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Resistance in a Conductor

There are three external factors that influence the resistance in a conductor.   Thickness (cross sectional area of the wire), length, and temperature all have some effect on the amount of resistance created in a conductor.  The fourth factor is the conductivity of the material we are using.  Some metals are just more electrically conductive than others.  This however, is considered an internal factor rather than an external one.

Cross Sectional Area
The cross-sectional area of a conductor (thickness) is similar to the cross section of a hallway.  If the hall is very wide, it will allow a high current through it, while a narrow hall would be difficult to get through due to it's Cross Sectional Arearestriction to a high rate of flow.  The animation at the left demonstrates the comparison between a wire with a small cross sectional area (A) and a larger one (A).  Notice that the electrons seem to be moving at the same speed in each one but there are many more electrons in the larger wire.   This results in a larger current which leads us to say that the resistance is less in a wire with a larger cross sectional area.

Length of the Conductor
The length of a conductor is similar to the length of a hallway.  A shorter hallway would allow people to move through at a higher rate than a longer one. 

Current in a cold conductorThe temperature of a conductor has a less obvious effect on the resistance of the conductor.  It would be as hard to apply the hallway analogy as it is hard to say whether a hot hallway would make us move faster or slower than a cold hallway.  To truly understand the effect you must picture what happens in a conductor as it is heated.   Remember, heat on the atomic or molecular scale is a direct representation of the vibration of the atoms or molecules.  Higher temperature means more vibrations.   Imagine a hallway full of people.  Half of the people (the electrons) are trying to move in the same direction you are and the other half (the protons) are evenly spaced but stationary in the hallway.  This would represent a cold wire.  Since the wire is cold, the protons are not vibrating much, so the electrons can run between them fairly rapidly. 
Current in a warm conductorAs the conductor (hallway) heats up, the protons start vibrating and moving slightly out of position.  As their motion becomes more erratic they are more likely to get in the way and disrupt the flow of the electrons.  As a result, the higher the temperature, the higher the resistance.  A prime example of this is when you turn on a light bulb.  The first instant, the wire (filament) is cold and has a low resistance but as the wire heats up and gives off light it increases in resistance.   As a result we can say that Ohm's law holds true unless temperature changes.
   At extremely low temperatures, some materials have no measurable resistance.  This is called superconductivity.  The materials are known as superconductors.  Gradually, we are creating materials that become superconductors at higher temperatures and the race is on to find or create materials that superconduct at room temperature.  We are painfully far away from the finish line. 

In conclusion, we could say that a short fat cold wire makes the best conductor.

If you were to create a formula that related cross sectional area, length, and electrical conductivity (resistivity) to the resistance of the wire it would look like this:

Formula: Resistance in a wire. R is the resistance of the conductor in Ohms
A is the cross sectional area in m2
Lenght of the wireis the length of the wire in meters
Rho:  Resistivityis the resistivity of the material in Ohm(meters)

The resistivity is a value that only depends on the material being used.  For example, gold would have a lower value than lead or zinc, because it is a better conductor than they are.

In general it is important to realize that: