The equation for calculating resistance is:
R = ρ * (L/A)
where R is resistance, ρ is resistivity, L is the length of the material, and A is the cross-sectional area of the material.
As the cross-sectional area increases, resistance decreases because there is more space for electrons to flow through. The larger the area, the more pathways electrons have to travel through, reducing the chance of collisions with other particles, thus lowering the resistance.
Regarding the continuity equation (A1v1=A2v2), it applies to the flow of fluids in a pipe or a tube. Electrical current does not follow this equation because it is not a fluid. However, the principle of conservation of charge applies, which means that the amount of current that enters a point in a circuit must be equal to the amount of current that leaves that point.