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The Relationship Between the Length of a Wire & Its Resistance

Metals are materials in which electrons are freed from their individual atoms and turned loose to float in a sea of electrons. Insulators, by contrast, have electrons tightly tied to each atom. If you try to push current through an insulator there's no room to put the "new" electrons, so you don't get very far. When you push current through a metal, though, the electrons that are already there just flow right out the other end of the metal creating an easily flowing current. Although the current flows easily, it's not completely unobstructed. The amount of obstruction is the resistance of the wire and it gets higher as the wire gets longer.

Resistivity
- Current is the flow of electrons, but that doesn't mean an electron that comes in one end of a wire zips all the way through the metal to the other end. Instead an electron that comes in the wire pushes the electrons in front of it along. You can think of the flow of current as similar to the movement of a caterpillar, with each section moving forward only as the section in front of it scoots out of the way. The pushing takes energy -- the little kick necessary to move that whole train of electrons along. The amount of push required is different for each type of material. It's quantified in a value called the resistivity. Copper, for example, has a resistivity of 1.72 x 10^(-8) ohm-meters, while the resistivity of aluminum is 2.65 x 10^(-8) ohm meters.
The Influence of Area
- If you think of electric current as a flow of water, then a wire is kind of like a hose. If the hose has a small diameter like a straw then it won't be easy to push a lot of water through it. If the hose is larger, though, it's easier to push a lot of current through. In the same way, the larger the diameter of a wire, the smaller its resistance.
The Influence of Length
- A length of unconnected wire is full of free electrons. They could move, if they were pushed, but without being connected to a circuit there is no push, so there is no current. When the wire is connected to a circuit all the electrons that were stopped need to get moving. Each one takes a certain amount of push and the total amount of push required is the sum of the little pushes for all the electrons from one end of the wire to the other. The longer the wire, the more electrons lined up from end-to-end. So the longer the wire, the higher the resistance.
Resistance
- The resistance of a wire is given by the product of the material's resistivity and its length divided by its area. Twelve gauge copper wire, for example, has a diameter of 80.81 mils (2.05 millimeters). So a 1-meter (3.28-foot) length has a resistance of 0.0052 ohms. A 10-meter (32.8-foot) length has a resistance of 0.052 ohms. That is, the resistance of an arbitrary length of 12-gauge copper wire is its length in meters times 0.0052. The same physics is at work for other sizes of wire and wire made of other metals: twice the length will have twice the resistance and half the length will have half the resistance. In mathematical terms, the resistance of a wire is directly proportional to the length.

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