In general, how does resistance change with length when all other factors are constant?

Resistance in a conductor is directly proportional to its length when all other factors, such as material, cross-sectional area, and temperature, are held constant. According to the formula for resistance, which is given by ( R = \rho \frac{L}{A} ) (where ( R ) is resistance, ( \rho ) is resistivity, ( L ) is length, and ( A ) is cross-sectional area), it is clear that increasing the length of the conductor while keeping the material properties (resistivity) and the area constant will lead to an increase in resistance.

This relationship is fundamentally due to the fact that a longer conductor provides more opportunity for electrons to collide with atoms within the material, which hinders their flow and effectively increases resistance. Hence, as the length of the conductor increases, the resistance proportionally increases as well.