Combination of Cells: EMF, Series & Parallel

Electricity is one of the most fundamental necessities in human daily life, as it is used to power many things, from basic torches to complex communication systems. At the centre of many electrical circuits, there is a source of electrical energy in the form of an electric cell or battery. An electric cell, such as a dry cell, converts chemical energy into electrical energy. However, in many situations, a single cell cannot supply the required voltage or current. To overcome this limitation, cells are connected in different ways. This arrangement is known as the combination of cells.

The combination of cells is a significant concept in physics since it demonstrates how electric energy sources are connected in order to fulfil given circuit conditions. Depending on the requirement of higher voltage, greater current, or both, cells may be connected in series, in parallel, or in a series–parallel combination.

Types of Batteries

An electric cell is a device that generates electrical energy using chemical reactions that take place inside the cell. The cell has two terminals: a positive terminal and a negative terminal. When the cell is connected to an external circuit, electrons flow through the external circuit from the negative terminal to the positive terminal, producing electric current.

In every cell, there are two key values:

Electromotive Force

The electromotive force (emf) of a cell is the potential difference between its terminals when no current is drawn from the cell. The energy a cell produces per unit charge is the electromotive force of the cell, measured in volts (V).

Internal Resistance

Each cell will have some resistance within it, known as internal resistance. The internal resistance resists the current flow in the cell, resulting in a reduction in terminal voltage while in use.

The value of the terminal voltage in a cell depends upon its emf and internal resistance, especially when the current is passing through the circuit.

Requirement for a Combination of Cells

A single cell will provide only a small voltage and current. For instance, in a dry cell, the voltage supplied will only be 1.5V. Most devices will need higher voltages or currents than those supplied in single cells. As such, the required output will thus be obtained by joining several cells together.

The reasons for cell combination are as follows: for increasing the overall voltage supplied to the circuit; to increase the current capacity; to avoid the influence of internal resistance; for the longer operation of devices.

The way cells are combined depends on the requirements of the external circuit.

Kinds of Combination of Cells

The three types of combinations of cells include: cells coupled in series; cells connected in parallel; series–parallel combination of cells. Every type has its own features and uses.

Cells in Series

When the cells are joined end to end, with the positive end of one cell joined to the negative end of the next cell, then the cells are said to be connected in series.

Equivalent emf

If n identical cells each having emf E are connected in series, the equivalent emf is:

E eq = n E

Consequently, the value of emf increases with the number of cells.

Similar Internal Resistance

If each cell has internal resistance r, then the total internal resistance in the series combination will be:

$r_{eq} = n r$

Current in Series Addition

If the series combination is connected to an external resistance R, then the current I in the circuit is:

$I = \frac{n E}{R + n r}$

Advantages

Higher Voltage Output: When cells are connected in series, their emfs add up to yield a higher total voltage that is appropriate for devices needing a high potential difference.

Simple Layout: The series connection is easy to design and construct; thus, it's convenient in basic electrical circuits.

Suitable for High-Resistance Circuits: Series combination works efficiently in circuits where the external resistance is high compared to the internal resistance.

Disadvantages

Increase in Internal Resistance: The internal resistances of all the cells add up and hence reduce the current flowing in the circuit.

Failure of One Cell: When one cell fails, the whole circuit is affected. The failure or weakening of one cell may break the entire circuit.

Limited Current Supply: A large current is not provided through a series combination. Hence, it cannot be used for low-resistance or high-current devices.

Applications

Electric Torches: The cells are connected in series to obtain sufficient voltage for proper glowing of the bulb.

Remote Controls: Voltage in a series combination provides the required voltage for the smooth operation of electronic components.

Electric Bells: A higher voltage from series-connected cells helps in the effective operation of the electromagnet.

Cells Connected in Parallel

When all the positive terminals of the cells are connected, and all the negative terminals are connected, the cells are said to be connected in parallel.

Equivalent emf

In the case of n identical cells connected in parallel, the value of the equivalent emf remains the same as that of a single cell:

$Equivalent emf = E$

Equal Internal Resistance

The total internal resistance in the parallel combination will decrease and will be given by the following expression:

$Equivalent internal resistance = \frac{r}{n}$

Current in Parallel Combination

If a parallel combination is joined to a resistance R, then the current is given by:

$I = \frac{E}{R + r / n}$

Advantages

Greater Current Supply: The cells connected in a parallel arrangement can deliver a large amount of current.

Minimized Internal Resistance: The effective internal resistance will decrease since there will be many paths available for the currents to flow through.

Extended Battery Life: The load is shared between the cells. They discharge slowly, and they last longer.

Disadvantages

Voltage does not increase: The magnitude of the entire voltage equals that of the single battery. This restricts its applications.

Risk of Energy Loss with Unequal Cells: If the cells have different emf values or internal resistances, current could flow between them.

More Complex Connections: The parallel connection is relatively more complex and demands more attention to insulation.

Applications

Emergency lighting systems: Cells are often connected in parallel to provide higher current and longer backup time.

Power Banks: The cells are joined in parallel for high current supply and prolonged backup time.

Uninterrupted Power Supply (UPS): It provides continuous current in case of a power failure because of parallel connectivity.

Conclusion

A combination of cells involves a fundamental concept of electricity and magnetism. In series, parallel, and series–parallel combinations of cells, any reasonable voltage and current can be obtained for different electrical appliances. Series combinations are suitable for obtaining higher voltage, while parallel combinations are suitable for supplying larger currents with reduced internal resistance. In practical applications, a series–parallel arrangement is followed that may provide some reasonable compromise between voltage and current.

A proper understanding of the combination of cells not only helps in solving numerical problems in physics but also plays an important role in the practical design and safe use of electrical and electronic systems.

FAQs

1. Why should cells of unequal EMFs not be connected in parallel?
If the cells have a different emf value and are connected in parallel, there may be a flow of current from the cell with a high emf to the cell with a low emf.

2. What will happen if a cell in the series combination fails?
A faulty cell can break the circuit, and thus the entire series circuit will not supply current.

3. Why does the internal resistance decrease when it is combined in parallel?
In a parallel circuit, there are several paths that exist for the flow of current, which reduces the effective resistance of the combination.

4. Under what condition does a combination of cells deliver maximum power to the external circuit?
The maximum power will be achieved when the internal resistance of the combination is equal to the external resistance.