Applications: Grouping Of Cells

Multiple cells can be grouped together to form any desired cell. In Practical situations in real life, we need the resistance and voltage of different values compared to what the cell has. The arrangement or grouping of the cells here can play a very important role to get the desired cell potential. For example, Suppose we have 5V and 3V cells. But we need an 8 V cell. So this can be easily done by grouping the cells in a series combination.

The combination of multiple cells in a circuit is known as a battery.

Series-Parallel Grouping of Cell

What is Grouping of Cells?

Grouping of cells is a way to organise multiple cells to get a battery of desired EMF. Mainly there are two types of grouping called Series and parallel grouping and the third combination of both is called Series-Parallel Grouping of Cell.

Series combination:

Two cells are said to be connected in series if the positive terminal of one cell is connected to the negative terminal of another cell. Let E1 and E2 be two cells connected with each other in a series combination. Let R1, R2 be their internal resistance. VA, VB,VC are the voltage across the points A, B, C respectively. Here A, B, C are the points connected to the negative terminal of the first cell any random point between the cells, and the point connected to the positive terminal of the second cell.

The potential difference between the two points A and B as per the definition of potential difference is given by= VB-VA

Similarly, the potential difference between B and C is given by=VC-VB

Hence, the potential difference between a and c in the series combination of the cells=

VAC = VA-VC = (VA-VB) + (VB-VC) = (E1+E2) – I(R1+R2)

We can imagine another cell, say E which will give the same emf as that of the combination of this cell. 

So,

V=E-IR

Now comparing the equations we get:

This can be generalised for n cells. Let  n be the number of cells that are connected in series:

E1,  E2…………..En

The equivalent combination of the series is given by:

E = E1 +E2…………..En

Example: If three cells 5V, 7V, 9V are connected in series, what are the equivalent combinations of the cells when connected in series?

Since the cells are connected in series the equivalent combination of cells:

E = (5+7+9)V

E = 21V

Rules for series combination:

1. The equivalent EMF of a series combination of cells is equal to the sum of the internal EMF s.

2. The equivalent internal resistance of the series combinations of the cells is equal to the sum of individual resistances.

Parallel combination:

Two cells are said to be connected in parallel or grouped in parallel if the positive terminal of all the cells is connected to a point and their negative terminals are connected to another point. Let E1  and E2 be two cells connected with each other in a parallel combination. Let R1, R2 be their internal resistance.VA, VB be the potential difference across the cells.

Let E be the equivalent potential and R be the equivalent resistance.

For the first cell,V = VB-VA = E1-I1*R1

For the second cell V = VB-VA = E2-I2*R1

I1 = E1 – V/R1

I2 = E2 – V/R2

After substituting the values of I1, I2 we get:

V= (E1R1+E2R2)/(R1+R2) – (IR1R2)/(R1+R2)

Comparing with the standard equation we have:

E = (E1R1+E2R2)/(R1+R2)

R = (R1R2)/(R1+R2)

Generalisation:

This can be generalised for n cells. Let  n be the number of cells that are connected in parallel:

E1,  E2…………..En

The equivalent combination of the series is given by:

E/R = E1/R1 + E2/R2 +…….+ En/Rn

Rules for parallel combinations of cells

• The equivalent EMF of multiple cells connected in parallel is equal to the weighted mean of the EMF of the cells and their internal resistance.
• The reciprocal of the equivalent internal resistance in parallel combination is equal to the sum of the reciprocal of the internal resistance of each cell.

Example:

Suppose there are 3 cells of 2 V and 4 V and let their internal resistances be 1 ohm each. What is the equivalent cell combination when grouping of cells is done in parallel?

=Since they are connected in parallel the equivalent cell combination =1.2 V

It is not necessary to only adapt either series or parallel combinations for grouping. We can use a combination of both the groupings to get the desired cell output.

Conclusion:

Grouping of cells is a technique to arrange the cells either in the series or parallel combination or mixed called Series-Parallel Grouping of Cell in order to get some desired EMF from what we have. Cells are said to be connected in series if the positive terminal of one cell is connected to the negative terminal of another cell in a linear fashion. On the other hand, cells are said to be connected in parallel if the positive terminal of all the cells are connected to a point and the negative terminal of the cells are connected to another point. In the series combination, the current passing through all the cells remains constant but the voltage across them depends on the resistance of the cells. In the case of parallel combination, the voltage across the cells remains the same.