Two wires of same material have length L and 2 L and cross– sectional areas 4 A and A respectively. The ratio of their specific resistance would be

Options

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

Answer

To find the ratio of the specific resistances of two wires made of the same material, we can follow these steps:

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

### Step 2: Identify Given Information
We have two wires:
- Wire 1: Length \( L \), Cross-sectional area \( 4A \)
- Wire 2: Length \( 2L \), Cross-sectional area \( A \)

### Step 3: Determine Specific Resistance
Since both wires are made of the same material, their specific resistances will be equal. Therefore, we can express this mathematically as:
- Specific resistance of Wire 1: \( \rho_1 = \rho \)
- Specific resistance of Wire 2: \( \rho_2 = \rho \)

### Step 4: Calculate the Ratio of Specific Resistances
The ratio of the specific resistances of the two wires can be calculated as follows:
\[ \text{Ratio} = \frac{\rho_1}{\rho_2} = \frac{\rho}{\rho} = 1 \]

### Conclusion
The ratio of the specific resistances of the two wires is \( 1:1 \).

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

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