Batteries in Series & Parallel

Intuition

Standing on shoulders, or standing side by side

An acrobat climbing onto a partner's shoulders makes the pair twice as tall — but no stronger, and if either one tires the tower comes down. Standing side by side they are no taller than before, and between them they can hold twice as much for twice as long. Cells offer the same choice, and it carries the same trade.

In series, cells are joined positive terminal to negative terminal in a chain, and their voltages add. Four ordinary 1.5 V cells in a torch give 6 V. Almost every battery above 1.5 V is built this way, the rectangular 9 V one included: it holds six small cells stacked inside its case.

In parallel, cells are joined positive to positive and negative to negative, and the voltage stays exactly what one cell provides. The group gains elsewhere. It holds more charge, and it can supply more current without complaint. Two identical cells in parallel run a torch for twice as long, at the same brightness.

Which arrangement you want follows from whatever is short. A device needing more volts than one cell gives calls for a series string; a device that runs down too soon, or whose cell sags badly the moment current is drawn, calls for cells in parallel. Real packs — in a laptop, in an electric vehicle — do both at once, a group of parallel cells forming one unit, with units stacked in series to reach the working voltage.

The acrobat picture carries the warning too. A tower is only as good as its weakest member, and a series string behaves the same way: one tired cell drags the whole pack down, and the healthy cells around it can do that tired one real harm.

Practitioner

Series: volts add, and so does resistance

For identical cells in series, the pack voltage is the cell voltage multiplied by the count:

Internal resistance stacks along with it, which is the part people forget. Each cell contributes its own in series with all the others, so a stack is a stiffer source in voltage and a softer one in current than a single cell:

A cell fitted backwards in a series string subtracts its voltage instead of adding it, so a four-cell pack with one reversed reads the voltage of two cells rather than four. That is the standard explanation for a pack that reads far too low and a device that will not start.

Parallel connection makes the opposite trade. Voltage stays at one cell's value, capacity in ampere-hours adds, and the internal resistances combine the way parallel resistances do, so the group sags less under the same current. A design that needs more voltage and more current uses both arrangements together: a pack described as "4S3P" has three cells in parallel forming a unit, with four such units in series.

Cells wired together have to belong together, which means matching on chemistry, nominal capacity, manufacturer, age and state of charge. Put an old cell alongside a new one, or an alkaline alongside a rechargeable, and the others will drive one of them outside its intended operating range.

Ampere-hours and watt-hours do not measure the same thing. Series connection multiplies the voltage and leaves the ampere-hour figure alone; parallel connection does the reverse. Multiplying the two gives energy in watt-hours, and that is the quantity actually conserved — the same six cells store the same energy in either arrangement, only packaged differently. See electrical energy.

Engineer

Parallel, and why series strings need watching

A series string carries one failure mode that a parallel group does not. Every cell in the string sees the same current, so the weakest is exhausted first, and once it is empty the rest keep driving current through it — backwards. Reverse-charging a discharged cell heats it, generates gas and can rupture or vent it. That is the specific reason equipment warns against mixing old and new cells, and the reason a series pack is replaced as a set.

Parallel groups have a difficulty of their own, and it arrives at connection time. Two cells at different states of charge, wired directly together, equalise through their own internal resistances with nothing to limit the current, which can run very large for a short while. So cells are paralleled at matched voltage, or through a current-limiting arrangement, and the connection is made before charge rather than after.

Pack performance is decided largely by internal resistance, and internal resistance moves. It climbs as cells age and as they discharge, and it climbs sharply in the cold. A pack that performed well when new and cuts out under load a year later has usually gained internal resistance rather than lost capacity, which is why cell testers measure resistance rather than voltage, as voltage sources explains.

The acrobat image understates the series case. In a string a strong cell actively damages a weak one, while in parallel the same pair works the other way round and the strong cell supports the weak. That asymmetry is why parallel groups tolerate mismatch better, and why cell balancing is a series-string problem.

Capacity across a mixed pack rarely adds up the way people expect. A series string's usable capacity is set by its smallest cell rather than by the average, so adding one high-capacity cell to a string of tired ones changes nothing useful.

Professional

Real packs, and the reasons they are managed

Any lithium pack of consequence carries a battery management system. It monitors each series group's voltage, disconnects on over-voltage, under-voltage, over-current and over-temperature, and balances the groups so that none runs ahead of the rest. Series strings drift apart over time because no two cells are identical, and without balancing the weakest group reaches its limits first on every cycle, ages faster, and drags the string down further.

Fusing belongs at the string rather than at the pack. In a parallel arrangement of series strings, a fault in one string can be fed by all the others, so cell-level or string-level fusing is what keeps one failure from becoming a pack-wide event. It also sets the rating: the fuse is chosen against the fault current the rest of the pack can deliver, not against the working current.

One cell on its own is already a serious energy source. A lithium cell of 3.7 V with an internal resistance of 30 mΩ can deliver 123 A into a dead short, out of an object that fits in a pocket. Multiply that across a parallel group and the figure becomes an installation hazard rather than a bench one.

The load chooses the topology. High voltage at low current reduces the copper needed and the resistive loss for a given power, which is why electric vehicles use long series strings. Low voltage at high current keeps the system below the thresholds where safety and insulation requirements escalate. Most designs land somewhere between the two, at whatever the motor or converter needs.

Chemistry sets the rules. Cell voltage, permissible charge and discharge rates, tolerance of over-discharge, behaviour when reversed and behaviour when abused all differ by chemistry — see battery types and battery charging. Lead-acid is happy on a float charge and dislikes deep discharge, while lithium-ion accepts neither float nor over-discharge. Nickel chemistries put up with more abuse than either, and self-discharge faster. A pack whose topology arithmetic is right will still fail early if it ignores the constraints its chemistry imposes.

The interconnect counts as part of the pack. Nickel strip, spot welds, busbars and connectors all add resistance in series with the cells, and an uneven interconnect makes some cells work harder than others inside a parallel group. Symmetry in the interconnect is designed in for exactly that reason.