Introduction:
When a given length of wire is doubled on itself, the process essentially involves folding the wire in half, resulting in two parallel sections of wire. This process is then repeated once again, resulting in four parallel sections of wire. To understand how the resistance of the wire changes, we need to consider the factors that affect resistance.

Factors affecting resistance:
Resistance is influenced by three main factors:
1. Length of the wire: The longer the wire, the higher the resistance.
2. Cross-sectional area of the wire: The smaller the cross-sectional area, the higher the resistance.
3. Material of the wire: Different materials have different resistivity values, which affect resistance.

Effect of doubling the wire:
When the wire is doubled on itself, the length of the wire effectively becomes twice the original length. This doubling of length has the following implications:

1. Length:
The resistance of a wire is directly proportional to its length. When the length is doubled, the resistance also doubles. This is because the longer path increases the number of collisions between the free electrons and the atoms in the wire, resulting in higher resistance.

2. Cross-sectional area:
When the wire is folded, the cross-sectional area remains the same. Doubling the length while keeping the cross-sectional area constant increases the total length of the wire but does not change the cross-sectional area. Therefore, the cross-sectional area does not affect the resistance in this scenario.

3. Material:
The material of the wire remains unchanged during the doubling process. Different materials have different resistivity values, which determine their inherent resistance. However, since the material remains the same, the resistivity and resistance of the wire do not change.

Overall change in resistance:
Doubling the wire on itself effectively doubles the length of the wire, while keeping the cross-sectional area and material constant. Therefore, the resistance of the wire also doubles due to the increased length.