Cells in Series and Parallel

Electricity powers our daily lives, and batteries—or electrochemical cells—serve as portable sources of electrical energy. To meet the voltage or current requirements of various devices, individual cells are often connected in series or parallel configurations. Understanding how these arrangements affect voltage, current, internal resistance, and energy is essential for designing circuits, powering devices efficiently, and optimizing battery life.

This article explores cells in series and parallel in depth, covering their theory, mathematical treatment, advantages, disadvantages, and real-world applications.

1. Introduction: What Are Cells?

A cell is an electrochemical device that converts chemical energy into electrical energy through redox reactions. The basic components of a cell include:

Electrodes: Two conductors where oxidation and reduction occur (anode and cathode)
Electrolyte: A medium that allows ionic conduction
External circuit: Path for electron flow

Cells are categorized as:

Primary cells: Non-rechargeable, e.g., alkaline batteries, zinc-carbon cells
Secondary cells: Rechargeable, e.g., lead-acid, lithium-ion batteries

2. Need for Connecting Cells

Individual cells have limitations in voltage and current. For example:

Standard AA battery: ~1.5 V
Required for a device: 6 V or 12 V

To meet voltage or current demands:

Series connection: Increases total voltage
Parallel connection: Increases total current capacity

These arrangements are foundational in battery packs for electronics, vehicles, and renewable energy systems.

3. Cells in Series

3.1 Definition

When the positive terminal of one cell is connected to the negative terminal of the next, the cells are in series. This increases the total voltage while keeping current capacity nearly the same as that of a single cell.

Diagram:

+ | | - + | | - + | | -

3.2 Voltage in Series

For nnn identical cells of EMF EEE: Vtotal=nEV_{total} = nEVtotal=nE

If the internal resistance of each cell is rrr: Rinternal,total=nrR_{internal, total} = n rRinternal,total=nr

The total current supplied to an external load RRR is: I=nER+nrI = \frac{nE}{R + n r}I=R+nrnE

Example:
Three 1.5 V AA batteries in series with 2 Ω internal resistance and external load 4 Ω: Vtotal=3×1.5=4.5 VV_{total} = 3 \times 1.5 = 4.5\, \mathrm{V}Vtotal=3×1.5=4.5V Rtotal=4+3×2=10 ΩR_{total} = 4 + 3 \times 2 = 10\, \OmegaRtotal=4+3×2=10Ω I=4.510=0.45 AI = \frac{4.5}{10} = 0.45\, \mathrm{A}I=104.5=0.45A

3.3 Advantages of Series Connection

Higher voltage: Meets voltage requirements for devices
Simple connection: Easy to implement
Uniform current: Current through all cells is the same

3.4 Disadvantages of Series Connection

Limited current: Cannot increase current capacity
Weakest cell limitation: If one cell fails, the total voltage drops
Charging complexity: Recharging series-connected cells requires careful monitoring

3.5 Practical Applications

Flashlights and torches
Remote control devices
Laptops and mobile phones (battery packs with multiple series cells)
Electric vehicles (EVs) for higher voltage battery packs

4. Cells in Parallel

4.1 Definition

When the positive terminals of all cells are connected together, and negative terminals connected together, the cells are in parallel. This increases the current capacity (ampere-hour rating) while keeping the voltage nearly the same as that of a single cell.

Diagram:

+ | | -  
+ | | -  
+ | | -

4.2 Voltage in Parallel

For nnn identical cells of EMF EEE: Vtotal=EV_{total} = EVtotal=E

Internal resistance for each cell rrr, total internal resistance for nnn parallel cells: Rinternal,total=rnR_{internal, total} = \frac{r}{n}Rinternal,total=nr

Total current delivered to a load RRR: I=ER+r/nI = \frac{E}{R + r/n}I=R+r/nE

Example:
Three 1.5 V batteries in parallel, each with 1 Ω internal resistance, load 2 Ω: Rinternal,total=1/3≈0.333 ΩR_{internal,total} = 1/3 \approx 0.333\, \OmegaRinternal,total=1/3≈0.333Ω I=1.52+0.333≈0.643 AI = \frac{1.5}{2 + 0.333} \approx 0.643\, \mathrm{A}I=2+0.3331.5≈0.643A

4.3 Advantages of Parallel Connection

Higher current capacity: Can supply more total current
Redundancy: If one cell fails, others continue to supply current
Reduced effective internal resistance: Improves efficiency

4.4 Disadvantages of Parallel Connection

Voltage limitation: Cannot increase total voltage
Charging complexity: Cells must have similar voltage to avoid circulating currents
Uneven discharge: Mismatched cells may reduce overall performance

4.5 Practical Applications

UPS (Uninterruptible Power Supply) systems
High-current applications like power tools
Electric vehicles for higher capacity at fixed voltage
Solar battery banks for extended backup

5. Combining Series and Parallel (Series-Parallel Connections)

Many practical battery packs require both higher voltage and higher current. Series-parallel connections combine series strings of cells in parallel.

Example:

12 V requirement with high current:
4 series strings of 3.0 V cells in series, then 2 such strings in parallel

5.1 Calculation of Total Voltage

Vtotal=Voltage per series stringV_{total} = \text{Voltage per series string}Vtotal=Voltage per series string

5.2 Calculation of Total Current Capacity

Itotal=Sum of currents of parallel stringsI_{total} = \text{Sum of currents of parallel strings}Itotal=Sum of currents of parallel strings

This combination maximizes both voltage and energy capacity.

6. Internal Resistance of Cells

All real cells have internal resistance (rrr), which affects:

Terminal voltage: Vterminal=E−IrV_{terminal} = E – I rVterminal=E−Ir
Current output: Reduces maximum current
Energy loss: Dissipates power as heat (P=I2rP = I^2 rP=I2r)

Series connection: Rinternal,total=nrR_{internal, total} = n rRinternal,total=nr
Parallel connection: Rinternal,total=r/nR_{internal, total} = r/nRinternal,total=r/n

Minimizing internal resistance improves battery efficiency and performance.

7. Energy Stored in Cells

Energy stored depends on the EMF, current, and capacity: W=VItW = V I tW=VIt

7.1 Series Connection

Total energy: Wseries=nE⋅I⋅tW_{series} = n E \cdot I \cdot tWseries=nE⋅I⋅t

7.2 Parallel Connection

Total energy: Wparallel=E⋅nI⋅tW_{parallel} = E \cdot nI \cdot tWparallel=E⋅nI⋅t

Series increases voltage; parallel increases current capacity. Energy depends on both voltage and current delivered.

8. Charging Considerations

Series Charging:

Requires uniform charging to prevent overcharging weaker cells
Often uses constant current or voltage-regulated chargers

Parallel Charging:

Cells should have identical voltage
Circulating currents may occur if voltages differ
Reduces effective internal resistance, improving efficiency

9. Practical Examples

Flashlight: 3 AA batteries in series → higher voltage for the bulb
UPS Battery Pack: Multiple lead-acid batteries in parallel → higher current for longer backup
Electric Cars: Thousands of Li-ion cells in series-parallel → meet high voltage and high current needs
Solar Storage: Parallel strings of series-connected batteries → optimize capacity and voltage

10. Experiments and Demonstrations

10.1 Series Connection Experiment

Materials: 3 identical batteries, voltmeter, ammeter, load resistor

Procedure:

Connect batteries in series
Connect voltmeter across series string
Connect resistor as load
Measure voltage and current
Calculate resistance and compare with theory

10.2 Parallel Connection Experiment

Materials: Same as above