Series and parallel circuits: Difference between revisions

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[[File:Series circuit.svg|thumb|A serialseries circuit with a [[voltage source]] (such as a battery, or in this case a cell) and three resistance units]]

[[Terminal (electronics)|Two-terminal]] components and [[electrical networks]] can be connected in '''series''' <ref>{{Cite web |title=Serial - the Definition of Serial by The Free Dictionary |url=https://www.thefreedictionary.com/serial |access-date=2024-02-10 |website=The Spruce |language=en}}</ref>or '''parallel'''. The resulting electrical network will have two terminals, and itself can participate in a series or parallel [[Topology (electrical circuits)|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 serialseries/parallel networks.

Components connected in a serial circuitseries 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.<ref name="Resnick_1966"/><ref name="Smith_1966"/>

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.

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The two preceding statements are equivalent, except for [[Duality (electrical circuits)|exchanging the role of voltage and current]].

A circuit composed solely of components connected in series is known as a '''serialseries circuit'''; likewise, one connected completely in parallel is known as a '''parallel circuit'''. Many circuits can be analyzed as a combination of serialseries and parallel circuits, along with [[Topology (electrical circuits)|other configurations]].

In a serialseries 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 drop]]s across each component.<ref name="Resnick_1966"/> 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.<ref name="Resnick_1966"/>

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 serialseries circuit, every device must function for the circuit to be complete. If one bulb burns out in a serialseries 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.

==SerialSeries circuits<span class="anchor" id="Zseries"></span><span class="anchor" id="Xseries"></span><span class="anchor" id="Yseries"></span><span class="anchor" id="Bseries"></span>==

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{{Electromagnetism|Network}}

'''SerialSeries circuits''' are sometimes referred to as current-coupled or [[Daisy chain (electrical engineering)|daisy chain]]-coupled. The current in a serialseries circuit goes through every component in the circuit. Therefore, all of the components in a serialseries connection carry the same current.

A serialseries circuit has only one path through which its current can flow. Opening or breaking a serialseries circuit at any [[Single point of failure|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<span class="anchor" id="Iseries"></span>===

<math display="block">I = I_1 = I_2 = \cdots = I_n</math>

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

===Voltage===

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

<math display="block">V = V_1 + V_2 + \dots + V_n = I \left( R_1 + R_2 + \dots + R_n \right)</math>

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==== Conductance ====

[[Electrical conductance]] presents a reciprocal quantity to resistance. Total conductance of a serialseries circuitcircuits of pure resistances, therefore, can be calculated from the following expression:

<math display="block">\frac{1}{G_\text{total}} = \frac{1}{G_1} + \frac{1}{G_2} + \cdots + \frac{1}{G_n}.</math>

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==Applications==

A common application of serialseries 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.

SerialSeries 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. SerialSeries circuits for train lighting were superseded, first by [[motor-generator]]s, then by [[Solid state (electronics)|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: {{math|1=''R''_total = ''R''_artery + ''R''_arterioles + ''R''_capillaries}}. The largest proportion of resistance in this series is contributed by the arterioles.<ref name="BRS"/>

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==Further reading==

==<ref>{{Citation |title=serial |work=The Free Dictionary |url=https://www.thefreedictionary.com/serial |access-date=2024-02-10}}</ref>Further reading==

* {{cite book |author-last=Williams |author-first=Tim |title=The Circuit Designer's Companion |publisher=[[Butterworth-Heinemann]] |date=2005 |isbn=0-7506-6370-7 }}

* {{cite magazine |url=http://www.edn.com/design/components-and-packaging/4421194/Resistor-combinations--How-many-values-using-1kohm-resistors-- |title=Resistor combinations: How many values using 1K ohm resistors? |magazine=[[EDN magazine]] }}