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Series and parallel circuits - WikipediaPage 1 of 10Series and parallel circuitsFrom Wikipedia, the free encyclopediaComponents of an electrical circuit or electronic circuit can beconnected in many different ways. The two simplest of these arecalled series and parallel and occur frequently. Componentsconnected in series are connected along a single path, so thesame current flows through all of the components.[1][2]Components connected in parallel are connected, so the samevoltage is applied to each component.[3]A circuit composed solely of components connected in series isknown as a series circuit; likewise, one connected completely inparallel is known as a parallel circuit.A series circuit with a voltage source(such as a battery, or in this case acell) and 3 resistorsIn a series circuit, the current through each of the components isthe same, and the voltage across the circuit is the sum of the voltages across each component.[1] In aparallel circuit, the voltage across each of the components is the same, and the total current is the sum ofthe currents through each component.[1]Consider a very simple circuit consisting of four light bulbs and one 6 V battery. If a wire joins thebattery to one bulb, to the next bulb, to the next bulb, to the next bulb, then back to the battery, in onecontinuous 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, there is same currentthrough all of them, and the voltage drop is 1.5 V across each bulb, which may not be sufficient to makethem glow. If the light bulbs are connected in parallel, the currents through the light bulbs combine toform the current in the battery, while the voltage drop is across each bulb and they all glow.In a series circuit, every device must function for the circuit to be complete. One bulb burning out in aseries circuit breaks the circuit. In parallel circuits, each light has its own circuit, so all but one lightcould be burned out, and the last one will still function.Simply put, in a parallel circuit current increases but the voltage stays the same, and in a series circuitcurrent stays the same but the voltage decreases.Contents 1 Series circuits 1.1 Current 1.2 Resistors 1.3 Inductors 1.4 Capacitors 1.5 Switches 1.6 Cells and batteries and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 2 of 10 2 Parallel circuits 2.1 Voltage 2.2 Current 2.3 Resistors 2.4 Inductors 2.5 Capacitors 2.6 Switches 2.7 Cells and batteries 3 Combining conductances 4 Notation 5 Applications 6 See also 7 Notes 8 References 9 External linksSeries circuitsSeries circuits are sometimes called current-coupled or daisy chain-coupled. The current in a seriescircuit goes through every component in the circuit. Therefore, all of the components in a seriesconnection carry the same current. There is only one path in a series circuit in which the current canflow.A series circuit's main disadvantage or advantage, depending on its intended role in a product's overalldesign, is that because there is only one path in which its current can flow, opening or breaking a seriescircuit at any point causes the entire circuit to "open" or stop operating. For example, if even one of thelight bulbs in an older-style string of Christmas tree lights burns out or is removed, the entire stringbecomes inoperable until the bulb is replaced.CurrentIn a series circuit the current is the same for all of elements.ResistorsThe total resistance of resistors in series is equal to the sum of their individual resistances: and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 3 of 10Electrical conductance presents a reciprocal quantity to resistance. Total conductance of a series circuitsof pure resistors, therefore, can be calculated from the following expression:.For a special case of two resistors in series, the total conductance is equal to:InductorsInductors follow the same law, in that the total inductance of non-coupled inductors in series is equal tothe sum of their individual inductances:However, in some situations it is difficult to prevent adjacent inductors from influencing each other, asthe magnetic field of one device couples with the windings of its neighbours. This influence is definedby the mutual inductance M. For example, if two inductors are in series, there are two possibleequivalent 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 thecoils influence each other complicates the calculation. For a larger number of coils the total combinedinductance is given by the sum of all mutual inductances between the various coils including the mutualinductance of each given coil with itself, which we term self-inductance or simply inductance. For three,,and,and. There are also the threecoils, there are six mutual inductancesself-inductances of the three coils:,and.ThereforeBy reciprocity so that the last two groups can be combined. The first three terms representthe sum of the self-inductances of the various coils. The formula is easily extended to any number ofseries coils with mutual coupling. The method can be used to find the self-inductance of large coils ofwire of any cross-sectional shape by computing the sum of the mutual inductance of each turn of wire inthe coil with every other turn since in such a coil all turns are in series. and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 4 of 10CapacitorsSee also Capacitor networksCapacitors follow the same law using the reciprocals. The total capacitance of capacitors in series isequal to the reciprocal of the sum of the reciprocals of their individual capacitances:.SwitchesTwo or more switches in series form a logical AND; the circuit only carries current if all switches areclosed. See AND gate.Cells and batteriesA battery is a collection of electrochemical cells. If the cells are connected in series, the voltage of thebattery will be the sum of the cell voltages. For example, a 12 volt car battery contains six 2-volt cellsconnected in series. Some vehicles, such as trucks, have two 12 volt batteries in series to feed the 24 voltsystem.Parallel circuitsIf two or more components are connected in parallel they have the same potential difference (voltage)across their ends. The potential differences across the components are the same in magnitude, and theyalso have identical polarities. The same voltage is applicable to all circuit components connected inparallel. The total current is the sum of the currents through the individual components, in accordancewith Kirchhoff’s current law.VoltageIn a parallel circuit the voltage is the same for all elements.CurrentThe current in each individual resistor is found by Ohm's law. Factoring out the voltage gives and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 5 of 10.ResistorsTo find the total resistance of all components, add the reciprocals of the resistancesof eachcomponent and take the reciprocal of the sum. Total resistance will always be less than the value of thesmallest resistance:.For only two resistors, the unreciprocated expression is reasonably simple:This sometimes goes by the mnemonic "product over sum".For N equal resistors in parallel, the reciprocal sum expression simplifies to:.and therefore to:.To find the current in a component with resistance, use Ohm's law again:.The components divide the current according to their reciprocal resistances, so, in the case of tworesistors, and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 6 of 10.An old term for devices connected in parallel is multiple, such as a multiple connection for arc lamps.Since electrical conductance is reciprocal to resistance, the expression for total conductance of aparallel circuit of resistors reads:.The relations for total conductance and resistance stand in a complementary relationship: the expressionfor a series connection of resistances is the same as for parallel connection of conductances, and viceversa.InductorsInductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equalto the reciprocal of the sum of the reciprocals of their individual inductances:.If the inductors are situated in each other's magnetic fields, this approach is invalid due to mutualinductance. If the mutual inductance between two coils in parallel is M, the equivalent inductor is:IfThe sign ofdepends on how the magnetic fields influence each other. For two equal tightly coupledcoils the total inductance is close to that of each single coil. If the polarity of one coil is reversed so thatM is negative, then the parallel inductance is nearly zero or the combination is almost non-inductive. Itis assumed in the "tightly coupled" case M is very nearly equal to L. However, if the inductances are notequal and the coils are tightly coupled there can be near short circuit conditions and high circulatingcurrents for both positive and negative values of M, which can cause problems. and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 7 of 10More than three inductors becomes more complex and the mutual inductance of each inductor on eachother inductor and their influence on each other must be considered. For three coils, there are threemutual inductances,and. This is best handled by matrix methods and summing the termsof the inverse of the matrix (3 by 3 in this case).The pertinent equations are of the form:CapacitorsThe total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:.The working voltage of a parallel combination of capacitors is always limited by the smallest workingvoltage of an individual capacitor.SwitchesTwo or more switches in parallel form a logical OR; the circuit carries current if at least one switch isclosed. See OR gate.Cells and batteriesIf the cells of a battery are connected in parallel, the battery voltage will be the same as the cell voltagebut the current supplied by each cell will be a fraction of the total current. For example, if a batterycomprises four identical cells connected in parallel and delivers a current of 1 ampere, the currentsupplied by each cell will be 0.25 ampere. Parallel-connected batteries were widely used to power thevalve filaments in portable radios but they are now rare. Some solar electric systems have batteries inparallel to increase the storage capacity; a close approximation of total amp-hours is the sum of allbatteries in parallel.Combining conductances and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 8 of 10From Kirchhoff's circuit laws we can deduce the rules for combining conductances. For twoconductancesandin parallel the voltage across them is the same and from Kirchhoff's CurrentLaw the total current isSubstituting Ohm's law for conductances givesand the equivalent conductance will be,For two conductancesandin series the current through them will be the same and Kirchhoff'sVoltage Law tells us that the voltage across them is the sum of the voltages across each conductance,that is,Substituting Ohm's law for conductance then gives,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 thisfor two components.NotationThe value of two components in parallel is often represented in equations by two vertical lines, ,borrowing the parallel lines notation from geometry.[4][5]This simplifies expressions that would otherwise become complicated by expansion of the terms. Forinstance: and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 9 of 10.ApplicationsMost common application of series circuit in consumer electronics is the 9 volt block battery, the firealarm battery, which is internally built of six cells, 1.5 volts each.Series circuits were formerly used for lighting in electric multiple unit trains. For example, if the supplyvoltage was 600 volts there might be eight 70-volt bulbs in series (total 560 volts) plus a resistor to dropthe remaining 40 volts. Series circuits for train lighting were superseded, first by motor-generators, thenby solid state devices.Series resistance can also be applied to the arrangement of blood vessels within a given organ. Eachorgan 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 thearterioles.[6]Parallel resistance is illustrated by the circulatory system. Each organ is supplied by an artery thatbranches off the aorta. The total resistance of this parallel arrangement is expressed by the followingequation: 1/Rtotal 1/Ra 1/Rb . 1/Rn. Ra, Rb, and Rn are the resistances of the renal, hepatic, andother arteries respectively. The total resistance is less than the resistance of any of the individual arteries.[6]See also network analysis (electrical circuits)Wheatstone bridgeY-Δ transformVoltage dividerCurrent dividerCombining impedancesEquivalent impedance transformsResistance distanceSeries-parallel partial orderNotes1. et al. (1966), Chapter 32, Example 1.Smith, R.J. (1966), page 21Resnick et al. (1966), Chapter 32, Example 4. 7912/how-to-draw-the-parallel-circuits-signBoard Review Series: Physiology by Linda S. Costanzo pg. 74 and parallel circuits12/28/2016

Series and parallel circuits - WikipediaPage 10 of 10References Resnick, Robert and Halliday, David (1966), Physics, Vol I and II, Combined edition, WileyInternational Edition, Library of Congress Catalog Card No. 66-11527 Smith, R.J. (1966), Circuits, Devices and Systems, Wiley International Edition, New York.Library of Congress Catalog Card No. 66-17612 Williams, Tim, The Circuit Designer's Companion, Butterworth-Heinemann, 2005 ISBN 0-75066370-7.External links Series circuit ( circuits/circ114.html), Parallelcircuit ( circuits/circ122.html) Series and Parallel Circuits DC/DC 5.html)chapter from Lessons In Electric Circuits Vol 1 s/DC/index.html) free ebook and Lessons InElectric Circuits ) series. Series-Parallel Combination ircuits/DC/DC 7.html) chapter from Lessons InElectric Circuits Vol 1 DC DC/index.html) freeebook and Lessons In Electric Circuits ) series. Sameen Ahmed Khan ( s 1), How many equivalent s/17/05/0468-0475.pdf), Resonance Journal of ScienceEducation (, Vol. 17, No. 5, 468-475 (May 2012).Retrieved from " Series and parallel circuits&oldid 751201514"Categories: Electrical circuits This page was last modified on 24 November 2016, at 00:56. Text is available under the Creative Commons Attribution-ShareAlike License; additional termsmay apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia is aregistered trademark of the Wikimedia Foundation, Inc., a non-profit organization. and parallel circuits12/28/2016

Simply put, in a parallel circuit current increases but the voltage stays the same, and in a series circuit current stays the same but the voltage decreases. Contents 1 Series circuits 1.1 Current 1.2 Resistors 1.3 Inductors 1.4 Capacitors 1.5 Switches 1.6 Cells and batteries Series and parallel circuits -

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