Introduction:
Reluctance is a property of a material that opposes the flow of magnetic flux. It is analogous to resistance in an electrical circuit. The reluctance of a material depends on its geometry and magnetic properties, such as permeability. The cross-sectional area of a material is one of the factors that affect its reluctance.

Explanation:
1. Definition of Reluctance:
Reluctance is defined as the opposition offered by a material to the flow of magnetic flux. It is represented by the symbol R and is measured in ampere-turns per weber (A-turns/Wb).

2. Relationship between Reluctance and Cross-Sectional Area:
Reluctance is inversely proportional to the cross-sectional area of the material. In other words, as the area of the cross section of the material increases, the reluctance decreases. This relationship can be explained using the following points:

- The larger the cross-sectional area of a material, the easier it is for the magnetic flux to flow through it. This is because a larger area provides more space for the magnetic field lines to pass through, resulting in a lower opposition to the flow of magnetic flux.
- Conversely, if the cross-sectional area is reduced, the material offers more resistance to the magnetic flux. This is because the reduced area restricts the passage of magnetic field lines, leading to an increase in reluctance.

3. Mathematical Relationship:
The relationship between reluctance (R) and cross-sectional area (A) can be mathematically expressed as:

R ∝ 1/A

where ∝ represents proportionality.

4. Example:
Consider a cylindrical iron core with a certain length and a fixed permeability. If the cross-sectional area of the core is doubled while keeping the other parameters constant, the reluctance of the core will decrease by a factor of 2. This demonstrates that an increase in the area of the cross section leads to a decrease in reluctance.

Conclusion:
When the area of cross section of a material increases, the reluctance of the material decreases. This is because a larger cross-sectional area provides more space for the magnetic flux to flow through, resulting in a lower opposition to its passage. Conversely, if the area is reduced, the material offers more resistance to the magnetic flux. Understanding this relationship is crucial in designing magnetic circuits and optimizing their performance.