3.6 Limitations of Ohm’s Law

Although Ohm’s law has been found valid over a large class of materials, there do exist materials and devices used in electric circuits where the proportionality of $V$ and $I$ does not hold. The deviations broadly are one or more of the following types:

• $V$ ceases to be proportional to $I$ (Fig. 3.5).

• The relation between $V$ and $I$ depends on the sign of $V$. In other words, if $I$ is the current for a certain $V$, then reversing the direction of $V$ keeping its magnitude fixed, does not produce a current of the same magnitude as $I$ in the opposite direction (Fig. 3.6). This happens, for example, in a diode which we will study in semiconductor chapter.

• The relation between $V$ and $I$ is not unique, i.e., there is more than one value of $V$ for the same current $I$ (Fig. 3.7). A material exhibiting such behaviour is GaAs.