Created it, 05/10/15
Update it, 05/12/18
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CONNECTIONS SERIES - CONNECTIONS PARALLEL “2nd PART”
ASSOCIATION OF PILES
After having seen what occurs in the circuit external of the piles, according to the type of connection adopted for resistances, we let us examine the interior circuit with the piles.
The current which turns over to the poles negative of the pile, after having traversed the external circuit, must cross the electrolytic solution inside the pile to go on the positive pole, from where it starts again to circulate in the external circuit.
The electrolytic solution of the pile offers a resistance to the current which crosses it. As this resistance does not belong to the external circuit, it is called internal resistance of the pile.
Figure 9, the part located on the left of points A and B constitutes the internal circuit of the pile.
The pile having an internal resistance, it is possible to materialize it on the electric circuit, it is what we did with resistance Ri.
If we regard this resistance Ri as a resistance to whole share, being crossed by current I, a tension Vi will be born on its terminals. Ri produces a voltage drop but as Ri is located inside the pile, this drop voltage is carried out in the pile. For this reason the voltage resistance and drop which it causes are symbolized by an i, (i being used to recall that these two parameters are internal with the pile).
Consequently, the tension necessary to the terminals of the pile is not the total power provided by the pile, but is equal to this decreased tension of the internal voltage drop.
According to the law of Ohm, the tension which appears at the boundaries of Ri obtains by multiplying Ri by the current which crosses it, but this current is not other than the current crossing the circuit and provided by the pile.
We thus note that the internal voltage drop to the pile is all the more high as the current output by this one increases.
Conversely, this internal voltage drop is null when the pile is connected to no external circuit. Under such conditions, at the boundaries of the pile the totality of the power appears which it can provide.
This tension is called electromotive force of a pile and is symbolized by the letter E as in figure 9.
It should be retained this that the electromotive force of a pile is the tension present at its terminals when the pile does not provide any current. The unit of the electromotive force is of course the volt.
In the majority of the cases, the internal resistance of a pile is by far much lower than the resistance of the external circuit and during possible calculations, this value is neglected without that bringing appreciable error in the results.
In these cases, we consider that the power provided by the pile is equal to its electromotive force. Henceforth, for the term forces electromotive, we will use the universally recognized abbreviation f.e.m. (We defer the same circuit to facilitate the task to you).
To illustrate what has been just said, let us give values to the elements of figure 9 :
Current I circulating in the circuit is given by the relationship between the f.e.m. and the equivalent resistance of this circuit made up of R and Ri.
The voltage drop Vi intern to the pile is of :
The tension available at the boundaries of resistance R when the pile outputs a current of 1 A is of :
As you can note it, the tension dropped in Ri is tiny in comparison with the tension really available at the boundaries of R. For other calculations, Vi could thus be neglected.
Let us see now various realizable associations starting from several piles.
Figure 10 is represented the type of association which you will have to generally meet, it is about an association in series.
This association is carried out by connecting the positive terminal of the one on the negative terminal of the other. Since each pile has a f.e.m. of 1,5 V between points B and A, there is a potential difference of 1,5 V just as between the point C and B.
The point C an electric potential higher of 1,5 V than that of the point B, which itself has a higher potential of 1,5 V compared to point A. We will thus have an electric potential of 3 V between points C and A, terminals of the unit.
We can then conclude :
By putting several piles in series, one obtains a total f.e.m. equal to the sum of the f.e.m. of each pile.
One has recourse to this type of association when one needs a tension higher than that provided by only one pile. In this case, the whole of the piles connected in series is also called battery primary. This is the case of the pile of 4,5 V which you use for your practices since it is made of three elements of 1,5 V each one connected in series.
With regard to internal resistance, it is obvious that a primary battery has an internal resistance equal to the sum of internal resistances of each element which composes it. Lastly, all the elements being in series, they are crossed by the same current, as in all associations of this type. In addition, it is necessary to know that a pile should never provide a current of intensity higher than a value determined, which depends on its characteristics of manufacture, under penalty of involving its deterioration quickly.
Therefore the circuit external of a pile is never consisted a simple copper wire : indeed, because of the very low resistance of the wire, the pile would be obliged to provide a current of very high intensity which would deteriorate it very quickly. In this case, one says that the pile is in short-circuit ; for the good conservation of the piles, it is thus necessary to avoid putting them in short-circuit, by directly connecting their poles by a simple driver of negligible resistance.
When a current more important than that which only one pile can deliver is necessary, we use several piles connected in parallel as shown in the figure 11.
In this figure, we see that the total current provided by several piles in parallel is equal to the sum of the currents which each pile can provide.
Naturally, so that that occurs, one needs that the positive poles of each pile are connected between them, just as the negative poles, as on figure 11. At the boundaries of the unit, the f.e.m. is equal to that provided by only one pile, characteristic common to all associations in parallel.
In practice, this type of association is seldom used because if internal resistances and the f.e.m. of each pile are not rigorously identical, one will observe the discharge of a pile in the other involving their mutual deterioration.
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