Limitations of the Ohm's Law

Ohm's law is obeyed by many, but by no means all, materials and devices. Devices for which the current-versus-potential-difference (I-V) graph is a straight line passing through the origin (Fig. 11.4) are called LINEAR or OHMIC devices; their resistance is constant, independent of the value of $V$ or $I$ used to measure it. Most simple metallic conductors follow this linear characteristic.

Devices for which the I-V graph is NOT a straight line (Fig. 11.5) are called NON-OHMIC devices; common examples include liquid electrolytes, vacuum tubes, junction diodes, and thermistors. Because the graph curves, the ratio $V/I$ is different at different points along the curve, so these devices do not have one single, constant resistance value. Instead, the resistance at a particular operating point (a particular value of $V$) must be defined as the LOCAL slope of the curve there:

$R=\frac{\Delta V}{\Delta I}=\lim_{\Delta I\to 0}\frac{\Delta V}{\Delta I}=\frac{dV}{dI}\qquad\text{--- (11.16)}$ …