# Non linear relationship between voltage and current

### Voltage-Current Characteristics and Nonlinearities [gtfd.infontinc]

Figure 3 shows a possible nonlinear voltage-current relationship. However, many nonlinear resistors exhibit an approximately linear voltage-current. "Linear" is a term that applies to a system with inputs and outputs, since it describes a particular kind of relationship between them. This means. materials were focused on the strong coupling between spin and charge, and the ceramic devices with highly nonlinear current-voltage characteristics. nonlinear behavior appears in association with a remarkable charge order- disorder.

As with any other component, all resistors are nonlinear, to some extent. That is, the voltage-current relationship is not exactly a straight line for all values of current for example, all electrical devices will fail if enough current is passed through them. Figure 3 shows a possible nonlinear voltage-current relationship. However, many nonlinear resistors exhibit an approximately linear voltage-current characteristic over some range of voltages and currents; this is also illustrated in Fig.

We will assume for now that any resistor we use is operating within a range of voltages and currents over which its voltage-current characteristic is linear and can be approximated by equation 1.

## Current and voltage relationships

Ohm's law provides a voltage-current characteristic for linear resistors. The voltage and current must be assigned according to the passive sign convention.

Ohm's law is an approximation to real resistor behavior. The i-v characteristic of any real resistor will be nonlinear to some extent.

For example, very high currents will tend to burn out a resistor, changing its i-v characteristics. For now, we will just say that, for a linear system, the parameters change in proportion to one another.

**P5 L4 - relationship between voltage, current and resistance**

For example, in Ohm's law, if we double the current, the voltage doubles. So, for linear systems, plots of voltage-current relations will tend to be straight lines. The nonlinearity is caused by the effects of high temperature on the metal wire of the lamp filament.

Another example of nonlinear current conduction is through gases such as air. At standard temperatures and pressures, air is an effective insulator. Once ionized, air and other gases become good conductors of electricity, allowing electron flow where none could exist prior to ionization.

If we were to plot current over voltage on a graph as we did with the lamp circuit, the effect of ionization would be clearly seen as nonlinear: The graph shown is approximate for a small air gap less than one inch.

## Voltage-Current Characteristics and Nonlinearities

Incidentally, this is the reason lightning bolts exist as momentary surges rather than continuous flows of electrons. The voltage built up between the earth and clouds or between different sets of clouds must increase to the point where it overcomes the ionization potential of the air gap before the air ionizes enough to support a substantial flow of electrons.

Once it does, the current will continue to conduct through the ionized air until the static charge between the two points depletes. Once the charge depletes enough so that the voltage falls below another threshold point, the air de-ionizes and returns to its normal state of extremely high resistance. Many solid insulating materials exhibit similar resistance properties: Once a solid insulating material has been compromised by high-voltage breakdown, as it is called, it often does not return to its former insulating state, unlike most gases.

It may insulate once again at low voltages, but its breakdown threshold voltage will have been decreased to some lower level, which may allow breakdown to occur more easily in the future.

This is a common mode of failure in high-voltage wiring: Such failures may be detected through the use of special resistance meters employing high voltage volts or more. There are circuit components specifically engineered to provide nonlinear resistance curves, one of them being the varistor.

### Nonlinear Conduction | Ohm's Law | Electronics Textbook

Unlike the breakdown of an insulator, varistor breakdown is repeatable: A picture of a varistor is shown here: There are also special gas-filled tubes designed to do much the same thing, exploiting the very same principle at work in the ionization of air by a lightning bolt.

Some devices actually experience a decrease in current as the applied voltage increases. Most notably, high-vacuum electron tubes known as tetrodes and semiconductor diodes known as Esaki or tunnel diodes exhibit negative resistance for certain ranges of applied voltage. For the benefit of the student, however, we will assume that resistances specified in example circuits are stable over a wide range of conditions unless otherwise specified.

I just wanted to expose you to a little bit of the complexity of the real world, lest I give you the false impression that the whole of electrical phenomena could be summarized in a few simple equations. The resistance of most conductive materials is stable over a wide range of conditions, but this is not true of all materials.

Any function that can be plotted on a graph as a straight line is called a linear function.