Series and parallel circuits: Difference between revisions

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===Resistance units<span class="anchor" id="Rseries"></span>===

The total resistance of two or more resistors connected in series is equal to the sum of their individual resistances:

[[File:Resistors in seriesResistors_in_series.svg|alt=This is a diagram of several resistors, connected end to end, with the same amount of current through each.|border|center|x100px]]

[[File:Resistors in series.svg|This is a diagram of several resistors, connected end to end, with the same amount of current through each.]]

<math display="block">R = \sum_{i=1}^n R_i = R_1 + R_2 + R_3 \cdots + R_n.</math>

{{anchor|Lseries}}

Here, the subscript ''s'' in {{math|''R''_s}} denotes "series", and {{math|''R''_s}} denotes resistance in a series.

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<math display="block">G = \frac{G_1 G_2}{G_1 + G_2}.</math>

===Inductors <span class="anchor" id="Lseries"></span>===

[[Inductor]]s follow the same law, in that the total [[inductance]] of non-coupled inductors in series is equal to the sum of their individual inductances:

[[File:Inductors in series.svg|A diagram of several inductors, connected end to end, with the same amount of current going through each.|border|center|x100px]]

<math display="block">L = \sum_{i=1}^n L_i = L_1 + L_2 + L_3 \cdots + L_n.</math>

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[[Capacitor]]s follow the same law using the reciprocals. The total [[capacitance]] of capacitors in series is equal to the reciprocal of the sum of the [[Multiplicative inverse|reciprocals]] of their individual capacitances:

[[File:Capacitors in seriesCapacitors_in_series.svg|alt=A diagram of several capacitors, connected end to end, with the same amount of current going through each.|border|center|x100px]]

[[File:Capacitors in series.svg|A diagram of several capacitors, connected end to end, with the same amount of current going through each.]]

<math display="block">C = \left(\sum_{i=1}^n{1\over C_i}\right)^{-1} = \left({1\over C_1} + {1\over C_2} + {1\over C_3} + \dots + {1\over C_n}\right)^{-1}.</math>

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===Resistance units===

To find the total [[Electrical resistance|resistance]] of all components, add the [[Multiplicative inverse|reciprocals]] of the resistances <math>R_i</math> of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance:

[[File:Resistors in parallelResistors_in_parallel.svg|alt=A diagram of several resistors, side by side, both leads of each connected to the same wires.|border|center|x120px]]

[[File:Resistors in parallel.svg|A diagram of several resistors, side by side, both leads of each connected to the same wires.]]

<math display="block">R = \left(\sum_{i=1}^n{1\over R_i}\right)^{-1} = \left({1\over R_1} + {1\over R_2} + {1\over R_3} + \dots + {1\over R_n}\right)^{-1}</math>

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===Inductors<span class="anchor" id="Lparallel"></span>===

[[Inductor]]s 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:

[[File:Inductors in parallelInductors_in_parallel.svg|alt=A diagram of several inductors, side by side, both leads of each connected to the same wires.|border|center|x120px]]

[[File:Inductors in parallel.svg|A diagram of several inductors, side by side, both leads of each connected to the same wires.]]

<math display="block">L = \left(\sum_{i=1}^n{1\over L_i}\right)^{-1} = \left({1\over L_1} + {1\over L_2} + {1\over L_3} + \dots + {1\over L_n}\right)^{-1}.</math>

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===Capacitors<span class="anchor" id="Cparallel"></span>===

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

[[File:Capacitors in parallelCapacitors_in_parallel.svg|alt=A diagram of several capacitors, side by side, both leads of each connected to the same wires.|border|center|x120px]]

[[File:Capacitors in parallel.svg|A diagram of several capacitors, side by side, both leads of each connected to the same wires.]]

<math display="block">C = \sum_{i=1}^n C_i = C_1 + C_2 + C_3 \cdots + C_n.</math>

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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-generatormotor–generator]]s, then by [[Solid 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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==See also==

{{div col}}

* [[Anti-parallel (electronics)]]

* [[Electrical impedance#Combining impedances|Combining impedances]]

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* [[Wheatstone bridge]]

* [[Y-Δ transform]]

{{div col end}}

==References==