Resistance and Resistivity
If we apply the same potential difference between the ends of geometrically similar rods of copper and of glass, very different currents result. The characteristic of the conductor that enters here is its electrical resistance. We determine the resistance between any two points of a conductor by applying a potential difference I’ those points and measuring the current i that results. The resistance R .
we see that “resistance” is aptly named. For a given potential difference, the greater the resistance (to current), the smaller the current. The resistance of a conductor depends on the manner in which the potential difference is applied to it. , for example, shows a given potential difference applied in two different ways to the same conductor. As the current density streamline suggest, the currents in the two cases-hence the measured resistances-will be different. Unless otherwise stated, we shall assume that any given potential difference is applied as in 8b. As we have done several times in other connections, we often wish to take a general view and deal not with particular objects but with materials. Here we do so by focusing not on the potential difference V across a particular resistor but on the electric field E at a point in a resistive material. Instead of dealing with the current i through the resistor, we deal with the current density 7at the point in question. Instead of the resistance R of an object, we deal with the resistivity p of the material .