The correct option is It is doubled.
Explanation
The electrical resistance ($R$) of a conductor is determined by its physical dimensions and material properties. The relationship is governed by the formula:
$R = \rho \frac{L}{A}$
Where:
- $\rho$ (Rho): Resistivity of the material (constant for a specific material at a given temperature).
- $L$: Length of the conductor.
- $A$: Cross-sectional area of the conductor.
Analysis:
According to the formula, resistance is directly proportional to the length of the wire ($R \propto L$) provided the cross-sectional area ($A$) and resistivity ($\rho$) remain constant.
- Initial State: Let the original length be $L$ and resistance be $R$.
- Changed State: The length is doubled, so the new length $L' = 2L$. The question explicitly states that the cross-sectional area remains constant ($A$).
- Calculation: The new resistance $R'$ is calculated as:
$R' = \rho \frac{2L}{A} = 2 \left( \rho \frac{L}{A} \right) = 2R$
Consequently, the new resistance is twice the original resistance.
Key Takeaway:
Resistance is directly proportional to the length of a conductor. If the length increases while the area remains unchanged, the resistance increases by the same factor.