What effect does decreasing the length of a wire conductor have on its resistance?

Decreasing the length of a wire conductor results in a decrease in its resistance due to the fundamental relationship described by Ohm's law and the formula for resistance in a conductor. Resistance (R) is directly proportional to the length (L) of the wire and is given by the equation ( R = \rho \frac{L}{A} ), where ( \rho ) is the resistivity of the material and ( A ) is the cross-sectional area of the wire.

As the length of the conductor decreases, the overall path that electrons have to travel through the material becomes shorter, which means there are fewer atoms to impede the flow of electrons. This shorter path reduces the number of collisions between moving electrons and the atomic lattice of the conductor, leading to a reduction in resistance.

Therefore, as the length is reduced, the resistance declines proportionally, confirming that decreasing the length of a wire conductor will indeed decrease its resistance.