The term "resistance" is used to describe what impedes the flow of charge between to points. The absence of all resistance is called "super conductivity." There are several factors that affect the flow of charge in a wire. There are several models used to describe what affects resistance. Some models are only good for few conditions. Think of this model.

Hallway/Student Model
The battery provides the electric field to the wires. This field provides a force to push the charges through the wires. Imagine the school hallway is crowded. A large intimidating green dragon is at the back of the hallway behind the students in the hallway. The students react with fear because they don't know that the dragon is looking for a partner to play checkers. The students in the hallway feel a pressure pushing their backs in the hallway as more students try to push into the hallway and get to the exit at the end of the hallway. The current is the measured by the number of students that pass the physics doorway in a second. The battery is like the dragon, it provides the push to move the charges through the wires. Describe how the current would change if their were three dragons in the hallway.

The wire is represented by the hallway outside the physics classroom's door. This time imagine a wider hallway. The wider hallway models a wider/fatter wire. The students in the hallways are the positive charges. One out of five students don't know where they are going. These students stop, change direction and get in the way of others. They slow down the flow of students in the hallway. The current is modeled by the number of people that exit the hallway in a second. The higher the number of people exiting the hallway per second, the lower the resistance. Look at the current because the resistance describes how the current is controlled. Answer questions below by comparing the the flow to the model shown below.

Using the students in the hallway model, how would the resistance change if a wire was wider or had a larger diameter?

Using the students in the hallway model, how would the resistance change if the hallway was longer?

Using the students in the hallway model, how would the resistance change if the wire had other atoms in it that hindered their flow. Like large trash cans placed in the hallway.

Using the students in the hallway model, explain how the resistance would change if a second hallway was opened up parallel the first. The pair of hallways open and close as the same location.

In order to control AND PREDICT the resistance of the hallway to student flow, much needs to be looked in the hallway. Are there trash cans in the hallway? How big are they? What happens to the traffic flow if the hallway is hotter or colder than normal? What would happen if we widened the hallway? What would happen if the hallway was longer and more crowded?

This has been thought through with resistance in wires. The unit of resistance is the Ohm. It is named after Georg Simon Ohm. The letter for the unit is the Greek capital omega, . Physicists want to make materials of a specific resistance, so they studied conductors and insulators and came up with this model for resistance.

The resistivity is a property of a material that affects its resistance. It exact values varies with the materials being used, e.g. gold,silver, iron, etc. The resistivity is defined for various materials listed below. (Many more materials can be found on the web, Google it.)

Material

Resistivity
[ Ω•m ]

Temperature Coefficient
[ 1/K ]

Aluminum

2.82 x 10^{-8}

0.0039

Carbon

3.5 x 10^{-5}

–0.0005

Copper

1.68 x 10^{-8}

0.0039

Gold

2.44 x 10^{-8}

0.0034

Lead

2.2 x 10^{-7}

0.0039

Nichrome

1.1 x 10^{-6}

0.0004

Platinum

1.06 x 10^{-6}

0.0039

Note that carbon's resistance deceases with a rise in temperature.

Extension cords can demonstrate this formula for resistance well. Click on the three buttons to see what happens.

Did you notice how the longer and thinner wire heats up leaving less energy for the lamp? According to the resistance formula above. Longer, thinner, wires increase the resistance. By adding extension cords end-to-end, you will create a fire hazard because they can over heat and catch fire. Plugging too may "things" into a single outlet can also cause the wires to over heat and catch fire.

Resistance and resistivity both are temperature dependent. In the table above, there is a column of temperature coefficients. These coefficients are given the symbol alpha, α. The resistivity is modeled from

ρ = ρ_{o} + α(ΔT)(ρ_{o})

because R is proportional to ρ ...

R = R_{o} + α(ΔT)(R_{o})

Another way to look at the previous formula is like this

Final Resistance = Initial Resistance + (% Change)(Initial Resistance)

ρ = Final resistivity
ρ_{o}= Initial resistivity
R = Final resistance
R_{o}= Initial resistance
α = the temperature coefficient found in the table above
ΔT = the change in temperture in either °C or K.

According to the table above, nearly everything listed will have a resistance that increases with an increasing temperature. This is very typical of metals. However, some materials, such as carbon, have a resistance the decreases as the temperature increases.

Example

A "toaster" works by heating up some long coiled wires next to a slice of bread. (See the image to the right.) These wires are connected to 120 Volt power source when the toaster is plugged into the wall. Because these wire are energized by the wall you should NEVER stick a knife into the toaster to dislodge a piece of burnt toast. You may accidentally touch a wire and electrocute yourself.

Suppose this toaster uses 3.5 m of nichrome wire to heat up 2 slices of bread. The wire has a cross sectional area of
3.0 x 10^{-7}m^{2}. The final resistance is of the whole wire is 13 Ω's. The initial resistance of the wire is 12 Ω's.
(a) What is the change in temperature of the toaster's wire?
(b) Using the initial resistance of the nichrome wire, calculate the cross sectional area of the wire.