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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 restriction to a high rate of flow. The animation at the left demonstrates the comparison between a wire with a small cross sectional area and a larger one. 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. Temperature The 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. As 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 creates materials that superconductor 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. Electrical resistance Voltage can be thought of as the pressure pushing charges along a conductor, while the electrical resistance of a conductor is a measure of how difficult it is to push the charges along. Using the flow analogy, electrical resistance is similar to friction. For water flowing through a pipe, a long narrow pipe provides more resistance to the flow than does a short fat pipe. The same applies for flowing currents: long thin wires provide more resistance than do short thick wires. The resistance (R) of a material depends on its length, cross-sectional area, and the resistivity (the Greek letter rho), a number that depends on the material: The resistivity and conductivity are inversely related. Good conductors have low resistivity, while poor conductors (insulators) have resistivities that can be 20 orders of magnitude larger. Resistance also depends on temperature, usually increasing as the temperature increases. For reasonably small changes in temperature, the change in resistivity, and therefore the change in resistance, is proportional to the temperature change. Ohm's Law In many materials, the voltage and resistance are connected by Ohm's Law: Ohm's Law : V = IR The connection between voltage and resistance can be more complicated in some materials.These materials are called non-ohmic. We'll focus mainly on ohmic materials for now, those obeying Ohm's Law. Electric power Power is the rate at which work is done. It has units of Watts. 1 W = 1 J/s Electric power is given by the equations: The power supplied to a circuit by a battery is calculated using P = VI. Batteries and power supplies supply power to a circuit, and this power is used up by motors as well as by anything that has resistance. The power dissipated in a resistor goes into heating the resistor; this is know as Joule heating. In many cases, Joule heating is wasted energy. In some cases, however, Joule heating is exploited as a source of heat, such as in a toaster or an electric heater. The electric company bills not for power but for energy, using units of kilowatt-hours. 1 kW-h = 3.6 x 106 J Although power is cheap, it is not limitless. Electricity use continues to increase, so it is important to use energy more efficiently to offset consumption. Appliances that use energy most efficiently sometimes cost more but in the long run, when the energy savings are accounted for, they can end up being the cheaper alternative. Resistivity The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made. Experimentally, the dependence upon these properties is a straightforward one for a wide range of conditions, and the resistance of a wire can be expressed as