If the resistivity of a metallic wire is X. If the length of the wire is doubled. What will be the new resistivity ?

Options

A. Unchanged
B. Doubled.
C. Tripled.
D. Six Times

Explanation

To solve the problem, we need to understand the relationship between resistivity, resistance, length, and cross-sectional area of a wire.

### Step-by-Step Solution:

1. **Understand Resistivity**:
- Resistivity (ρ) is a property of the material itself. It is defined as the resistance of a unit length of the material with a unit cross-sectional area.

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

3. **Effect of Doubling Length**:
- If the length of the wire is doubled (i.e., \( L \) becomes \( 2L \)), the new resistance can be calculated as:
\[ R' = \frac{\rho (2L)}{A} = \frac{2\rho L}{A} = 2R \]
This shows that the resistance doubles when the length is doubled, assuming the cross-sectional area remains constant.

4. **Resistivity Remains Unchanged**:
- However, resistivity (ρ) is a characteristic of the material and does not change with the dimensions of the wire. Therefore, even if the length of the wire is doubled, the resistivity remains the same.

5. **Conclusion**:
- The new resistivity after doubling the length of the wire is still \( \rho = X \).

### Final Answer:
The new resistivity remains unchanged.

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