: Calculate the resistance \( R \)
Now plug the values into the formula:

\[
R = \frac{2.82 \times 10^{-8} \times 150}{\pi \times 2.25 \times 10^{-6}}
\]

Let me compute that for you.The resistance of the 150-meter aluminum wire with a radius of 1.5 mm is approximately \( 0.598 \, \Omega \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the length of the wire affect its resistance?
2. What would the resistance be if the wire were made of copper instead of aluminum?
3. How does temperature affect the resistance of a metal wire?
4. How would the resistance change if the radius of the wire were doubled?
5. What are some practical applications of knowing a wire's resistance?

**Tip:** For wires of the same material, resistance is directly proportional to length and inversely proportional to the cross-sectional area.

What is the resistance of a 150 m aluminum wire of radius 1.5 mm?

Find the resistance of a 150-meter aluminum wire with a radius of 1.5 mm using the formula R = ρL / A. This problem explores key concepts like resistivity, wire length, and cross-sectional area, making it suitable for Grades 10-12 physics students.

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