Two wire of copper have length `L` and `2L` and cross section `2A` and A respectively .The ratio of their specific resistance would be would be

Options

A. `1:2`
B. `8:1`
C. `1:8`
D. `1:1`

Answer

To solve the problem of finding the ratio of the specific resistance (resistivity) of two copper wires with given dimensions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Specific Resistance**:
Specific resistance (or resistivity, denoted by ρ) is a property of the material itself and does not depend on the dimensions of the wire. For copper, this value is constant.

2. **Identify the Given Parameters**:
- Wire 1: Length = L, Cross-sectional area = 2A
- Wire 2: Length = 2L, Cross-sectional area = A

3. **Use the Formula for Resistance**:
The resistance (R) of a wire is given by the formula:
\[ R = \frac{\rho \cdot L}{A} \]
where:
- R is the resistance,
- ρ is the resistivity (specific resistance),
- L is the length of the wire,
- A is the cross-sectional area.

4. **Calculate the Specific Resistance for Both Wires**:
- For Wire 1:
\[ R_1 = \frac{\rho \cdot L}{2A} \]
- For Wire 2:
\[ R_2 = \frac{\rho \cdot 2L}{A} \]

5. **Determine the Ratio of Specific Resistances**:
Since the specific resistance (ρ) is a property of the material (copper in this case) and is the same for both wires, we can express the ratio of their specific resistances as:
\[ \text{Ratio} = \frac{\rho_1}{\rho_2} = \frac{\rho}{\rho} = 1 \]

6. **Conclusion**:
Therefore, the ratio of the specific resistance of the two copper wires is:
\[ \text{Ratio} = 1 : 1 \]