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:

1. \( V \) ceases to be proportional to \( I \) (Fig. 3.5).
   

   3.5
   
   The dashed line represents the linear Ohm’s law. The solid line is the voltage \( V \) versus current \( I \) for a good conductor.
2. 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 Chapter 14.
   

   3.6
   
   Characteristic curve of a diode. Note the different scales for negative and positive values of the voltage and current.
3. 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. Materials and devices not obeying Ohm’s law in the form of Eq. (3.3)
   

   3.7
   
   Variation of current versus voltage for GaAs.

Materials and devices not obeying Ohm’s law in the form of Eq. (3.3) are actually widely used in electronic circuits. In this and a few subsequent chapters, however, we will study the electrical currents in materials that obey Ohm’s law.