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 find the length of the copper wire given its resistance, radius, and specific resistance, we can use the formula for resistance in terms of resistivity:

### Step-by-Step Solution:

1. **Write the formula for resistance**:
The resistance \( R \) of a wire can be expressed as:
\[ R = \frac{\rho L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the specific resistance (resistivity),
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire.

2. **Identify the given values**:
- Resistance \( R = 0.1 \, \Omega \)
- Specific resistance \( \rho = 3.14 \times 10^{-8} \, \Omega \cdot m \)
- Radius \( r = 1 \, mm = 1 \times 10^{-3} \, m \)

3. **Calculate the cross-sectional area \( A \)**:
The area \( A \) of the wire can be calculated using the formula for the area of a circle:
\[ A = \pi r^2 \]
Substituting the radius:
\[ A = \pi (1 \times 10^{-3})^2 = \pi \times 10^{-6} \, m^2 \]

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

5. **Calculate the length**:
First, simplify the expression:
\[ L = \frac{0.1 \cdot \pi \times 10^{-6}}{3.14 \times 10^{-8}} \]
Since \( \pi \approx 3.14 \), we can cancel \( \pi \):
\[ L \approx \frac{0.1 \cdot 3.14 \times 10^{-6}}{3.14 \times 10^{-8}} = \frac{0.1 \times 10^{-6}}{10^{-8}} = 0.1 \times 10^{2} = 10 \, m \]

### Final Answer:
The length of the wire is approximately \( 10 \, m \).

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