When the resistance of copper wire is `0.1 Omega` and the radius is 1mm, then the length of the wire is (specific resistance of copper is `3.14 xx 10^(-8) ohm xx m`)

Options

A. 10 cm
B. 10 m
C. 100 m
D. 100 cm

Explanation

To solve the problem of finding the length of a copper wire given its resistance, radius, and specific resistance, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Resistance (R) = 0.1 Ω
- Radius (r) = 1 mm = 1 x 10^(-3) m
- Specific Resistance (ρ) = 3.14 x 10^(-8) Ω·m

2. **Use the Formula for Resistance**:
The resistance of a wire can be calculated using the formula:
\[ R = \frac{\rho \cdot L}{A} \]
where:
- \( R \) = Resistance
- \( \rho \) = Specific Resistance
- \( L \) = Length of the wire
- \( A \) = Cross-sectional area of the wire

3. **Calculate the Cross-Sectional Area (A)**:
The cross-sectional area of a circular wire is given by:
\[ A = \pi r^2 \]
Substituting the radius:
\[ A = \pi (1 \times 10^{-3})^2 = \pi \times 10^{-6} \text{ m}^2 \]

4. **Substitute Known Values into the Resistance Formula**:
Rearranging the resistance formula to solve for \( L \):
\[ L = \frac{R \cdot A}{\rho} \]
Now substituting the values:
\[ L = \frac{0.1 \cdot (\pi \times 10^{-6})}{3.14 \times 10^{-8}} \]

5. **Simplify the Expression**:
Since \( \pi \approx 3.14 \), we can simplify:
\[ L = \frac{0.1 \cdot (3.14 \times 10^{-6})}{3.14 \times 10^{-8}} \]
The \( \pi \) cancels out:
\[ L = \frac{0.1 \times 10^{-6}}{10^{-8}} = 0.1 \times 10^{2} = 10 \text{ m} \]

6. **Final Answer**:
The length of the wire is \( L = 10 \) meters.