Serial Vs Parallel Battery Connection

A series circuit with a voltage source (such as a battery, or in this case a cell) and 3 resistance units

Serial Vs Parallel Battery Wiring
Parallel Vs Series Battery Connection
Parallel Battery Connection

If we connect two pairs of two batteries in series and then connect these series connected batteries in parallel, then this configuration of batteries would be called series-parallel connection of batteries. In other words, It is series, nor parallel circuit, but known as series-parallel circuit.

Components of an electrical circuit or electronic circuit can be connected in series, parallel, or series-parallel. The two simplest of these are called series and parallel and occur frequently. Components connected in series are connected along a single conductive path, so the same current flows through all of the components but voltage is dropped (lost) across each of the resistances. In a series circuit, the sum of the voltages consumed by each individual resistance is equal to the source voltage.^[1]^[2] Components connected in parallel are connected along multiple paths so that the current can split up; the same voltage is applied to each component.^[1]

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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.

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 amperage 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.

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1Series circuits
2Parallel circuits

Series circuits[edit]

Electromagnetism
Part of a series of articles about
Electric flux / potential energy

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 in 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 bulb is replaced.

Current[edit]

{displaystyle I=I_{1}=I_{2}=cdots =I_{n}}

In a series circuit, the current is the same for all of the elements.

Voltage[edit]

In a series circuit, the voltage is the sum of the voltage drops of the individual components (resistance units).

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{displaystyle V=V_{1}+V_{2}+dots +V_{n}}

Resistance units[edit]

The total resistance of resistance units in series is equal to the sum of their individual resistances:

{displaystyle R_{text{total}}=R_{text{s}}=R_{1}+R_{2}+cdots +R_{n}}

Rs=>Resistance in 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:

{displaystyle {frac {1}{G_{mathrm {total} }}}={frac {1}{G_{1}}}+{frac {1}{G_{2}}}+cdots +{frac {1}{G_{n}}}}

For a special case of two resistances in series, the total conductance is equal to:

{displaystyle G_{text{total}}={frac {G_{1}G_{2}}{G_{1}+G_{2}}}.}

Inductors[edit]

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:

{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 coupled with the windings of its neighbours. 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 we term self-inductance or simply inductance. For three coils, there are six mutual inductances ${displaystyle M_{12}}$ , ${displaystyle M_{13}}$ , ${displaystyle M_{23}}$ and ${displaystyle M_{21}}$ , ${displaystyle M_{31}}$ and ${displaystyle M_{32}}$ . There are also the three self-inductances of the three coils: ${displaystyle M_{11}}$ , ${displaystyle M_{22}}$ and ${displaystyle M_{33}}$ .

Therefore

{displaystyle L_{mathrm {total} }=(M_{11}+M_{22}+M_{33})+(M_{12}+M_{13}+M_{23})+(M_{21}+M_{31}+M_{32})}

By reciprocity ${displaystyle M_{ij}}$ = ${displaystyle M_{ji}}$ 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[edit]

Serial Vs Parallel Battery Wiring

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:

{displaystyle {frac {1}{C_{mathrm {total} }}}={frac {1}{C_{1}}}+{frac {1}{C_{2}}}+cdots +{frac {1}{C_{n}}}}

Switches[edit]

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[edit]

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[edit]

If 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[edit]

In a parallel circuit, the voltage is the same for all elements.

{displaystyle V=V_{1}=V_{2}=ldots =V_{n}}

Current[edit]

The current in each individual resistor is found by Ohm's law. Factoring out the voltage gives

{displaystyle I_{mathrm {total} }=Vleft({frac {1}{R_{1}}}+{frac {1}{R_{2}}}+cdots +{frac {1}{R_{n}}}right)}

Resistance units[edit]

To find the total resistance of all components, add the reciprocals of the resistances ${displaystyle R_{i}}$ of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance:

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{displaystyle {frac {1}{R_{mathrm {total} }}}={frac {1}{R_{1}}}+{frac {1}{R_{2}}}+cdots +{frac {1}{R_{n}}}}

For only two resistances, the unreciprocated expression is reasonably simple:

{displaystyle R_{mathrm {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:

{displaystyle {frac {1}{R_{mathrm {total} }}}=N{frac {1}{R}}}

and therefore to:

{displaystyle R_{mathrm {total} }={frac {R}{N}}}

To find the current in a component with resistance ${displaystyle R_{i}}$ , use Ohm's law again:

{displaystyle I_{i}={frac {V}{R_{i}}},}

The components divide the current according to their reciprocal resistances, so, in the case of two resistors,

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{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.

Since electrical conductance ${displaystyle G}$ is reciprocal to resistance, the expression for total conductance of a parallel circuit of resistors reads:

{displaystyle G_{mathrm {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[edit]

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:

{displaystyle {frac {1}{L_{mathrm {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:

{displaystyle {frac {1}{L_{mathrm {total} }}}={frac {L_{1}+L_{2}-2M}{L_{1}L_{2}-M^{2}}}}

If ${displaystyle L_{1}=L_{2}}$

{displaystyle L_{text{total}}={frac {L+M}{2}}}

The sign of ${displaystyle M}$ 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 ${displaystyle M_{12}}$ , ${displaystyle M_{13}}$ and ${displaystyle M_{23}}$ . This is best handled by matrix methods and summing the terms of the inverse of the ${displaystyle L}$ matrix (3 by 3 in this case).

The pertinent equations are of the form: ${displaystyle v_{i}=sum _{j}L_{i,j}{frac {di_{j}}{dt}}}$

Capacitors[edit]

The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:

{displaystyle C_{mathrm {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[edit]

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[edit]

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. 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[edit]

From Kirchhoff's circuit laws we can deduce the rules for combining conductances. For two conductances ${displaystyle G_{1}}$ and ${displaystyle G_{2}}$ in parallel, the voltage across them is the same and from Kirchhoff's current law (KCL) the total current is

{displaystyle I_{text{eq}}=I_{1}+I_{2}. ,}

Substituting Ohm's law for conductances gives

{displaystyle G_{text{eq}}V=G_{1}V+G_{2}V ,}

and the equivalent conductance will be,

{displaystyle G_{text{eq}}=G_{1}+G_{2}. ,}

For two conductances ${displaystyle G_{1}}$ and ${displaystyle G_{2}}$ in series the current through them will be the same and Kirchhoff's Voltage Law tells us that the voltage across them is the sum of the voltages across each conductance, that is,

{displaystyle V_{text{eq}}=V_{1}+V_{2}. ,}

Substituting Ohm's law for conductance then gives,

{displaystyle {frac {I}{G_{text{eq}}}}={frac {I}{G_{1}}}+{frac {I}{G_{2}}}}

which in turn gives the formula for the equivalent conductance,

{displaystyle {frac {1}{G_{text{eq}}}}={frac {1}{G_{1}}}+{frac {1}{G_{2}}}.}

This equation can be rearranged slightly, though this is a special case that will only rearrange like this for two components.

{displaystyle G_{text{eq}}={frac {G_{1}G_{2}}{G_{1}+G_{2}}}.}

Notation[edit]

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.

{displaystyle R_{mathrm {eq} }equiv R_{1}|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:

{displaystyle R_{1}|R_{2}|R_{3}equiv {frac {R_{1}R_{2}R_{3}}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}}}

Applications[edit]

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.

Parallel Vs Series Battery Connection

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. Xenoblade chronicles emulator download.

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: R_total = R_artery + R_arterioles + R_capillaries. 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/R_total = 1/R_a + 1/R_b + . 1/R_n. R_a, R_b, and R_n 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]

References[edit]

^ ^a^b^c^dResnick, Robert; Halliday, David (1966). 'Chapter 32'. Physics. Volume I and II (Combined international ed.). Wiley. LCCN66-11527. Example 1.
^Smith, R. J. (1966). Circuits, Devices and Systems (International ed.). New York: Wiley. p. 21. LCCN66-17612.
^ ^a^bCostanzo, Linda S. Physiology. Board Review Series. p. 74.

External links[edit]

Series circuit, Parallel circuit
Series and Parallel Circuits chapter from Lessons In Electric Circuits Vol 1 DC free ebook and Lessons In Electric Circuits series.
Series-Parallel Combination Circuits chapter from Lessons In Electric Circuits Vol 1 DC free ebook and Lessons In Electric Circuits series.
Sameen Ahmed KhanHow many equivalent resistances?, Resonance Journal of Science Education, Vol. 17, No. 5, 468-475 (May 2012).
Video “What’s a Circuit, Series and Parallel (ElectroBOOM101–005)” by ElectroBOOM.

Retrieved from 'https://en.wikipedia.org/w/index.php?title=Series_and_parallel_circuits&oldid=918793789'

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Introduction: DC vs AC

Batteries are everywhere around us; our cars, our MP3 players, our cellphones and laptops. Every portable device needs some source of energy, and that comes from batteries installed inside them.
Batteries are sources of Direct Current electricity (DC). That means, if the output is connected to an oscilloscope so the graph of the voltage is shown, it will be a flat line located at the output volts amount. DC current is way different from the electricity sockets we have in our houses, which provide Alternating Current electricity (AC); in an AC system, the output is constantly switching from positive to negative through a sinusoidal graph with frequency same as the line frequency (60 Hz in the US, 50 Hz in most of Europe, etc.) and magnitude same as the line's voltage (120V for US, 220 or 230V for European countries).

Series Connection

Batteries Characteristics

Batteries come in many different sizes, capacities and types; however, technically all batteries share some characteristics which derive from their nature as a DC voltage source. Like any DC source, batteries have a contact which is marked with + and is the receptacle for positive voltage and a - contact where 0 V is applied. Don't let the - tag confuse you, batteries do not have negative voltage; the 0 V receptacle is almost always considered the ground and is connected as ground in DC circuits too. The voltage difference between the + and the - receptacles is what is called the DC Voltage of the battery.
Aside voltage, another crucial characteristic of a battery is its capacity, or, put simply, for how long the battery can keep a device operating. Battery capacity is typically measured with Ah, mAh or Wh. Let's show some examples so the units are understood:
A stands for Ampere; one ampere is 1000 mA - ampere is a unit for electrical current.
h stands for hour
The unit Ah indicates for how many hours the battery can supply 1 ampere before it empties. An example:
A 52 Ah battery (if totally full) can provide 52 A for 1 hour, or 26 A for 2 hours or 13 A for 4 hours, etc.
W stands for Watt and is a power unit; power can be calculated when the Volts are multiplied with the Amperes, W= V*I.
As a result, a battery which is rated at say 100 Wh can supply, if full, 100 W for one hour, or 50 W for 2 hours, etc.

Parallel Connection

Batteries Interconnections

Batteries can be connected with each other in multiple ways, to provide different voltages, to have higher capacity or both.
Series Connection:
In a series connection, the + contact of a battery is connected with the - contact of another battery, thus forming one 'new' battery. In the two ends of this battery (from now on called battery bank) there are one + and one - contact unconnected. These two contacts are the positive and negative pole of the bank. A battery bank which has been formed through series connection has the same capacity (Ah) as the batteries it consists from but its voltage is the sum of the voltages batteries. As you understand, series connection is used when our circuit or appliance needs more voltage than the voltage one battery can supply; supposing you need 48 Volts, you would connect 4 batteries of 12V in series.
Parallel Connection:
In a parallel connection, the positive poles of the batteries are connected together and the negative poles are connected together too. The receptacles for the battery bank that is formed are any + contact and any - contact of the batteries. One would choose to connect his batteries in parallel when he needs higher capacity; the battery bank has same voltage as the batteries its consists from, but its capacity is the sum of the batteries capacity. Supposing you need 12 V but 104 Ah, you could connect two 12 V 52 Ah batteries in parallel.
Series-Parallel Connection:
This is a combination of the previous connection methods. You can achieve increased voltage and increased capacity, depending on the batteries you connect.

Series and Parallel Connection

Advice and Tips on Batteries and Connections

1. Regardless of the connection method, you must avoid the following:

connecting batteries of different age together (shelf age before you bought them also counts)
connecting different capacity batteries
connecting batteries with different nominal voltage
connecting batteries which at the moment of connection have different charge status

All of the above are typical mistakes made by people who feel in urge to get the advantages of a battery bank; most of them will not cause a problem at once, but eventually the capacity of the batteries will decrease.
For example, if you connect a full battery with an empty battery in parallel, the full will attempt to charge the empty one - a large current will be formed instantly, causing temperature increase in both batteries, sparks and possible insulation breakdowns. You could instantly end up, in the worst scenario, with two batteries which are damaged.
If a recent battery is connected with an older one, eventually the fresh battery will degrade faster because it will be constantly 'supporting' the older battery whose capacity has surely dropped over time.
2. Connections between large batteries of many Ah, for example car batteries, should be accomplished with the proper gauge wire for the current. Car batteries can provide huge amounts of instant current and if the wire is thinner than what it should, it could break or melt and cause further problems in the circuit. Proper contacts should also be used, sufficient for the power distribution. If solder is used, the joints should be stress-tested and held firmly by additional hardware. Fuses of the appropriate rating are also a must; should a short be caused in any part of the circuit, the fuse will melt and break the circuit, possibly protecting other devices.
3. Selecting the proper way of connecting batteries to form a battery bank has to do with our application and devices. We cannot have a 12V battery bank if our devices need 24V and we cannot push a small capacity battery to the limit by applying constant high loads which empty it in a matter of minutes.
4. The power rating, in Watts, of the battery bank is always the sum of power ratings of the batteries it consists from, regardless the connection method.

Hello
I have 30 3.6V 2600 mah Li-ion battery which i wanted to connect in 10 series and 3 parallel to get 36V 7.8 ah capacity to use for E-cycle. So please could you provide an opinion, any protective circuit to be used for the above combination. Pl Suggest
Thank You
When 2 Batteries of different voltage & capacity (say, 12V/5Ahr & 24V/15Ahr) are connected IN PARALLEL, what will be the resultant output in V/Ahr ?
And what will be the resultant output in V/Ahr when the same 2 batteries are connected in SERIES ?
WHY, what is the mathematical formula ?

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Serial Vs Parallel Battery Connection

Series circuits[edit]

Current[edit]

Voltage[edit]

Resistance units[edit]

Inductors[edit]

Capacitors[edit]

Serial Vs Parallel Battery Wiring

Switches[edit]

Cells and batteries[edit]

Parallel circuits[edit]

Voltage[edit]

Current[edit]

Resistance units[edit]

Inductors[edit]

Capacitors[edit]

Switches[edit]

Cells and batteries[edit]

Combining conductances[edit]

Notation[edit]

Applications[edit]

Parallel Vs Series Battery Connection

See also[edit]

References[edit]

Further reading[edit]

Parallel Battery Connection

External links[edit]

Introduction: DC vs AC

Series Connection

Batteries Characteristics

Parallel Connection

Batteries Interconnections

Series and Parallel Connection

Advice and Tips on Batteries and Connections

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