Battery Associations in Series and Parallel "2nd part" :
BATTERY ASSOCIATION :
After seeing what happens in the external circuit of the batteries, depending on the type of connection adopted for the resistors, we will examine the internal circuit to the batteries.
The current which returns to the negative poles of the battery, after having traversed the external circuit, must pass through the electrolytic solution inside the cell to reach the positive pole, where it starts to circulate in the external circuit.
The electrolytic solution of the cell provides resistance to the current flowing through it. Since this resistor does not belong to the external circuit, it is called the internal resistance of the battery.
Figure 9, the part to the left of points A and B is the internal circuit of the battery.
The battery has an internal resistance, it is possible to materialize on the electrical circuit, that's what we did with the resistance Ri.
If we consider this resistance Ri as a resistor in its own right, when the current I passes through it, a voltage Vi will be born at its terminals. Ri produces a voltage drop, but since Ri is located inside the cell, this voltage drop occurs in the cell. It is for this reason that the resistance and the voltage drop that it causes are symbolized by an i, (i serving to remind that these two parameters are internal to the battery).
As a result, the voltage required at the terminals of the battery is not the total voltage supplied by the battery, but is equal to this voltage less the internal voltage drop.
According to Ohm's law, the voltage which appears across Ri is obtained by multiplying Ri by the current flowing through it, but this current is none other than the current flowing through the circuit and supplied by the battery.
We therefore note that the internal voltage drop in the stack is all the higher as the current output by it increases.
Conversely, this internal voltage drop is zero when the battery is not connected to any external circuit. Under such conditions, at the terminals of the battery appears all the voltage it can provide.
This voltage is called electromotive force of a battery and is symbolized by the letter E as in figure 9.
It should be remembered that the electromotive force of a battery is the voltage present at its terminals when the battery supplies no current. The unit of the electromotive force is of course the volt.
In most cases, the internal resistance of a cell is far below the resistance of the external circuit and in any calculations, this value is neglected without any appreciable error in the results.
In these cases, we consider that the voltage supplied by the battery is equal to its electromotive force. From now on, for the term electromotive force, we will use the universally recognized abbreviation f.e.m. (We post the same circuit for your convenience).
To illustrate what has just been said, give values to the elements in Figure 9 :
E = 9 V
Ri = 0,3 Ohm
R = 8,7 Ohms
The current I flowing in the circuit is given by the ratio between the f.e.m. and the equivalent resistance of this circuit consisting of R and Ri.
I = E / Req = E / R + Ri = 9 V / 0,3 + 8,7 = 9 / 9 = 1 A
The voltage drop Vi internal to the battery is :
Vi = Ri x I = 0,3 x 1 = 0,3 V
The voltage available across the resistor R when the battery delivers a current of 1 A is :
V = E - Vi = 9 - 0,3 = 8,7 V
As you can see, the voltage drop in Ri is minimal compared to the voltage actually available across R. For further calculations, Vi could be neglected.
Now let's see the different combinations that can be made from several stacks.
Figure 10 shows the type of association you will meet most often, this is a serial association.
This association is made by connecting the positive terminal of one to the negative terminal of the other. Since each pile has a f.e.m. 1.5 V between points B and A, there is a potential difference of 1.5 V as well as between points C and B.
Point C has an electrical potential 1.5 V greater than that of point B, which itself has a potential greater than 1.5 V compared to point A. We will therefore have an electric potential of 3 V between points C and A, terminals of the set.
We can then conclude :
By putting several batteries in series, we obtain a f.e.m. total equal to the sum of the f.e.m. from each pile.
This type of association is used when a higher voltage is required than that provided by a single battery. In this case, all the batteries connected in series is also called battery of batteries. This is the case of the 4.5 V battery that you use for your practices since it consists of three elements of 1.5 V each connected in series.
As regards the internal resistance, it is obvious that a battery of batteries has an internal resistance equal to the sum of the internal resistances of each element which composes it. Finally, all the elements being in series, they are crossed by the same current, as in all associations of this type. On the other hand, it should be known that a battery must never provide a current of intensity higher than a determined value, which depends on its manufacturing characteristics, otherwise it will quickly lead to its deterioration.
This is why the outer circuit of a battery is never made of a single copper wire : indeed, because of the very low resistance of the wire, the battery would have to provide a current of very high intensity high which would deteriorate very quickly. In this case, it is said that the battery is short-circuited ; for the good conservation of the batteries, it is thus necessary to avoid putting them in short circuit, by directly connecting their poles by a simple conductor of negligible resistance.
When a current greater than that which can be delivered by a single battery is necessary, we use several batteries connected in parallel as shown in Figure 11.
In this figure,we see that the total current supplied by several cells in parallel is equal to the sum of the currents that each cell can provide.
Naturally, for this to happen, it is necessary that the positive poles of each stack are connected together, as well as the negative poles, as in Figure 11. At the terminals of the set, the f.e.m. is equal to that provided by a single stack, a feature common to all associations in parallel.
In practice, this type of association is rarely used because if internal resistances and f.e.m. each stack is not exactly identical, we will observe the discharge of one battery in the other resulting in mutual deterioration.
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