Resistors in a circuit
A resistor is a device that impedes or limits the flow of electrical current in a circuit. It converts the current–s electrical energy into heat (thermal) energy.
Electrical resistance is a property of a substance which opposes flow of current. In a metal, the atoms are arranged in a crystal–like configuration.
Electrons can inhabit energy levels. Generally, only the "outer" electrons in an atom interact to form the bonds with other atoms. These outer electrons are held to the atom with a relatively small amount of energy. Normally, they inhabit an energy level we call the valence band. This is their "ground" state. The addition of energy can raise these electrons out of the valence band and into the "conduction" band. In the conduction band they are free to move about within the crystal structure. The application of an electric potential will influence them to move in a particular direction.
Now, in a metal, the valence band is relatively close to the conduction band–that is, very little energy is necessary to cause electrons to jump from their valence state into the conduction band. In fact, we think of metals as having a large population of free electrons in the conduction band all the time. So the application of electric potential will cause them to move–a current flow. Metals generally have a relatively low resistance. In a material such as glass, there is a large energy gap between the valence and conduction band. This means there are very few free electrons available for current flow, and it takes a large input of energy to raise any electrons into the conduction band.
Variable resistors
Within a metal conductor, even though there are free electrons, there is still resistance to current flow. One is impurities in the metal, which cause irregularities in the periodicity of the lattice. The other is the disturbance or "vibration" of the lattice caused by heat. Since some heat is always present (except at absolute zero) there is always some resistance from this source which prevents the electrons from sailing through.
The laws of resistance state that, electrical resistance R of a conductor or wire is,
1) directly proportional to its length, 'l' i.e, R ∝ l
2) inversely proportional to its area of cross–section, 'A'.