Resistance

In many materials there is a simple relation between the applied potential difference V across two points and the resulting current I between those points. Such materials are called Ohmic materials, and obey what is called Ohm's law:

 

V = IR. (3)

R is a constant called the resistance of the material, which has units of V/A, or Ohms ( $\Omega$ ).

The resistance depends on the type of material - materials with low resistance are called good conductors, while those with high resistance are good insulators. It also depends on the shape of the material. It is convenient in some circumstances to introduce a quantity called the resistivity, $\rho$ , which depends only on the type of material. If we consider a cylindrical wire of cross-sectional area A and length L , the resistivity is defined as

$$\rho {\frac{L}{A}}$$ (4)

The units of resistivity are thus $\Omega$ $\cdot$ m.