Grouping of Cells

Grouping of cells means connecting two or more cells in an electrical circuit. Sometimes a single cell can’t provide the amount of voltage and current required in the circuit that’s why cell grouping is done. Like combinations of resistance, cells can also be connected in many ways. We are also going to discuss what happens when we mix those two in a mix. When we combine a few cells the equivalent voltage and also equivalent internal resistance changes which results in high voltage or current. We can easily combine cells to fulfil our circuit demands. 

Discussion

In this section, we are going to discuss the current-voltage relationship of series, parallel, and mixed combinations of cells. 

Series combination

In series combination, we connect two or more cells in series with the outer circuit. If we connect n number of identical cells of emf E in series with the outer circuit having resistance R and internal resistance of each cell is r – 

The total resistance of the circuit = R + nr

Total emf of the circuit = nE

So current in the circuit I = (total emf / total resistance) 

                          I = nE/( R + nr) 

Potential difference across the external resistance V = IR = nER /(R + nr) 

Output power P = R ((nE/(R + nr)) 2

 There are two special cases – 

1. When R>>nr 

In this situation, we can neglect nr so the current I = n (E/R) which is n times the current of a single cell. With help of it, we can get a higher value of current hence a higher potential difference across the resistance. 

1.  When R<<nr

In this situation, we can neglect R so the current 

I = (E/r) which is equal to the current of a single cell. 

Parallel combination

In a parallel combination, we connect a few cells in parallel with the outer circuit. When we connect n numbers of identical cells of emf E and internal resistance r with an outer resistance R in this combination – 

Total resistance of the circuit = Rr/(r+nR) 

Total emf of the circuit = E 

 So current in the circuit I = E(r+nR)/Rr

The potential difference in outer circuit = E

Power output = (r+nR) E2/Rr

There are two special cases in parallel combination – 

1. When R>>r/n

In this situation, the current I=(E/r) is the same current of a single cell. 

1. When R<<r/n 

In this situation, the current I= n(E/r) is n times the current of a single cell. 

Mixed combination

In a mixed combination, we use both series and parallel combinations together. If we connect n identical cells in series and m such series in parallel with external resistance R then- 

Total resistance = R+(nr/m) 

Total emf = nE

Total current = nE/(R + nr/m) 

Current will be maximum when R/n= r/m

And maximum current Imax = nE/2R

Power will also be maximum in this condition. 

Maximum power P = n2E2/4R

Disadvantages

There are advantages and disadvantages to every combination. 

1. In series combination, if one of the cells or resistance breaks or stops working the whole circuit will fail.
2. In a series combination, the total resistance increases causing higher voltage and energy loss. 
3. As we have discussed above in parallel combination the effective potential difference across a resistor is equal to the potential difference due to a single cell. So we cannot increase the potential difference even if it is needed 
4. Parallel combination requires a large amount of wire and the circuit can become messy sometimes. 

Conclusion

 We combine or group cells to get high current and potential differences. The main two combinations have some limitations as well. So while constructing a circuit we should keep it in mind and choose what’s best for our circuit. The series and parallel combinations are the main two groupings.