This is an old revision of the document!

Nonlinear resistors

All resistors examined so far are linear resistors, for which the characteristic curve $I=f(U)$ is a straight line, s. figure 1. The resistance value of a linear resistor is independent of the current $I$ flowing through it or the applied voltage $U$.

Fig. 1: Characteristic curve of a linear resistor

With nonlinear resistors, there is no proportionality between current and voltage. The characteristic curve of such a resistor is shown in figure 2. With these resistors, we talk about static resistance ($R$) and dynamic (or differential) resistance ($r$). The static resistance is determined for a specific operating point: at a specific voltage, the current is read from the resistance characteristic curve.
The calculation is performed according to Ohm's law:

$$ R = \frac{U}{I} $$

The differential resistance around the operating point is calculated from the current difference caused by a change in the applied voltage:

$$ r = \frac{\Delta U}{\Delta I} $$

Fig. 2: Characteristic curve of a nonlinear resistor

A light bulb is examined as an example of a nonlinear resistor. Set up the measuring circuit shown in figure 3.

Fig. 3: Measuring circuit light bulb
Set the voltage on the power supply to the voltage values from table 1. Measure the corresponding current values and enter them in table 1.

Create the characteristic curve $I = f(U)$, s. figure 4

Fig. 4: Characteristic curve light bulb

Calculate the static resistance $R$ at the operating point $U = \rm 7.0 ~V$:



Calculate the dynamic resistance $r$ at the operating point $U = \rm 7.0 ~V$:



Compare the values with the values from table ## (direct resistance measurement)