Electrical Resistance

Resistance is an opposition to current flow - it is like an "electrical friction" between moving electrons (current) and the molecules in the material the current is flowing through. Resistance is temperature dependent. As temperature rises, so does resistance. This is because the molecules in the material become more excited and interfere more with the flow of electrons. We can create superconductors, or materials that provide essentially no opposition to current flow by cooling them down to temperatures near absolute zero. This temperature, for a material, is called the critical temperature. Below the critical temperature, resistance drops very suddenly.

What causes resistance? As electrons move through a conductor, they collide with the atoms in the conductor and their motion is affected. Different atoms (conductor materials) will cause varying amounts of energy to be lost. The more collisions, the harder it is for the electrons to move through the conductor. This means greater resistance. In some cases, such as toasters, light bulbs, and electric heaters resistance is desired. However, the resistance in wires in circuits and electric transmission lines is bad and should be minimized.

A German Physicist named Georg Ohm observed a relationship between voltage and current in a circuit. He found that if the temperature was held constant, the ratio of voltage to current remained constant as well. This relationship became known as Ohm's Law.

Graph of a current applied to an ohmic material

  • Ohmic materials have a constant resistance over a range of potential differences.
  • Non-ohmic materials defy Ohm's Law - they are used in components such as diodes to control the direction of flow of electricity in circuits.

Resistance is measured in ohms (W). A resistor is an electronic component that is designed specifically to take advantage of this relationship. Resistance is a measure of a material's ability to allow electron flow. We use the Greek letter r (rho) to symbolize resistivity and it can be looked up for various materials. Generally:

R = rL/A

Where R is the Resistance in ohms, r is the resistivity, L is the length of the conductor, and A is the cross sectional area of the conductor.

  • If a conductor has a longer length, there is more resistance.
  • If a conductor has a smaller cross sectional area, there is more resistance.

A resistor is a specific component placed in an electrical circuit to control the flow of current in the system. Going back to our water piping system analogy, it is equivalent to placing a throttle valve in the water pipe to control the amount of water that passes through.

Some Sample Problems:

1.) If you have a 20v circuit with a current of .7A, what is the resistance?

A) R= I/V = 20V/.7A= 28.57 W

2.) If you have an Aluminum wire 4m long with a radius of 2mm, what is the resistance?

A) rAluminum = 2.65x10-8 W m
R= rL/A 2.65X10-8
W m x 4m/.002m2 = 8.84x10-3 W

Try the following web sites for further study:

Some coding tips and interesting facts about resistors at: http://www.williamson-labs.com/resistors.htm

A really cool resistor simulation with color coding:


More about Ohm’s law some sample problems, and a simulated experiment at: http://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.intro.html

For Practice Problems, Try: Giancoli Multiple Choice Practice Questions (Go ahead - try a few.)