1. Why Combine Cells?
Sometimes one cell does not provide enough voltage or current for a circuit. To increase the total EMF or to increase the current capability, multiple cells are combined. The two common ways to do this are series and parallel combinations.
2. Cells in Series
Cells are said to be in series when the positive terminal of one is connected to the negative terminal of the next. This way, their voltages add up.
2.1. Definition of Series Combination
Series combination means connecting cells end-to-end so that the same current flows through each cell.
2.2. Equivalent EMF in Series
The total EMF is the sum of the EMFs of individual cells:
\( E_{\text{eq}} = E_1 + E_2 + E_3 + \cdots \)
2.2.1. Effect of Internal Resistance
The internal resistances also add up in series:
\( r_{\text{eq}} = r_1 + r_2 + r_3 + \cdots \)
So, the total resistance inside the combination becomes larger.
2.3. Small Example
Three cells each of EMF 1.5 V in series produce:
\( E_{\text{eq}} = 1.5 + 1.5 + 1.5 = 4.5\,\text{V} \)
3. Cells in Parallel
Cells are in parallel when all positive terminals are connected together and all negative terminals are connected together. This provides the same EMF as a single cell but allows the combination to supply more current.
3.1. Definition of Parallel Combination
Parallel combination means connecting all positive terminals together and all negative terminals together so that each cell experiences the same potential difference.
3.2. Equivalent EMF in Parallel
If all cells have the same EMF, the equivalent EMF remains the same as that of a single cell.
\( E_{\text{eq}} = E \)
3.2.1. Effect on Internal Resistance
The internal resistance decreases when cells are in parallel:
\( \dfrac{1}{r_{\text{eq}}} = \dfrac{1}{r_1} + \dfrac{1}{r_2} + \cdots \)
This allows the combination to supply more current.
3.3. Small Example
Two identical cells of 1.5 V in parallel still give 1.5 V, but the internal resistance is reduced to half.
4. Series vs Parallel Use Cases
The choice between series and parallel depends on the requirement of the circuit:
4.1. When to Use Series
- When higher EMF is needed
- When current requirement is moderate
4.2. When to Use Parallel
- When higher current is needed
- When EMF of one cell is sufficient
5. Mixed Combination
In many circuits, cells may be arranged partly in series and partly in parallel to achieve specific values of EMF and internal resistance.
This allows designing a combination that supplies both the needed voltage and adequate current.