Batteries in series and parallel Calculations

Like resistors and capacitors, batteries or cells can also be connected in series and parallel configurations. In this post you will know more about batteries in series and parallel configurations and calculations.

BATTERIES OR CELLS IN SERIES

Batteries in series are connected end to end that is; the positive electrode of one of the batteries is connected to the negative electrode of the other. At last, there are two different opposite terminals (positive and negative) remaining for external load connection. In this type of arrangements, when one of the batteries is disconnected, the other batteries cannot supply power to the external load. When two or more batteries are connected in series, their voltages(V) are summed up but the charge [in ampere-hours (Ah)] of the network remain the same.

Correct Series configuration

The above connection is the right way of connecting two batteries in series; both of the batteries are 12V40Ah. The total capacity of the above arrangement will be 24V40Ah.

Wrong Series configuration

The battery arrangement below is wrong because they are not of the same specs; one is 12V7.2Ah while the other is 12V40Ah, though this configuration can still power the external load. See batteries or cells maintenance tips

Also, the below connection is wrong because; the two terminals for external load connections are alike that is, (both are negative terminals).

 

The below connection also is wrong because; the two terminals for external load connections are alike that is, (both are positive terminals).

Output power of batteries in series configuration

The power in series configuration is the sum of the Voltage (V) of the batteries in series times the charge in Ampere-Hour (Ah) of one of them.

Formula

Pseries V1+V2+V3…….×Ah

Where Pseries is the power in series configuration, V1+V2+V3…….×are the voltages of the batteries, and Ah is the charge in Ampere-Hour of one of the batteries

Example

What is the total output power of the below configuration?

Solution

Pseries V1 + V2 + V3……. × Ah

=3.7 + 3.7 + 3.7 × 2

=11 × 2

=22.2VAh or 22.2Wh.

BATTERIES OR CELLS IN PARALLEL

When two or more batteries are in parallel configuration, their terminals (electrodes) are connected directly to each other. That is; all the positive electrodes of the batteries are connected together and also all their negative electrodes are connected together. In this configuration, when one of the batteries is disconnected from the arrangement, the others can still supply power to the external load. The charge in Ampere-Hour (Ah) of all the batteries connected in parallel are summed up while their voltage (V) remain the same.

Correct Parallel configurations

Below are the right ways of connecting two batteries in parallel configurations

 

The total capacity of the above arrangements is 12V80Ah.

Wrong Parallel configurations

The configuration below is wrong because, the batteries are not of the same specs; one is 12V40Ah while the other is 12V70Ah, thought they can still power an external load. The problem of this configuration is that one with less charge (Ah) will drain fast and after that, it will be draining the one with higher capacity. You can imagine what will happen to a battery that is designed to be 12V40Ah of capacity is forced to be 12V70Ah!

The below configuration is very dangerous, hazardous and can cause fire! If the capacities of the batteries are less than the below specs, they will still heat up and may “BOOOOOM” (burst) especially the Li-Ion type. This wrong configuration will lead to permanent damage of the batteries or cells. In fact, don’t even accidentally do this for electric cells or batteries especially secondary cells or batteries. When you study the arrangements, the batteries are connected in series first and then short circuited.

Output power of batteries in parallel configuration

The power in parallel configuration is the Voltage (V) of one of the batteries times the sum of the charges Ampere-Hour (Ah) of all the batteries in parallel.

Formula

P parallel = V × Ah1 + Ah2 + Ah3…….
Where P parallel is the power in parallel configuration in VAh or Wh, V is the voltage of one of the batteries in Volts (V), and Ah1 + Ah2 + Ah3……. are the total charges in Ampere-Hour of the batteries.

Example
What is the total output power of the configuration below?

Solutions

P parallel = V × Ah1 + Ah2 + Ah3…….
=3.7×2+2+2
=3.7×6
=22.2VAh or 22.2Wh

NOTES

From the above batteries in series and parallel calculations; the output powers are the same. This is because; batteries in series configuration delivers higher voltage but lower current; parallel configuration delivers higher current but lower voltage.

Read also batteries or cells maintenance tips and calculating Power inverter or UPS runtime

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