# Which metal has the lowest specific resistance value ### General

An ohmic resistor is the most common component used in discrete circuits. Ohmic resistors are so-called passive components because they do not have an amplifying character - on the contrary: a resistor hinders the flow of current. Resistors are used in a variety of ways, be it as current limiters, voltage dividers, pull-up or pull-down resistors, as load resistors, in connection with capacitors and / or coils in filter circuits and much more. In the following you can find out how resistors are constructed, how they work, what types there are and what you have to consider when using them.

### Basics I - What is a resistor?

Electricity, i.e. electrons, cannot move completely "frictionless" in an electrical conductor (with the exception of superconductors, but this is a special physical case). You can look at it with a In a very simplified way, imagine the metal grid in such a way that the electrons repeatedly collide with the positively charged ions on their way through the metal grid and thereby give up part of their kinetic energy to them. In order to move electrons through a conductor, one must therefore expend a certain amount of power. Due to the external energy supply that the electrons in the conductor give off to the metal ions, the metal ions are excited to vibrate more strongly, which heats the metal. Figure 1: Measurement of current and voltage on an electrical conductor

If you provide a variably adjustable voltage source with a voltage and an ammeter and connect an electrical conductor to this measuring circuit (shown in blue in Figure 1), you can observe how the current changes as a function of the applied voltage. At 0 V, as expected, no current flows, but if you slowly increase the voltage, the current also increases to the same extent. This results in the relationship between voltage and current shown in blue in Figure 2. Figure 2: Dependence of the current on the voltage in a resistor

As you can see, the curve is linear, i.e. the current increases proportionally with the voltage. If you replace the resistive conductor with another one, the result is a proportional curve, which is not identical to the first curve, but has a different gradient (shown in red or green). The constant of proportionality, i.e. the slope of the straight line, is called the resistance of the conductor. One can easily calculate this constant, i.e. the slope; one only needs to divide the voltage of a point on the straight line by the associated current. The resistor is given the formula letter R like resistor: This equation is called Ohm's law in honor of the German physicist Simon Ohm. The physical unit of resistance is volts per ampere (logical, because voltage is divided by current). Since such a unit is a bit unwieldy, the composite unit V / A is called ohm and, since mathematicians and physicists have a weakness for the Greek alphabet, the big omega, i.e. Ω, is used instead. Ohm's law says that you can calculate the resistance according to the above formula if you know how much current is flowing for a voltage value. This equation of Ohm's law can alternatively be solved for U or I and thus the following two formulas are obtained, which are often found in books of tables or formulas: or. This allows you to calculate the voltage across a resistor if you know the resistance value and the current, or the current if you know the resistance value and the applied voltage.

It is interesting to know what the level of the resistance value of an electrical conductor actually depends on. To do this, you can do the following little experiment: First you determine the resistance of a copper wire of a certain length as described above. Then you take a second, completely identical copper wire and connect its beginning to the beginning and its end to the end of the first wire, i.e. you double the cross-section. When determining the resistance of the combination, you will find that the resistance value drops to exactly half. This is not really surprising when you consider that the current has twice the conductor cross-section available compared to a single wire. Now, in a further experiment, hang the second wire behind the first, which results in a wire that is exactly twice as long. The resistance of the two wires connected in series is now twice as high as that of one wire alone. This is not surprising either, because the current must first flow through the first line, which has a certain resistance, and then immediately through the second, which has the same resistance. If the experiment is carried out with 3 or 4 identical wires, it is found that the resistance drops to a third or a quarter of the value of a single wire at three or four times the cross-section and to three at three or four times the length - or four times the value increases.

The resistance decreases in inverse proportion to an increase in cross-section, while it increases proportionally to the length when there is a change in length. This can be written as follows:
 1 Length: 2 Cross-section: These two formulas can be combined into one: This can also be written as follows: It's nice to know what the resistance of a conductor is proportional to, but you can't calculate anything with it. In order to turn this into an equation with which one can calculate the resistance as a numerical value, one has to know the constant of proportionality, which we want to call ρ (small Rho - you remember, mathematicians and physicists love the Greek alphabet). Using this constant one obtains the following equation: But how do you come to this proportionality constant, which is also called "specific resistance"? For this purpose a copper wire with a cross section of exactly 1 mm and exactly 1 m in length is used, the resistance of which is determined by measuring voltage and current with very precise measuring instruments. A value of slightly less than 0.018 Ω is obtained. The formula for calculating the resistance can be converted to ρ and then you get: The cross-section and length of the measured wire are just as known as the resistance, so that the values ​​only have to be entered. This results in copper according to VDE 0201: So the unit of resistivity is ohms times square millimeters divided by meters. Incidentally, the meter, which occurs in the numerator and denominator, is not abbreviated, although it would be mathematically possible to express that the specific resistance relates to a cross-section of one square millimeter and a wire length of one meter.

If you replace the copper wire with wires made of other materials, you will find that each material has a different specific resistance. The metal with the lowest resistivity is silver, closely followed by copper. The precious gold, on the other hand, is a comparatively poor electrical conductor. Below is a brief overview of the specific resistances of some of the materials that are often used as conductor or resistance material at a temperature of 20 ° C:

material ρ silver 0,0165 copper 0,01786 aluminum 0,02857 gold 0,023 iron 0,098 Constantan 0,49 mercury 0,958 Chrome nickel 1,12 coal 40-100 (depending on grain size and compression)

In the case of an electrical conductor, resistance is usually an undesirable property when one wants to conduct electricity from one place A to another place B. Because the resistance of the conductor shown in blue in Figure 3 ensures that a voltage can be measured between the beginning and the end of the conductor when current is flowing. In technical jargon, one speaks of a voltage drop on the line. As a result, the voltage at location B is lower by the voltage drop in the line than at location A. Fig. 3: Voltage drop on a resistive line

The voltage drop on the outgoing and return lines is proportional to the flowing current in accordance with Ohm's law explained above. In addition, of course, it depends on the resistance of the line.

When the current and voltage are multiplied, the result is a power. If you use the voltage drop on the conductor as the voltage and the current through the conductor as the current, you get the power that is converted into heat in this conductor. As a result, less power arrives at location B than it was at location A. For the application of current transport from A to B, one naturally strives to keep the resistance of the conductor as low as possible, which can be achieved by choosing a material with a small ρ and a sufficiently large cross-section.

However, if the goal is to literally put a resistance in the way of the current, a material with a high specific resistance and a small cross-section is cheaper, as you then need significantly less wire length to achieve the same resistance value. And at this point we come to resistors as a component, which are industrially produced in large numbers.

### Basics II - Why do electrical conductors have a resistance?

So far it has been discussed what can be found out by measuring and trying out. Perhaps you are now wondering why an electrical conductor conducts electricity in the first place and why it has an electrical resistance that also differs from material to material. In the following you will find simple answers to these questions, which do not describe the complex quantum mechanical processes correctly, but explain the mode of operation in a graphic way. If these details are not of interest to you or if they seem too complicated or too boring to you, you can simply skip this chapter.

With the exception of special superconductors, electricity cannot flow without obstacles. Rather, every material has a specific resistance that is determined by the chemical elements of which it is made and its internal structure. Materials are usually divided into 3 classes:

 1 Electrical conductors (small to very small specific resistance, e.g. metals or graphite) 2 Semiconductors (medium to high specific resistance, e.g. silicon or germanium) 3 Insulators (extremely high specific resistance, e.g. glass or ceramic)

Almost all electrical conductors are metals. The conduction of electricity in them is due to the fact that their atoms form a so-called metal bond. The atoms are arranged in a row and form a metal lattice (see Figure 4). Each atom releases the electrons of its outer shell and makes them available to the general public, i.e. the lattice, so to speak. The metal ions that are positively charged by the release of electrons and shown in green would repel each other (as is well known, the same charges repel each other), but the electrons released to the grid, shown in blue, buzz around the ions in random motion because they are carrying positive charges get dressed by. The negative charge of the electrons compensates for the repulsive forces between the ions because unequal charges attract each other. The electrons therefore act like an adhesive between the metal ions. Photo 4: metal grille

The electrons released to the grid are called free electrons because they are not permanently assigned to an atom but are freely movable and can float around here and there. This movement is absolutely frictionless because there is no material between the ions that could hinder the movement. The electrons can be imagined as comets that come into the area of ​​influence of stars and are deflected there in their direction of movement, but do not lose any energy during this process. When approaching a positively charged ion, an electron is accelerated and when it is removed it is decelerated again, but the original energy is absolutely retained. From the outside there is no detectable current flow, because on average there are the same number of electrons at every point of the material and on average there is no electron movement; To put it succinctly, on average, the same number of electrons always move to the left as to the right.

If you pass a current through the material, it means that on average the electrons have to move. To give you an impression of the situation: In order to allow a current of 1 A to flow, approx. 6,250,000,000,000,000,000 electrons per second have to march in one direction. One should expect that the electrons do not need any energy for this, despite the large number, because they move without friction in the lattice even without current flow. But this is not the case because here the electrons are not allowed to move naturally, but are set in motion with a little emphasis in one direction. Because the ions in the metal lattice oscillate around their position of rest, with the oscillation amplitude increasing with temperature, figuratively speaking they briefly jump in the way of the electrons (the physically correct relationships can only be correctly explained quantum mechanically). The electrons then collide with them like a billiard ball and in the process give off some of their kinetic energy to the ion and are also deflected from their direction.

The ion bound into the grid, even if it is a direct hit, cannot "splash away", but instead vibrates a little stronger than before due to the energy supplied, which corresponds to a higher temperature. The ion can be imagined as a large billiard ball that is fixed in a certain place with rubber bands: when another ball hits it, it changes its position, but some rubber bands are stretched and others are relieved. The rubber bands therefore pull the ion back again after the impact. Since it is a mass-spring system, the ion starts to vibrate. The probability that an electron emits energy on its way through the material increases with increasing temperature, because the oscillation amplitude of the ions increases with temperature and, figuratively speaking, they get further and further in the way of the electrons.

On average, therefore, as the temperature rises, more and more energy has to be expended in order to let electrons flow through a metal. There is a loss of energy in the material in relation to the electrons. Therefore, one speaks of the resistance of a material that opposes the electrons, i.e. the flow of current. The energy is of course by no means lost, but is only converted into the oscillation energy of the ions, i.e. heat. This "lost" energy becomes noticeable as a voltage difference between the point of supply and point of withdrawal of the current. This is referred to as a voltage drop across the resistor.

As you can imagine, the shape of the material has a big influence on the resistance. The thicker it is, the lower its resistance, because the gaps between the ions increase as the cross-section increases. The length also plays an important role, because the longer the distance to be covered, the higher the probability that an electron will collide with a metal ion. The resistance therefore decreases linearly with the cross-section and increases linearly with the length, as already under Basics I figured out experimentally.

The differences in specific resistance between the individual materials are due to the geometric differences in the grid. What is striking, however, is the high specific resistance of certain metal alloys such as constantan (consists of 55% copper, 44% nickel and 1% manganese). The reason for this is that the different metal atoms form a metal lattice, but because of the greatly different atom size and thus the arrangement of the ions in the lattice, they are more "in the way" of the electrons than in a lattice of similar atoms.

Graphite and carbon (both made of carbon) are not metals, but have a lattice that, like a metal lattice, has freely moving electrons. This is why both materials conduct electricity. Coal used in electrical engineering consists of many small grains that have been compressed at high temperatures. The specific resistance depends, among other things, on the grain size and the packing density.

In contrast to electrical conductors, insulators, i.e. non-conductors, ideally have no free electrons, which is why they cannot conduct electricity. However, real insulators always have a very low conductivity. However, their specific resistance is many orders of magnitude greater than that of metals. The reason for this lies on the one hand in the real and always present impurities. But high-purity insulators also conduct electricity a little. The reason for this is that the world is not always as simple as one would like it to be: The simplified statement that metals emit all valence electrons into the lattice and insulators none at all is not entirely correct.There are only probabilities of location for the valence electrons, which are ultimately related to the energy that the valence electrons need to be able to leave the atomic shell. In the case of insulators, this binding energy is very high. If you add energy to the material (e.g. thermal energy), not every electron absorbs the same amount of energy, but the energy distribution scatters quite a lot. Even in good insulators, the energy of individual valence electrons exceeds the binding energy, so that they can leave the respective atom and are available to conduct electricity. The higher the binding energy, the lower the probability that a single atom will have sufficient energy to release a valence electron. If you consider all atoms of the insulator in total, the number of free electrons decreases with increasing binding energy, which increases the specific resistance. This also explains why insulators do not all insulate equally well, but rather have reproducibly different specific resistances.

In so-called semiconductors, the conductivity lies between electrical conductors and insulators. They tend to behave like insulators, but the probability that a valence electron is available to conduct electricity is several orders of magnitude higher than that of insulators, but several orders of magnitude smaller than that of metals. This is because the binding energy of the valence electrons is significantly smaller than that of insulators. It is so low that at temperatures above absolute zero the heat energy supplied is sufficient for a number of atoms to detach the valence electrons from the atom, so that they conduct the current considerably better than insulators. The higher the temperature, the more energy is available for detachment, which significantly increases the probability that a valence electron can detach from the atom. As a result, the specific resistance drops sharply with increasing temperature.

### Requirements for resistors

The ideal resistance has exactly the ohmic value that is printed on the component, i.e. its tolerance is 0% even at extreme temperatures and does not change over time. It has unlimited resilience and is still very small. Its inductance and capacitance are both zero, i.e. it has the same resistance as with direct current even at infinitely high frequencies. In addition, it does not add any current noise to the signal.

Of course, there is no such ideal resistance in practice. You can only optimize individual points so that they come as close as possible to the ideal, while others tend to deteriorate as a result. For this reason there are different types of resistors. In practice, however, you will extremely rarely come up against technological limits, because firstly in most cases the metal film resistors customary today are far better than necessary for the function of the circuit and secondly you can mostly live very well with certain restrictions. As is so often the case in life, the limiting factor is the price, as one has to spend a disproportionately large amount of money for slightly better properties.

### Building a Resistance

To build up a resistor, it is preferable to use conductors with a high specific resistance such as carbon, constantan, chromium-nickel or other alloys. Even if it is obvious at first glance, semiconductors are not used even for very high resistance, because their resistance is extremely dependent on the temperature due to the special conduction mechanism. There are several ways in which a component can be produced from the resistor material. Some types of wired components are listed below.

### Winding resistance / wire resistance

An old and simple way of making a resistor is as follows: You wind a long, thin wire with a high specific resistance on a carrier, as shown in Figure 3. In this way, low-ohm wire resistances can be produced quite easily, down to the kilo-ohm range. This method is not suitable for very high resistance because the wire would be so thin that it could no longer be handled safely. Figure 3: Structure of a wire resistor

The major disadvantage of such winding resistors is that it is a winding. Such resistors have a comparatively high inductance (a winding is a coil) and also a non-negligible capacitance (winding capacitance). Such resistors are completely unsuitable for high frequency applications. However, they have the advantage of being able to withstand high loads if heat-resistant materials such as ceramics are used as the carrier material. Relatively low-ohm high-load resistors are therefore still manufactured in this design today. Thanks to a very low number of turns and a special type of winding, the high-frequency suitability of such resistors is hardly affected - especially with very low-resistance resistors.

### Carbon mass resistance

Ground resistors are almost as old as winding resistors. In a nutshell, they consist of a solid piece of poorly conductive material that is provided with two connections. Usually, it was a matter of carbon-mass resistors, in which a pressed block of small carbon grains was used as a poorly conductive material, which was placed in a non-conductive tube (mostly made of ceramic). The production tolerance of the resistor value was quite high at 10% or 20%. Fig. 4: Structure of a coal mass resistor

Carbon earth resistors are the worst resistances that can be imagined as a wired component: the numerous transitions from grain to grain are decisive for the resistance, as the cross-section is greatly reduced at the tips and edges and thus the resistance increases. If the grains change their position in relation to one another even very slightly, the resistance value suddenly changes a little at the moment of a break-off or a newly formed contact. This is noticeable as very strong noise. A slight thermal expansion (either caused by external temperature or internal current flow), vibration exposure (e.g. from sound) or the like is sufficient for this.

Furthermore, carbon resistances are not really linear, i.e. with increasing voltage the current does not increase exactly to the same extent. This is caused by the fact that, with the sometimes extremely small spacing of the grains, internal voltage flashovers occur very quickly, which ensure that grains are in contact with one another which are not in contact with one another at low voltages. As a result, the resistance is lower at higher voltages than at low voltages. The result is that the useful signal is distorted. Anyone who rejoices and believes they have found one of the causes of the tube sound should take into account that a sufficiently high voltage must be applied to the resistor for this effect to take place to a significant extent. This requires a voltage swing of the order of magnitude of 100 V. However, this does not at all match the fact that carbon-earth resistors were preferably used as cathode resistors. The cathode voltage swing is, however, much too low in the fully negative feedback case with just a few volts. It looks even worse when the cathode resistor is bridged with a capacitor in terms of AC voltage. Then the voltage swing across the resistor is almost zero. Even when used as an anode resistor, the voltage swing is usually not large enough, especially with pre-stages. The greatest chances of observing an effect worth mentioning are probably with driver tubes, the anodes of which usually have the largest voltage swings in a tube circuit.

Another negative point is that carbon mass resistances age very strongly due to irreversible grain displacements, i.e. they change their resistance value over the service life without external influences. In view of their many negative properties, one can only say: How good that they are as good as nonexistent.

### Sheet resistance Sheet resistors consist of a small tube made of a heat-resistant, non-conductive material such as ceramic, on which a more or less poorly conductive layer is applied (either as a complete coating, helical or meander-shaped). A wide range of values ​​can be covered by varying the coating material, the thickness and the shape. In the picture on the left you can see a carbon film resistor with a spiral-shaped layer, in which the brown-gray topcoat was more or less brutally removed by thermal overload and subsequent quenching in water. As expected, the carbon layer appears black, while the light-colored ceramic tube is visible in the gap between the "turns". Sheet resistors are the most frequently used resistors in electronics because they have good properties on the one hand and are inexpensive to manufacture on the other. The following types, which differ in the material of the resistance layer, are common:

Carbon film resistor
Historically, coal was the first material to be used. By the way, you can easily reproduce this in an experiment by drawing a thick, heavily blackened line on a sheet of paper with a soft pencil. You can then measure the resistance value with an ohmmeter (e.g. digital multimeter with an ohm range). For a long time, carbon film resistors were used as standard resistors in electronics. However, they have the disadvantage that their resistance value depends very much on the temperature and that they have a relatively strong noise - significantly less than carbon-mass resistors, but still relatively strong. Their use has decreased significantly in recent years.

Metal film resistor
Metal film resistors are built on the same principle as carbon film resistors. With them, only the carbon layer was replaced by a metal layer. The metal layer noises significantly less than a carbon layer, has a significantly lower temperature response and can withstand higher temperatures, which results in a higher load capacity for the same size. At the same time, such resistors can be manufactured with greater precision, with an accuracy of 1% being the absolute standard (cf. carbon film resistors: 5% or 10%). Metal film resistors with an accuracy of 0.5%, 0.25% or 0.1% are a bit difficult to get for electronics hobbyists, but they are absolutely commercially available in industry. The result of the higher accuracy is that in electronic circuits, compared to carbon film resistors, it is often possible to dispense with adjustment points and thus expensive and sensitive potentiometers or the expensive measurement / selection of resistors. Because of their very good properties, metal film resistors are the most frequently used type of resistor in industry, which also has a positive effect on the price due to the high production quantities.

Metal oxide resistance
They have a very similar structure to metal film resistors, but their resistance layer consists of metal oxide. Tin oxide is preferably used for this, less often titanium oxide. The carrier body is usually completely coated, which results in a very low inductance. Due to the full-surface coating of the carrier material, the resulting resistance can be controlled less precisely during manufacture than with metal film resistors, which is why they are sold with a slightly larger tolerance (usually 2%). It is very popular to manufacture resistors which, with a slightly larger design, have a slightly higher load than metal film resistors. They are therefore a high quality replacement for the unspeakable carbon mass resistors.

Metal film resistors
Metal film resistors do not consist of a thin layer like the metal film resistors but of a comparatively thick metal foil. They are almost always manufactured as planar resistors, i.e. the resistance layer forms a flat surface. The properties (noise, linearity, tolerance) of metal film resistors are even better compared to metal film resistors. Due to the rather thick film, not quite as high-resistance resistances are possible. With a sufficiently thick metal foil, however, high-load resistors of up to a few hundred watts of power loss can be produced, and this with extremely small tolerances and otherwise best properties. Unfortunately, due to the relatively small production quantities, the price is quite high, so that they are only used where their special properties are really needed.

### Standardized resistance values

Resistors cannot be bought with arbitrary values ​​but only in a certain grid called a series of resistors. Of the standardized resistor series, E12, E24, E48, E96 and E192 are common. The number behind the E indicates how many resistance values ​​are available per decade. With the E96 series there are between 1 kΩ and 10 kΩ (or every other decade), i.e. 96 resistance values. This number is closely related to the resistance tolerance. For example, the said E96 series is used for resistors with a 1% tolerance. The grading is chosen so that the tolerance windows fit together seamlessly with as little overlap as possible: A resistor with a nominal value of 10 Ω can have a value between 9.901 and 10.1 Ω with 1% tolerance. The next standard value is therefore 10.2 Ω, the real value of which can be between 10.099 and 10.302 Ω.

The alternative to standardized values ​​would be to have the resistors manufactured by the manufacturer so that their nominal value corresponds exactly to the value calculated for the circuit. The result would be that the manufacturers would have to produce an unmanageably large number of resistor values, of which only small numbers are required for the individual values. Standardization ensures that only a manageable number of resistance values ​​has to be produced, which can also be produced in large numbers and therefore at low prices. The resistor manufacturers naturally also produce resistors with very specific, non-standardized values ​​for special applications on request, but these are then quite expensive due to the special production. If the tolerance has not also been narrowed, however, only the mean value is the non-standard value. The resistance of an individual resistor can deviate from this, just as with resistors from the standard series, within the permissible tolerance.

### Use in electronic circuits

To buy resistors for replicating electronic circuits, it is usually sufficient to know the resistance value ("ohmic value") as well as the required minimum load capacity and the maximum permissible tolerance. If no load capacity is specified in the assembly instructions, standard types with 0.25 W are usually sufficient. You can also use resistors with a higher load capacity without any problems, as long as the maximum size specified on the circuit board is not exceeded. Unless explicitly stated otherwise, you should definitely buy metal film resistors. Carbon film resistors are still available, but the very low additional investment in metal film resistors avoids tolerance problems and is highly recommended for noise reasons, especially for measurement and audio circuits.

When you design circuits yourself, you usually have to round the result of the calculation up or down slightly to get to the next standard value. In many circuit parts, the resistance value is very uncritical anyway, so you don't have to feel guilty if you use a resistance value other than the one calculated: Whether the input resistance of an audio circuit is exactly 72.343 kΩ, together with the decoupling capacitor of 0.22 μF Achieving a lower limit frequency of exactly 10 Hz, or generously rounded up to 100 kΩ (then results in 7.2 Hz) does not really make a difference, especially since capacitors have quite large tolerances and the calculated limit frequency can therefore deviate significantly from the calculated value. In any case, you should recalculate your circuit with the selected standard values ​​including the tolerance for checking.

### Noise from resistors

There are two mechanisms of noise in resistors of all types: thermal resistance noise and current noise. The resistance noise is due to physics and occurs with every ohmic resistance, even with an ideal one. It is also known as thermal noise. It is zero at absolute zero (0 K = -273 ° C) and increases linearly with temperature. The noise voltage component is the same at every frequency and is called white noise in technical jargon. The resistance noise occurs independently of an applied voltage source, i.e. the noise voltage is generated in the resistor by externally supplied thermal energy. This noise can be greatly reduced by cooling with e.g. liquid nitrogen, which is used in highly sensitive special measuring devices. However, this effort is far too high for normal devices.As I said, the noise voltage obeys physical laws and can therefore be calculated very easily with a formula: With K = Boltzmann constant 1.38.10-23 Ws / K T = absolute temperature in Kelvin B = relevant bandwidth (with audio circuits usually 20,000 Hz)
In contrast to thermal noise, current noise only occurs when a voltage is applied to the resistor. Because of this effect, the current flowing through the resistor is not absolutely constant but is superimposed by a noise signal that is caused by the flowing current itself. In other words: the current "wriggles" around an average value, although the applied voltage is absolutely constant. The current noise is proportional to the applied voltage and depends heavily on the resistor material used, so it is a material constant. In the data sheets it is usually given in the unit μV / V, i.e. μV noise per volt of voltage on the resistor.

You can find more information about the noise of real resistors in Resistance noise.

### Load capacity / power loss

In a resistor, electrical energy is converted into thermal energy. This thermal energy heats the component, which in the end releases the heat to the environment. The maximum temperature of a resistor is of course limited. If it is exceeded, it suffers irreversible damage (i.e. deteriorates its properties) or burns out if it is significantly exceeded. It is therefore important that the heat energy is dissipated as effectively as possible.

In the case of low power types, this is done without great effort via the large surface compared to the permissible power loss: The warm / hot surface heats the air and thus gives off the heat to the environment. In addition, energy is emitted as radiant heat in the form of infrared radiation. With high-load resistors, very heat-resistant materials are often used in order to shift the maximum possible operating temperature upwards. This results in a large temperature difference between the surface and the environment, which improves the heat dissipation, since it is approximately proportional to the temperature difference. However, there are limits to this, since on the one hand the temperature at the connecting wires must not be so high that the melting temperature of the solder is exceeded, and on the other hand the resistor must not become so hot that nearby materials melt or even ignite. For this reason, high-load types are often equipped with a heat sink made of ribbed (to increase the surface) aluminum, which also have holes for mounting on an external heat sink in the interests of better heat dissipation.

You will always find information on the maximum load capacity in the data sheet. In the case of power types in particular, it is often specified as a function of the installation conditions. The power that a resistor converts into heat (often called power loss) is calculated as P = U * I; for alternating current, the rms values ​​are used. The resilience of the resistor should not be too tight based on the calculated value: On the one hand, a somewhat oversized resistor remains cooler during operation and, on the other hand, you have reserves for possible overloads. It can also be useful to connect two or more resistors of the same size in parallel in order to avoid the use of relatively expensive, large power types that are usually only available with a relatively large tolerance. It is important that you observe the so-called derating curve. It describes the decrease in the permissible power loss as a function of the ambient temperature. Usually, resistances of up to 70 ° C can be subjected to their nominal load capacity. Above this, it slowly decreases to zero. Incidentally, the ambient temperature does not mean the normally very low room temperature but the temperature of the cooling air. In a closed housing it can reach very high values ​​very quickly, especially if there are transformers or power components in the.

Since heat influences the behavior of electronic circuits, such resistors, which are subjected to a high electrical power (and not only in absolute terms but also with regard to their maximum permissible power loss), should be placed far away from components in which heat and in particular a heat gradient can lead to functional losses. This would be the case, for example, with differential amplifiers in which an offset voltage that is as small and constant as possible is important for the correct functioning of the circuit. Because even temperature-compensated circuits get out of hand if there is a heat gradient that leads the compensation to absurdity.