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Notion of Electrical Resistance - Ohm's Law :
NOTE :
The goal of electronics is to explain some rules that can help you in certain areas and especially on the operation of computers. We will start on different pages and at the bottom of these, you will see a link called "Next Lessons or Electronic Summary" that will allow you to navigate to guide you and, to follow the lessons in the corresponding order. So, We'll start with Ohm's law and then Joule's law and many more ... Some paragraphs are for beginners.
We also advise you to start the Basic E-Lessons, which aims to understand all the programs starting with Ohm's Law and following the lessons in order. Then test your knowledge so that you can see the accuracy of the lessons you learned earlier. You can choose the lessons of your choice for example digital electronics as well as the corresponding practice, (14 lessons and 14 digital practices). To do well, you must start the first digital theory lesson then the first digital practice lesson, then the second theoretical lesson and the second lesson of practice and so on to take full advantage of the education of this site.
1. - NOTION OF ELECTRIC RESISTANCE
Any electrical current in a conductor is due to an electron movement. During their displacement, these electrons encounter obstacles due to the driver's atoms.
A conductor presents a certain opposition to the passage of the electric current, opposition which is called electrical resistance.
The concept of electrical resistance can extend to any material, even insulators insofar as they oppose the displacement of electrical charges so much resistance that it virtually prevents any current flow.
Resistance ranks among the electrical quantities and has its unit.
1. 1. UNIT FOR MEASURING ELECTRIC RESISTANCE
The electrical resistance (symbol R) is measured in Ohm (symbole W).
W is the last letter of the Greek alphabet : Omega. To indicate the value of the resistances, multiples of the Ohm are frequently used such as the kiloohm (symbol kW) which is worth 1000 ohms or the megohm (symbol MW) which is worth 1 million ohms.
Resistance R of an electric driver is defined by three parameters :
its length
its section
its nature
1. 1. 1. - INFLUENCE OF SA LENGTH
It is obvious that the resistance met by the electric charges moving in a driver is all the more large as this driver is long, because the number of the atoms met by the loads on their way is more important.
The resistance of a driver is thus proportional to its length.
1. 1. 2. - INFLUENCE OF SA SECTION
The electric charges are driven all the more easily as the section of the driver is important. To imagine that, one can say that the electric charges have a more important space to move.
The resistance of a driver is thus inversely proportional to its section.
1. 1. 3. - NATURAL INFLUENCE OF SA AND CONCEPT OF RESISTIVITY
Two of the same drivers length and of the same section, but of nature different, i.e. made up from different materials (for example one coppers some, the other out of iron) have different electric resistances.
The difference between the electric properties of materials is characterized by their resistivity. The symbol of the resistivity is the Greek letter r (rhô) and its unit is the ohmmeter (W-m). Appear 1-a are gathered the resistivities of principal pure metals and alloys of everyday usage in electric technique.
Metal | Resistivity with 20°C |
Money | 1,6 x 10-8 W - m |
Copper | 1,7 x 10-8 W - m |
Aluminum | 2,8 x 10-8 W - m |
Tungsten | 5,6 x 10-8 W - m |
Iron | 9,6 x 10-8 W - m |
Platinize | 10 x 10-8 W - m |
Lead | 22 x 10-8 W - m |
Mercury | 95 x 10-8 W - m |
Alloy | Composition | Resistivity (in 10-8 W - m) |
Brasses |
Cu 60 to 70% Zn 40 to 30% |
Between 5 and 10 |
Copper nickel zinc alloy |
Cu 60% Zn 25% Nor 15% |
30 |
Manganin |
Cu 85 % Mn 11 % Ni 4 % |
40 |
Constantan |
Cu 60% Nor 40% |
50 |
Ferronickel |
Fe 75% Nor 25% |
80 |
Nickel-chromium |
Ni 65 % Fe 23 % Cr 12 % |
110 |
A small comment on these tables is necessary, one realizes that the resistivity is not expressed in W-m and this because this unit is too much large for the drivers. In the figure 1-a, one uses hundred millionth ohmmeter (10^{-8} W-m). But according to the works, you can find this resistivity expressed in µW-m (microohm-meter) which is worth 10^{-6} W-m or in µW-mm. Conversely for the insulators whose resistivity is important one uses the megger (MW-m) which is worth 10^{6} (1 million) W-m.
1. 1. 4. - MEASUREMENT OF THE ELECTRIC RESISTANCE OF DRIVER
As we have just seen, the electrical resistance of a conductor is defined by three parameters. We can therefore think that these parameters can be linked to each other by a relation making it possible to determine the resistance of a given driver knowing his dimensions and his nature.
We already know that this resistance is proportional to the length :
R = f (l) (is read R according to l).
We also know that this resistance is inversely proportional to the section :
The resistivity of the driver is also involved in this calculation. The resistivity unit being the ohm-meter ; thus, the longer the driver will be, the more the influence of its resistivity will be felt on the displacement of the electrons and therefore on the conduction resistance :
R = f (r)
From the combination of the three previous relationships, we can deduce the general formula for determining a driver's resistance :
Knowing this formula, we can as example calculate the resistance which has a copper driver 100 m length and 1 mm^{2} (10^{-6}m^{2}) of section, knowing that the resistivity of copper is 1,7 x 10^{-8} W-m.
To supplement our example, the figure 1-c gives the resistance of 100 m length drivers and 1 mm^{2} of section but made out of various materials, and this with an aim of carrying out a better comparative analysis of these metals at the point of the electric sight.
Metal | Resistance of a 100 m length wire and 1 mm^{2} of section |
Money | 1,6 W |
Copper | 1,7 W |
Aluminum | 2,8 W |
Tungsten | 5,6 W |
Iron | 9,6 W |
Platinize | 10 W |
Lead | 22 W |
Mercury | 95 W |
Lastly, to close this chapter on electric resistance, it should be known that this one varies with the temperature because the resistivity of the substance also varies with the temperature. However, all the substances do not react in an identical way. In general, the resistivity increases when the temperature increases but in different proportions according to the substances.
The alloys, although having a resistivity more important than pure metals (figure 1-b), have on the other hand a resistivity much more stable.
For example the manganin and the constantan (what justifies the name given to this alloy) are particularly used for the realization of calibrated resistances or the ohm-standards (resistances especially built to represent as exactly as possible the unit of electric resistance).
Some substances see, on the other hand, their resistivity decreasing when the temperature increases and it is in particular the case of certain mixtures of oxides or sulfides.
1. 2. - CONDUCTANCE AND CONDUCTIVITY
Until now, we considered the drivers from the point of view of the resistance which they oppose in the passing of the current, but as its name indicates it, this driver is used to convey the current of a point to another.
The aptitude of a driver to convey the current more or less well is called the electric conductance. A driver presents a all the more large conductance as its resistance is low. The conductance will be thus the reverse of resistance.
The symbol of the conductance is G and its unit is Siemens (symbol S).
As we defined a resistivity, we can define a conductivity which is the reverse of the resistivity.
G = 1 / r
The symbol of conductivity is g (is read gamma, letter of the Greek alphabet) and its unit is Siemens / meter (symbol S / m).
As we saw, we can call drivers all the elements which present the property to be easily let cross by the current, they thus have a high conductivity and offer a low resistance to this current : it is in particular the case of copper wire used to carry out the connections in the electric circuits.
In these circuits however it often presents the need for opposing to the current a more or less high resistance, this is obtained by the use of elements carried out starting from materials with high resistivity.
These elements cannot be regarded any more as drivers with whole share insofar as their specific role is to oppose to the electrical current a given resistance.
For this reason, these elements are called resistances and are characterized by the resistance, expressed in ohm, which they oppose to the current.
In the table of the figure 1-d are gathered the four sizes which we have just examined. For each one of them are deferred the unit, the symbol corresponding and the relations existing between these sizes.
Most important of these sizes without question resistance is because we can directly measure his value by comparison with known elements, as we will see it in good time.
2. - THE LAW OF OHM
All the electric quantities relating to a circuit are now defined. We know the tension, the current (or intensity) and resistance. We can pass on to the examination of a complete circuit and to see which influence have each one of these three sizes on its operation. Let us start with the very simple circuit such as it is represented figure 1-a).
This circuit consists of a resistance connected to a pile, the insertion of resistance is necessary so that the circuit presents a well defined resistive value.
Appear 1-a, the circuit components are represented under their real aspect but during the examination of the electric circuits one always considers the components under their aspect symbolic system. We thus obtain the electric diagram of the circuit to be analyzed.
Appear 1-b are given the electric symbols of the three components of our circuit, while the figure 1-c appears its electric diagram
The letters A, B, C and D of the figures 1-a and 1-c indicate the points where the two drivers connecting the pile and resistance are welded onto these two elements. The part of the diagram on the left of points A and B represents the internal circuit of the pile while the part on the right of these same points represents the circuit external with the pile, circuit consisted the drivers and resistance.
On the figure 1-c, we can indicate the various known electric quantities clearly.
The tension obtained at the boundaries of the pile between the points A and B is indicated by its symbol V. This symbol is registered between the two arrows which highlight point A and B, points between which appears this tension.
The same tension V is also present at the terminals of resistance R, that is to say between the point C and D, because the point (C) is connected directly to the item (A) and thus has the same electric potential as this point ; it is the same with the point D directly connected to B.
The resistance of the circuit external with the pile is located by its symbol R. One takes account only of the resistive value of resistance and one neglects those of the drivers and the pile which are very weak. Lastly, the current which crosses the circuit is indicated by its symbol (I) with the arrow showing the direction of its displacement following the conventional direction. We clearly see on this diagram that the current leaves the positive pole of the pile, crosses the driver AC then resistance R and returns to the negative pole of the pile via driver DB.
The existing tension V at the boundaries of the pile tends to cause the flow of current I while resistance R presents an obstacle at its passage : it is understood that the intensity will depend on the tension and resistance. In other words, it must exist a relation which binds between them these three fundamental electric quantities.
This relation was discovered by the German physicist George Simon OHM (1789-1854) and was called law of Ohm. The unit of resistance also bears the name of this physicist.
Ohm could state its law following many experiments and of meticulous measurements; to have an idea of the process which it adopted, one can make some simple remarks.
As the tension of the pile is the cause which determines the flow of the current in the circuit, if the tension is increased, one increases also the intensity of the current ; one can easily check this fact by successively connecting to the circuit piles which give tensions increasingly higher and by measuring the intensity of the current that each one of them makes circulate, but one can go further.
Indeed, if one divides the tension of each pile by the intensity of the current which it makes circulate, one always finds the same value; this value does not vary thus, although one varies the tension, and also consequently the intensity of the current.
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