In house wiring, copper wire `2.05 mm` in diameter is often used. Find the resistane of `35.0 m` long wire. Specific resistance of copper is `1.72xx10^-8Omega-m`.

Explanation

To find the resistance of a copper wire with a given diameter and length, we can use the formula for resistance in terms of resistivity, length, and cross-sectional area:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Diameter of the wire, \( d = 2.05 \, \text{mm} = 2.05 \times 10^{-3} \, \text{m} \)
- Length of the wire, \( L = 35.0 \, \text{m} \)
- Specific resistance (resistivity) of copper, \( \rho = 1.72 \times 10^{-8} \, \Omega \cdot \text{m} \)

2. **Calculate the Cross-Sectional Area (A) of the Wire:**
The cross-sectional area \( A \) of a wire with a circular cross-section is given by:
\[ A = \frac{\pi}{4} d^2 \]
Substituting the diameter:
\[ A = \frac{\pi}{4} (2.05 \times 10^{-3})^2 \]
\[ A \approx 0.785 \times (4.2025 \times 10^{-6}) \, \text{m}^2 \]
\[ A \approx 3.29 \times 10^{-6} \, \text{m}^2 \]

3. **Use the Resistance Formula:**
The resistance \( R \) of the wire can be calculated using the formula:
\[ R = \frac{\rho L}{A} \]
Substituting the values:
\[ R = \frac{(1.72 \times 10^{-8}) \times 35.0}{3.29 \times 10^{-6}} \]

4. **Calculate the Resistance:**
\[ R = \frac{6.02 \times 10^{-7}}{3.29 \times 10^{-6}} \approx 0.1829 \, \Omega \]
Converting to milli-ohms:
\[ R \approx 182.9 \, \text{m}\Omega \]

### Final Answer:
The resistance of the 35.0 m long copper wire is approximately **182.9 milli-ohms**.

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