6.5 Ohm’s Law from Office of Academic Technologies on Vimeo.

**6.05 Ohm’s Law**

We have seen that resistance is defined as the potential difference between two points divided by the amount of current passing through those points. And, also, resistivity was defined as the ratio of the electric field in the region of interest to the current density in that region. These relationships in physics are know as Ohm’s laws.

Here, we can express the potential difference between the two points as current times the resistance. If we plot potential difference between the two points versus the current passing through those points for different types of components of a typical electric circuit, we can end up with two different cases. One case is that the relationship between the potential difference and the current is a linear one, so this ratio, in other words, *V* over *i*, becomes always constant.

Of course, the second category is the case that whenever that ratio is not a constant, and as a result of that we end up with a curve. For example, something like this, which is the case of *pn* junction diodes. So, here is the example of the behavior of a resistor for example, and this is the case of *pn* junction diode.

Now, a conducting device is said to obey Ohm’s law if it’s resistance between any two points is independent of the magnitude and polarity of the potential difference applied between those points. So, if we make a statement of this, a conducting device obeys Ohm’s law, if its resistance between any two points is independent of the magnitude and polarity of the potential difference applied between those points. In other words, the ratio of *V* over *i*, or *i* over *V*, remains constant all the time, so that the slope of the curve remains constant. In other words, we end up with a straight line when ever we plot *i* versus *V*, or *V* versus *i*.

Now, *V* is equal to *i* times *R*. True for all conducting devices. We simply separate these devices whether they obey Ohm’s law or not simply by looking at the resistance, whether it remains constant or not. In other words, the ratio of *V* over *i*, current to potential difference to current, remains constant or not.

If that ratio remains constant, then we say that component obeys Ohm’s law. If it does not, then we say that that component does not obey Ohm’s law. So, if *i *versus *V* is linear, then this corresponds to the case of obeying Ohm’s law. On the other hand, if *i* versus *V*, the potential difference, is not linear, then that case is the one that we refer to as not obeying Ohm’s law.

Now, of course the local analog of Ohm’s law is associated with the definition of the resistivity, which was defined as the ratio of electric field to the current density. And, from here, we can express **E** as *ρ* times **J**. Of course this is true only for the isotropic materials. Materials whose electrical properties are the same in all directions. And, here again, in a similar way, if the ratio of electric field to the current density remains constant all the time, in other words, if the resistivity of the medium is constant, then that medium obeys Ohm’s law. On the other hand, if this ratio, electric field to the current density, is not constant, or **E** versus **J** is not a linear curve, then we end up by saying that that medium does not obey Ohm’s law.

So, so far we have introduced two different set of quantities, mainly microscopic quantities and these were electric fields, current density, resistivity. These quantities are important when we search fundamental electrical behavior of matter. So, let’s say that they are important when we search from the fundamental electrical properties of matter.

On the other hand, macroscopic properties, or macroscopic quantities, which are the potential difference, current, and resistance, and these quantities are important when we are making electrical instruments from specific conductors. So, these quantities are important when we are making electrical instruments, specific circuits, for example, on specific conductors.

So, in other words, whenever we are dealing with the circuits, we, therefore, deal with macroscopic quantities, namely potential difference, current, and resistance. On the other hand, if we are trying to understand the fundamental electrical properties of a specific medium, then we are going to deal with the electric field, current density, and resistivity or conductivity of that medium.