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:

(a) Voltage, V ceases to be proportional to current, I (Fig. 3.5).

FIGURE 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.

(b) 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).

FIGURE 3.6 Characteristic curve of a diode. Note the different scales for negative and positive values of the voltage and current.

This happens, for example, in a diode which we will study in Chapter 14.

(c) 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).

FIGURE 3.7 Variation of current versus voltage for GaAs.

A material exhibiting such a behaviour is gallium arsenide, GaAs, a mixed semiconductor.

Materials and devices not obeying Ohm’s law in the form of Equation (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.