A series circuit with a voltage source (such as a battery, or in this case a cell) and three resistance units
Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an electrical component (e.g. a resistor) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participates in the series/parallel networks.
Components connected in series are connected along a single "electrical path", and each component has the same electric current through it, equal to the current through the network. The voltage across the network is equal to the sum of the voltages across each component.[1][2]
Components connected in parallel are connected along multiple paths, and each component has the same voltage across it, equal to the voltage across the network. The current through the network is equal to the sum of the currents through each component.
The two preceding statements are equivalent, except for exchanging the role of voltage and current.
A circuit composed solely of components connected in series is known as a series circuit; likewise, one connected completely in parallel is known as a parallel circuit. Many circuits can be analyzed as a combination of series and parallel circuits, along with other configurations.
In a series circuit, the current that flows through each of the components is the same, and the voltage across the circuit is the sum of the individual voltage drops across each component.[1] In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents flowing through each component.[1]
Consider a very simple circuit consisting of four light bulbs and a 12-volt automotive battery. If a wire joins the battery to one bulb, to the next bulb, to the next bulb, to the next bulb, then back to the battery in one continuous loop, the bulbs are said to be in series. If each bulb is wired to the battery in a separate loop, the bulbs are said to be in parallel. If the four light bulbs are connected in series, the same current flows through all of them and the voltage drop is 3 volts across each bulb, which may not be sufficient to make them glow. If the light bulbs are connected in parallel, the currents through the light bulbs combine to form the current in the battery, while the voltage drop is 12 volts across each bulb and they all glow.
In a series circuit, every device must function for the circuit to be complete. If one bulb burns out in a series circuit, the entire circuit is broken. In parallel circuits, each light bulb has its own circuit, so all but one light could be burned out, and the last one will still function.
Series circuits
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Series circuits are sometimes referred to as current-coupled or daisy chain-coupled. The current in a series circuit goes through every component in the circuit. Therefore, all of the components in a series connection carry the same current.
A series circuit has only one path through which its current can flow. Opening or breaking a series circuit at any point causes the entire circuit to "open" or stop operating. For example, if even one of the light bulbs in an older-style string of Christmas tree lights burns out or is removed, the entire string becomes inoperable until the faulty bulb is replaced.
Current
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I = I 1 = I 2 = ⋯ = I n {\displaystyle I=I_{1}=I_{2}=\cdots =I_{n}}
In a series circuit, the current is the same for all of the elements.
Voltage
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In a series circuit, the voltage is the sum of the voltage drops of the individual components (resistance units).
V = V 1 + V 2 + ⋯ + V n = I ( R 1 + R 2 + ⋯ + R n ) {\displaystyle V=V_{1}+V_{2}+\dots +V_{n}=I\left(R_{1}+R_{2}+\dots +R_{n}\right)}
Resistance units
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The total resistance of two or more resistors connected in series is equal to the sum of their individual resistances:
R total = R s = R 1 + R 2 + ⋯ + R n . {\displaystyle R_{\text{total}}=R_{\text{s}}=R_{1}+R_{2}+\cdots +R_{n}.}
Here, the subscript s inRs
denotes "series", andRs
denotes resistance in a series.Conductance
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Here, the subscriptindenotes "series", anddenotes resistance in a series.
Electrical conductance presents a reciprocal quantity to resistance. Total conductance of a series circuits of pure resistances, therefore, can be calculated from the following expression:
1 G total = 1 G 1 + 1 G 2 + ⋯ + 1 G n . {\displaystyle {\frac {1}{G_{\text{total}}}}={\frac {1}{G_{1}}}+{\frac {1}{G_{2}}}+\cdots +{\frac {1}{G_{n}}}.}
For a special case of two conductances in series, the total conductance is equal to:
G total = G 1 G 2 G 1 + G 2 . {\displaystyle G_{\text{total}}={\frac {G_{1}G_{2}}{G_{1}+G_{2}}}.}
Inductors
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Inductors follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances:
L t o t a l = L 1 + L 2 + ⋯ + L n {\displaystyle L_{\mathrm {total} }=L_{1}+L_{2}+\cdots +L_{n}}
However, in some situations, it is difficult to prevent adjacent inductors from influencing each other as the magnetic field of one device couples with the windings of its neighbors. This influence is defined by the mutual inductance M. For example, if two inductors are in series, there are two possible equivalent inductances depending on how the magnetic fields of both inductors influence each other.
When there are more than two inductors, the mutual inductance between each of them and the way the coils influence each other complicates the calculation. For a larger number of coils the total combined inductance is given by the sum of all mutual inductances between the various coils including the mutual inductance of each given coil with itself, which is termed self-inductance or simply inductance. For three coils, there are six mutual inductances M 12 {\displaystyle M_{12}} , M 13 {\displaystyle M_{13}} , M 23 {\displaystyle M_{23}} and M 21 {\displaystyle M_{21}} , M 31 {\displaystyle M_{31}} and M 32 {\displaystyle M_{32}} . There are also the three self-inductances of the three coils: M 11 {\displaystyle M_{11}} , M 22 {\displaystyle M_{22}} and M 33 {\displaystyle M_{33}} .
Therefore
L total = ( M 11 + M 22 + M 33 ) + ( M 12 + M 13 + M 23 ) + ( M 21 + M 31 + M 32 ) {\displaystyle L_{\text{total}}=\left(M_{11}+M_{22}+M_{33}\right)+\left(M_{12}+M_{13}+M_{23}\right)+\left(M_{21}+M_{31}+M_{32}\right)}
By reciprocity, M i j {\displaystyle M_{ij}} = M j i {\displaystyle M_{ji}} so that the last two groups can be combined. The first three terms represent the sum of the self-inductances of the various coils. The formula is easily extended to any number of series coils with mutual coupling. The method can be used to find the self-inductance of large coils of wire of any cross-sectional shape by computing the sum of the mutual inductance of each turn of wire in the coil with every other turn since in such a coil all turns are in series.
Capacitors
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Capacitors follow the same law using the reciprocals. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:
1 C total = 1 C 1 + 1 C 2 + ⋯ + 1 C n . {\displaystyle {\frac {1}{C_{\text{total}}}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+\cdots +{\frac {1}{C_{n}}}.}
Equivalently using elastance (the reciprocal of capacitance), the total series elastance equals the sum of each capacitor's elastance.
Switches
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Two or more switches in series form a logical AND; the circuit only carries current if all switches are closed. See AND gate.
Cells and batteries
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A battery is a collection of electrochemical cells. If the cells are connected in series, the voltage of the battery will be the sum of the cell voltages. For example, a 12 volt car battery contains six 2-volt cells connected in series. Some vehicles, such as trucks, have two 12 volt batteries in series to feed the 24-volt system.
Parallel circuits
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Comparison of effective resistance, inductance and capacitance of two resistors, inductors and capacitors in series and parallelIf two or more components are connected in parallel, they have the same difference of potential (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applied to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff's current law.
Voltage
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In a parallel circuit, the voltage is the same for all elements.
V = V 1 = V 2 = ⋯ = V n {\displaystyle V=V_{1}=V_{2}=\dots =V_{n}}
Current
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The current in each individual resistor is found by Ohm's law. Factoring out the voltage gives
I total = I 1 + I 2 + ⋯ + I n = V ( 1 R 1 + 1 R 2 + ⋯ + 1 R n ) . {\displaystyle I_{\text{total}}=I_{1}+I_{2}+\cdots +I_{n}=V\left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}\right).}
Resistance units
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To find the total resistance of all components, add the reciprocals of the resistances R i {\displaystyle R_{i}} of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance:
1 R total = 1 R 1 + 1 R 2 + ⋯ + 1 R n . {\displaystyle {\frac {1}{R_{\text{total}}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}.}
For only two resistances, the unreciprocated expression is reasonably simple:
R total = R 1 R 2 R 1 + R 2 . {\displaystyle R_{\text{total}}={\frac {R_{1}R_{2}}{R_{1}+R_{2}}}.}
This sometimes goes by the mnemonic product over sum.
For N equal resistances in parallel, the reciprocal sum expression simplifies to:
1 R total = N 1 R . {\displaystyle {\frac {1}{R_{\text{total}}}}=N{\frac {1}{R}}.}
R total = R N . {\displaystyle R_{\text{total}}={\frac {R}{N}}.}
and therefore to:
To find the current in a component with resistance R i {\displaystyle R_{i}} , use Ohm's law again:
I i = V R i . {\displaystyle I_{i}={\frac {V}{R_{i}}}\,.}
The components divide the current according to their reciprocal resistances, so, in the case of two resistors,
I 1 I 2 = R 2 R 1 . {\displaystyle {\frac {I_{1}}{I_{2}}}={\frac {R_{2}}{R_{1}}}.}
An old term for devices connected in parallel is multiple, such as multiple connections for arc lamps.
Conductance
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Since electrical conductance G {\displaystyle G} is reciprocal to resistance, the expression for total conductance of a parallel circuit of resistors is simply:
G total = G 1 + G 2 + ⋯ + G n . {\displaystyle G_{\text{total}}=G_{1}+G_{2}+\cdots +G_{n}.}
The relations for total conductance and resistance stand in a complementary relationship: the expression for a series connection of resistances is the same as for parallel connection of conductances, and vice versa.
Inductors
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Inductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:
1 L total = 1 L 1 + 1 L 2 + ⋯ + 1 L n . {\displaystyle {\frac {1}{L_{\text{total}}}}={\frac {1}{L_{1}}}+{\frac {1}{L_{2}}}+\cdots +{\frac {1}{L_{n}}}.}
If the inductors are situated in each other's magnetic fields, this approach is invalid due to mutual inductance. If the mutual inductance between two coils in parallel is M, the equivalent inductor is:
1 L total = L 1 + L 2 − 2 M L 1 L 2 − M 2 {\displaystyle {\frac {1}{L_{\text{total}}}}={\frac {L_{1}+L_{2}-2M}{L_{1}L_{2}-M^{2}}}}
If L 1 = L 2 {\displaystyle L_{1}=L_{2}}
L total = L + M 2 {\displaystyle L_{\text{total}}={\frac {L+M}{2}}}
The sign of M {\displaystyle M} depends on how the magnetic fields influence each other. For two equal tightly coupled coils the total inductance is close to that of every single coil. If the polarity of one coil is reversed so that M is negative, then the parallel inductance is nearly zero or the combination is almost non-inductive. It is assumed in the "tightly coupled" case M is very nearly equal to L. However, if the inductances are not equal and the coils are tightly coupled there can be near short circuit conditions and high circulating currents for both positive and negative values of M, which can cause problems.
More than three inductors become more complex and the mutual inductance of each inductor on each other inductor and their influence on each other must be considered. For three coils, there are three mutual inductances M 12 {\displaystyle M_{12}} , M 13 {\displaystyle M_{13}} and M 23 {\displaystyle M_{23}} . This is best handled by matrix methods and summing the terms of the inverse of the L {\displaystyle L} matrix (3×3 in this case).
The pertinent equations are of the form:
v i = ∑ j L i , j d i j d t {\displaystyle v_{i}=\sum _{j}L_{i,j}{\frac {di_{j}}{dt}}}
Capacitors
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The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:
C total = C 1 + C 2 + ⋯ + C n . {\displaystyle C_{\text{total}}=C_{1}+C_{2}+\cdots +C_{n}.}
The working voltage of a parallel combination of capacitors is always limited by the smallest working voltage of an individual capacitor.
Switches
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Two or more switches in parallel form a logical OR; the circuit carries current if at least one switch is closed. See OR gate.
Cells and batteries
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If the cells of a battery are connected in parallel, the battery voltage will be the same as the cell voltage, but the current supplied by each cell will be a fraction of the total current. For example, if a battery comprises four identical cells connected in parallel and delivers a current of 1 ampere, the current supplied by each cell will be 0.25 ampere. If the cells are not identical in voltage, cells with higher voltages will attempt to charge those with lower ones, potentially damaging them.
Parallel-connected batteries were widely used to power the valve filaments in portable radios. Lithium-ion rechargeable batteries (particularly laptop batteries) are often connected in parallel to increase the ampere-hour rating. Some solar electric systems have batteries in parallel to increase the storage capacity; a close approximation of total amp-hours is the sum of all amp-hours of in-parallel batteries.
Combining conductances
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From Kirchhoff's circuit laws the rules for combining conductance can be deducted. For two conductances G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} in parallel, the voltage across them is the same and from Kirchhoff's current law (KCL) the total current is
I eq = I 1 + I 2 . {\displaystyle I_{\text{eq}}=I_{1}+I_{2}.}
Substituting Ohm's law for conductances gives
G eq V = G 1 V + G 2 V {\displaystyle G_{\text{eq}}V=G_{1}V+G_{2}V}
G eq = G 1 + G 2 . {\displaystyle G_{\text{eq}}=G_{1}+G_{2}.}
and the equivalent conductance will be,
For two conductances G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} in series the current through them will be the same and Kirchhoff's Voltage Law says that the voltage across them is the sum of the voltages across each conductance, that is,
V eq = V 1 + V 2 . {\displaystyle V_{\text{eq}}=V_{1}+V_{2}.}
Substituting Ohm's law for conductance then gives,
I G eq = I G 1 + I G 2 {\displaystyle {\frac {I}{G_{\text{eq}}}}={\frac {I}{G_{1}}}+{\frac {I}{G_{2}}}}
1 G eq = 1 G 1 + 1 G 2 . {\displaystyle {\frac {1}{G_{\text{eq}}}}={\frac {1}{G_{1}}}+{\frac {1}{G_{2}}}.}
which in turn gives the formula for the equivalent conductance,
This equation can be rearranged slightly, though this is a special case that will only rearrange like this for two components.
G eq = G 1 G 2 G 1 + G 2 . {\displaystyle G_{\text{eq}}={\frac {G_{1}G_{2}}{G_{1}+G_{2}}}.}
G eq = G 1 G 2 G 3 G 1 G 2 + G 1 G 3 + G 2 G 3 . {\displaystyle G_{\text{eq}}={\frac {G_{1}G_{2}G_{3}}{G_{1}G_{2}+G_{1}G_{3}+G_{2}G_{3}}}.}
Notation
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For three conductances in series,
The value of two components in parallel is often represented in equations by the parallel operator, two vertical lines (∥), borrowing the parallel lines notation from geometry.
R e q ≡ R 1 ∥ R 2 ≡ ( R 1 − 1 + R 2 − 1 ) − 1 ≡ R 1 R 2 R 1 + R 2 {\displaystyle R_{\mathrm {eq} }\equiv R_{1}\parallel R_{2}\equiv \left(R_{1}^{-1}+R_{2}^{-1}\right)^{-1}\equiv {\frac {R_{1}R_{2}}{R_{1}+R_{2}}}}
This simplifies expressions that would otherwise become complicated by expansion of the terms. For instance:
R 1 ∥ R 2 ∥ R 3 ≡ R 1 R 2 R 3 R 1 R 2 + R 1 R 3 + R 2 R 3 . {\displaystyle R_{1}\parallel R_{2}\parallel R_{3}\equiv {\frac {R_{1}R_{2}R_{3}}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}}.}
If n components are in parallel, then
R eq = ( ∑ i n R i − 1 ) − 1 {\displaystyle R_{\text{eq}}=\left(\sum _{i}^{n}{R_{i}}^{-1}\right)^{-1}}
Applications
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A common application of series circuit in consumer electronics is in batteries, where several cells connected in series are used to obtain a convenient operating voltage. Two disposable zinc cells in series might power a flashlight or remote control at 3 volts; the battery pack for a hand-held power tool might contain a dozen lithium-ion cells wired in series to provide 48 volts.
Series circuits were formerly used for lighting in electric multiple units trains. For example, if the supply voltage was 600 volts there might be eight 70-volt bulbs in series (total 560 volts) plus a resistor to drop the remaining 40 volts. Series circuits for train lighting were superseded, first by motor-generators, then by solid state devices.
Series resistance can also be applied to the arrangement of blood vessels within a given organ. Each organ is supplied by a large artery, smaller arteries, arterioles, capillaries, and veins arranged in series. The total resistance is the sum of the individual resistances, as expressed by the following equation: Rtotal = Rartery + Rarterioles + Rcapillaries. The largest proportion of resistance in this series is contributed by the arterioles.[3]
Parallel resistance is illustrated by the circulatory system. Each organ is supplied by an artery that branches off the aorta. The total resistance of this parallel arrangement is expressed by the following equation: 1/Rtotal = 1/Ra + 1/Rb + ... + 1/Rn. Ra, Rb, and Rn are the resistances of the renal, hepatic, and other arteries respectively. The total resistance is less than the resistance of any of the individual arteries.[3]
See also
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References
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Costanzo, Linda S. Physiology. Board Review Series. p. 74.
Further reading
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BU-302: Configuraciones de Baterías en Serie y Paralelo (Español)
Batteries achieve the desired operating voltage by connecting several cells in series; each cell adds its voltage potential to derive at the total terminal voltage. Parallel connection attains higher capacity by adding up the total ampere-hour (Ah).
Some packs may consist of a combination of series and parallel connections. Laptop batteries commonly have four 3.6V Li-ion cells in series to achieve a nominal voltage 14.4V and two in parallel to boost the capacity from 2,400mAh to 4,800mAh. Such a configuration is called 4s2p, meaning four cells in series and two in parallel. Insulating foil between the cells prevents the conductive metallic skin from causing an electrical short.
Most battery chemistries lend themselves to series and parallel connection. It is important to use the same battery type with equal voltage and capacity (Ah) and never to mix different makes and sizes. A weaker cell would cause an imbalance. This is especially critical in a series configuration because a battery is only as strong as the weakest link in the chain. An analogy is a chain in which the links represent the cells of a battery connected in series (Figure 1).
Figure 1: Comparing a battery with a chain. Chain links represent cells in series to increase voltage, doubling a link denotes parallel connection to boost current loading.A weak cell may not fail immediately but will get exhausted more quickly than the strong ones when on a load. On charge, the low cell fills up before the strong ones because there is less to fill and it remains in over-charge longer than the others. On discharge, the weak cell empties first and gets hammered by the stronger brothers. Cells in multi-packs must be matched, especially when used under heavy loads. (See BU-803a: Cell Mismatch, Balancing).
The single-cell configuration is the simplest battery pack; the cell does not need matching and the protection circuit on a small Li-ion cell can be kept simple. Typical examples are mobile phones and tablets with one 3.60V Li-ion cell. Other uses of a single cell are wall clocks, which typically use a 1.5V alkaline cell, wristwatches and memory backup, most of which are very low power applications.
The nominal cell voltage for a nickel-based battery is 1.2V, alkaline is 1.5V; silver-oxide is 1.6V and lead acid is 2.0V. Primary lithium batteries range between 3.0V and 3.9V. Li-ion is 3.6V; Li-phosphate is 3.2V and Li-titanate is 2.4V.
Li-manganese and other lithium-based systems often use cell voltages of 3.7V and higher. This has less to do with chemistry than promoting a higher watt-hour (Wh), which is made possible with a higher voltage. The argument goes that a low internal cell resistance keeps the voltage high under load. For operational purposes these cells go as 3.6V candidates. (See BU-303 Confusion with Voltages)
Portable equipment needing higher voltages use battery packs with two or more cells connected in series. Figure 2 shows a battery pack with four 3.6V Li-ion cells in series, also known as 4S, to produce 14.4V nominal. In comparison, a six-cell lead acid string with 2V/cell will generate 12V, and four alkaline with 1.5V/cell will give 6V.
If you need an odd voltage of, say, 9.50 volts, connect five lead acid, eight NiMH or NiCd, or three Li-ion in series. The end battery voltage does not need to be exact as long as it is higher than what the device specifies. A 12V supply might work in lieu of 9.50V. Most battery-operated devices can tolerate some over-voltage; the end-of-discharge voltage must be respected, however.
High voltage batteries keep the conductor size small. Cordless power tools run on 12V and 18V batteries; high-end models use 24V and 36V. Most e-bikes come with 36V Li-ion, some are 48V. The car industry wanted to increase the starter battery from 12V (14V) to 36V, better known as 42V, by placing 18 lead acid cells in series. Logistics of changing the electrical components and arcing problems on mechanical switches derailed the move.
Some mild hybrid cars run on 48V Li-ion and use DC-DC conversion to 12V for the electrical system. Starting the engine is often done by a separate 12V lead acid battery. Early hybrid cars ran on a 148V battery; electric vehicles are typically 450–500V. Such a battery needs more than 100 Li-ion cells connected in series.
High-voltage batteries require careful cell matching, especially when drawing heavy loads or when operating at cold temperatures. With multiple cells connected in a string, the possibility of one cell failing is real and this would cause a failure. To prevent this from happening, a solid state switch in some large packs bypasses the failing cell to allow continued current flow, albeit at a lower string voltage.
Cell matching is a challenge when replacing a faulty cell in an aging pack. A new cell has a higher capacity than the others, causing an imbalance. Welded construction adds to the complexity of the repair, and this is why battery packs are commonly replaced as a unit.
High-voltage batteries in electric vehicles, in which a full replacement would be prohibitive, divide the pack into modules, each consisting of a specific number of cells. If one cell fails, only the affected module is replaced. A slight imbalance might occur if the new module is fitted with new cells. (See BU-910: How to Repair a Battery Pack)
Figure 3 illustrates a battery pack in which “cell 3” produces only 2.8V instead of the full nominal 3.6V. With depressed operating voltage, this battery reaches the end-of-discharge point sooner than a normal pack. The voltage collapses and the device turns off with a “Low Battery” message.
Figure 3: Series connection with a faulty cell[1]
Batteries in drones and remote controls for hobbyist requiring high load current often exhibit an unexpected voltage drop if one cell in a string is weak. Drawing maximum current stresses frail cells, leading to a possible crash. Reading the voltage after a charge does not identify this anomaly; examining the cell-balance or checking the capacity with a battery analyzer will.
There is a common practice to tap into the series string of a lead acid array to obtain a lower voltage. Heavy duty equipment running on a 24V battery bank may need a 12V supply for an auxiliary operation and this voltage is conveniently available at the half-way point.
Tapping is not recommended because it creates a cell imbalance as one side of the battery bank is loaded more than the other. Unless the disparity can be corrected by a special charger, the side effect is a shorter battery life. Here is why:
When charging an imbalanced lead acid battery bank with a regular charger, the undercharged section tends to develop sulfation as the cells never receive a full charge. The high voltage section of the battery that does not receive the extra load tends to get overcharged and this leads to corrosion and loss of water due to gassing. Please note that the charger charging the entire string looks at the average voltage and terminates the charge accordingly.
Tapping is also common on Li-ion and nickel-based batteries and the results are similar to lead acid: reduced cycle life. (See BU-803a: Cell Matching and Balancing) Newer devices use a DC-DC converter to deliver the correct voltage. Electric and hybrid vehicles, alternatively, use a separate low-voltage battery for the auxiliary system.
If higher currents are needed and larger cells are not available or do not fit the design constraint, one or more cells can be connected in parallel. Most battery chemistries allow parallel configurations with little side effect. Figure 4 illustrates four cells connected in parallel in a P4 arrangement. The nominal voltage of the illustrated pack remains at 3.60V, but the capacity (Ah) and runtime are increased fourfold.
Figure 4: Parallel connection of four cells (4p)[1]A cell that develops high resistance or opens is less critical in a parallel circuit than in a series configuration, but a failing cell will reduce the total load capability. It’s like an engine only firing on three cylinders instead of on all four. An electrical short, on the other hand, is more serious as the faulty cell drains energy from the other cells, causing a fire hazard. Most so-called electrical shorts are mild and manifest themselves as elevated self-discharge.
A total short can occur through reverse polarization or dendrite growth. Large packs often include a fuse that disconnects the failing cell from the parallel circuit if it were to short. Figure 5 illustrates a parallel configuration with one faulty cell.
Figure 5: Parallel/connection with one faulty cell[1]A weak cell will not affect the voltage but provide a low runtime due to reduced capacity. A shorted cell could cause excessive heat and become a fire hazard. On larger packs a fuse prevents high current by isolating the cell.
The series/parallel configuration shown in Figure 6 enables design flexibility and achieves the desired voltage and current ratings with a standard cell size. The total power is the sum of voltage times current; a 3.6V (nominal) cell multiplied by 3,400mAh produces 12.24Wh. Four 18650 Energy Cells of 3,400mAh each can be connected in series and parallel as shown to get 7.2V nominal and a total of 48.96Wh. A combination with 8 cells would produce 97.92Wh, the allowable limit for carry on an aircraft or shipped without Class 9 hazardous material. (See BU-704a: Shipping Lithium-based Batteries by Air) The slim cell allows flexible pack design but a protection circuit is needed.
Li-ion lends itself well to series/parallel configurations but the cells need monitoring to stay within voltage and current limits. Integrated circuits (ICs) for various cell combinations are available to supervise up to 13 Li-ion cells. Larger packs need custom circuits, and this applies to e-bike batteries, hybrid cars and the Tesla Model 85 that devours over 7000 18650 cells to make up the 90kWh pack.
The battery industry specifies the number of cells in series first, followed by the cells placed in parallel. An example is 2s2p. With Li-ion, the parallel strings are always made first; the completed parallel units are then placed in series. Li-ion is a voltage based system that lends itself well for parallel formation. Combining several cells into a parallel and then adding the units serially reduces complexity in terms of voltages control for pack protection.
Building series strings first and then placing them in in parallel may be more common with NiCd packs to satisfy the chemical shuttle mechanism that balances charge at the top of charge. “2s2p” is common; white papers have been issued that refer to 2p2s when a serial string is paralleled.
Positive Temperature Coefficient Switches (PTC) and Charge Interrupt Devices (CID) protect the battery from overcurrent and excessive pressure. While recommended for safety in a smaller 2- or 3-cell pack with serial and parallel configuration, these protection devices are often being omitted in larger multi-cell batteries, such as those for power tool. The PTC and CID work as expected to switch of the cell on excessive current and internal cell pressure; however the shutdown occurs in cascade format. While some cells may go offline early, the load current causes excess current on the remaining cells. Such overload condition could lead to a thermal runaway before the remaining safety devices activate.
Some cells have built-in PCT and CID; these protection devices can also be added retroactively. The design engineer must be aware than any safety device is subject to failure. In addition, the PTC induces a small internal resistance that reduces the load current. (See also BU-304b: Making Lithium-ion Safe)
[1] Courtesy of Cadex