Understanding the Relationship
* Resistance and Diameter: The resistance of a wire is inversely proportional to its cross-sectional area. This means that if the diameter (and therefore the area) increases, the resistance decreases.
* Area and Diameter: The area of a circle is calculated by the formula: Area = π * (radius)² Since the radius is half the diameter, doubling the diameter increases the area by a factor of 4.
Calculations
1. Initial Area: Let's assume the initial diameter is 'd'. The initial area is π * (d/2)².
2. Doubled Diameter: Doubling the diameter gives us a new diameter of '2d'. The new area is π * (2d/2)² = π * d².
3. Resistance Change: The new area is four times larger than the initial area. Since resistance is inversely proportional to area, the resistance will be one-fourth of the initial resistance.
Conclusion
If the diameter of the circular wire is doubled, the resistance will become 1/4 ohm (0.25 ohms).
