This is an old revision of the document!

Non-linear resistors

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

Fig. 1: Characteristic of a linear resistor

For non-linear resistors, there is no proportionality between current and voltage. The characteristic of such a resistor is shown in figure 2. For these resistors, one distinguishes between static resistance $R$ and dynamic (or differential) resistance $r$.

The static resistance is determined for a specific operating point: at a given voltage, the current is read from the characteristic. The calculation is carried out according to Ohm's law:

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

The dynamic 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 of a non-linear resistor

An incandescent lamp is investigated as an example of a non-linear resistor. Build the measurement circuit shown in figure 3.

Fig. 3: Measurement circuit for incandescent lamp

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.

Plot the characteristic $I = f(U)$.

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

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

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