Why Do Longer Wires Have More Resistance?

longer-wires-resistance Credit: Rennett Stowe/CC-BY-2.0

Resistance occurs when the electrons carrying an electrical charge collide with the atoms of a wire and are impeded. A longer wire provides more opportunities for collisions, which in turn creates greater resistance.

The Jefferson Lab describes the atoms of a metal as crystal-like in configuration. Only the outer layer of electrons interact with other atoms. These electrons are held to the atom with a small amount of energy called the valence band. Providing additional energy raises these electrons into the conductive band, where they are free to move throughout the crystal structure. It is this movement that can encounter different levels of resistance, depending on the type of material and its length.

The formula for resistance of a wire is R = pL/A, where R stands for resistance, p for resistivity (in ohm? meters), L for length of the wire (in meters) and A for cross-sectional area (in meters squared). Ohm's law, named after German scientist Georg Simon Ohm, also provides the formula for calculating resistance as R = V/I, where R again stands for resistance, V for potential difference and I for current. Resistance is measured in ohms, while potential difference and current are measured in volts and amperes, respectively.