Two copper wire of length l and 2l have radii, r and 2r respectively. What si the ratio of their specific resistance.?

Options

A. `1:2`
B. `2:1`
C. `1:1`
D. `1:3`

Explanation

To solve the problem, we need to determine the ratio of specific resistances (resistivities) of two copper wires with different lengths and radii.

### Step-by-Step Solution:

1. **Understand Specific Resistance (Resistivity)**:
- Specific resistance (or resistivity) is a property of the material that does not depend on its dimensions (length and cross-sectional area). It is denoted by the symbol \( \rho \).

2. **Identify the Wires**:
- We have two wires:
- Wire 1: Length \( l \), Radius \( r \)
- Wire 2: Length \( 2l \), Radius \( 2r \)

3. **Recognize Material**:
- Both wires are made of copper. Therefore, they have the same resistivity \( \rho \).

4. **Calculate the Ratio of Specific Resistances**:
- Since both wires are made of the same material (copper), their specific resistances (resistivities) are equal:
\[ \frac{\rho_1}{\rho_2} = \frac{\rho}{\rho} = 1 \]

5. **Conclusion**:
- The ratio of the specific resistances of the two copper wires is \( 1 \).

### Final Answer:
The ratio of their specific resistance is \( 1:1 \).

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