36Chapter2Voltage and Current2.3VoltageWhen charges are detached from onebody and transferred to another,apotentialdifferenceorvoltageresultsbetweenthem.Afamiliarexampleisthevoltagethatdevelops whenyouwalk acrossa carpet.Voltagesin excessof ten thousand volts can be created in this way.(We will define the volt rig-orouslyvery shortly.)This voltage is dueentirelytothe separation of posi-tive and negative charges.Figure2-7illustrates another example.During electrical storms,elec-+Voltagetrons inthunderclouds arestrippedfromtheirparentatomsbytheforcesofdifferenceturbulenceand carriedtothebottom of thecloud,leavingadeficiencyofelectrons (positivecharge)atthetopandan excess (negativecharge)atthebottom.Theforce of repulsion then drives electrons awaybeneaththe cloudleavingtheground positivelycharged.Hundreds of millions of volts arecre-ated in this way. (This is what causes the air to break down and a lightningVoltagedifferencedischarge to occur.)Practical Voltage SourcesFIGURE2-7 Voltages createdbyseparation of charges in a thunderAs the preceding examples show, voltage is created solely by the separationcloud. The force of repulsion drivesof positive and negative charges.However,static discharges and lightningelectrons away beneath the cloud, cre-strikes are not practical sources of electricity.We now look at practicalating a voltagebetween the cloud andground as well.If voltage becomessources.A common example is the battery.In a battery,charges are sepa-largeenough,theairbreaks down and arated by chemical action.An ordinaryflashlight battery(dry cell)illustrateslightning discharge occurs.the concept in Figure 2-8.The inner electrode is a carbon rod and the outerelectrodeisazinccase.Thechemicalreactionbetweentheammonium-chlo-ride/manganese-dioxidepaste and thezinc case creates an excess of elec-Metal cover andpositive terminalSeal- Insulated SpacerCarbon rod (+)AmmoniumNOTESchlorideand manganeseThe source of Figure 2-8 isdioxide mixmore properly called a cell thanZinc case (-)a battery,since“"cell"refers to asingle cell while“battery"refersJacketto a group of cells.However,through common usage, such(b) C cell, commonly called a flashlightcells are referred to as batteries.(a) Basic construction.battery.In what follows,wewill alsocall them batteries.FIGURE2-8Carbon-zinc cell.Voltage is created by the separation of charges due tochemical action.Nominal cellvoltageis1.5V
2.3 Voltage When charges are detached from one body and transferred to another, a potential difference or voltage results between them. A familiar example is the voltage that develops when you walk across a carpet. Voltages in excess of ten thousand volts can be created in this way. (We will define the volt rigorously very shortly.) This voltage is due entirely to the separation of positive and negative charges. Figure 2–7 illustrates another example. During electrical storms, electrons in thunderclouds are stripped from their parent atoms by the forces of turbulence and carried to the bottom of the cloud, leaving a deficiency of electrons (positive charge) at the top and an excess (negative charge) at the bottom. The force of repulsion then drives electrons away beneath the cloud, leaving the ground positively charged. Hundreds of millions of volts are created in this way. (This is what causes the air to break down and a lightning discharge to occur.) Practical Voltage Sources As the preceding examples show, voltage is created solely by the separation of positive and negative charges. However, static discharges and lightning strikes are not practical sources of electricity. We now look at practical sources. A common example is the battery. In a battery, charges are separated by chemical action. An ordinary flashlight battery (dry cell) illustrates the concept in Figure 2–8. The inner electrode is a carbon rod and the outer electrode is a zinc case. The chemical reaction between the ammonium-chloride/manganese-dioxide paste and the zinc case creates an excess of elec- 36 Chapter 2 ■ Voltage and Current Voltage difference Voltage difference FIGURE 2–7 Voltages created by separation of charges in a thunder cloud. The force of repulsion drives electrons away beneath the cloud, creating a voltage between the cloud and ground as well. If voltage becomes large enough, the air breaks down and a lightning discharge occurs. (b) C cell, commonly called a flashlight (a) Basic construction. battery. Metal cover and positive terminal Carbon rod () Seal Zinc case () Ammonium chloride and manganese dioxide mix Jacket Insulated Spacer FIGURE 2–8 Carbon-zinc cell. Voltage is created by the separation of charges due to chemical action. Nominal cell voltage is 1.5 V. The source of Figure 2–8 is more properly called a cell than a battery, since “cell” refers to a single cell while “battery” refers to a group of cells. However, through common usage, such cells are referred to as batteries. In what follows, we will also call them batteries. NOTES.
37Section2.3Voltagetrons;hence, the zinc carries a negative charge.An alternate reaction leavesthe carbonrod with a deficiencyof electrons,causingitto bepositivelycharged. These separated charges create a voltage (1.5 V in this case)between the two electrodes.The battery is useful as a source since its chemi-cal action creates a continuous supply of energy that is able to do usefulwork,suchaslightalamporrunamotorPotential EnergyThe concept of voltage is tied into the concept of potential energy.We there-forelookbriefly at energyIn mechanics, potential energy is the energy that a body possessesbecause of its position. For example, a bag of sand hoisted by a rope over apulley has the potential to do work when it is released. The amount of workthat went into giving it this potential energy is equal to the product of forcetimes the distance through which the bag was lifted (i.e., work equals forcetimes distance).In a similar fashion, work is required to move positive and negativecharges apart.This gives thempotential energy.To understand why,consideragain the cloud of Figure 2-7. Assume the cloud is initially uncharged. Nowassume a charge of Q electrons is moved from the top of the cloud to thebottom.The positive charge left at the top of the cloud exerts a force on theelectrons thattriestopull thembackasthey arebeingmoved away.Sincethe electrons are being moved against thisforce, work (force times distance)is required.Since the separated charges experience a force to return to thetop of the cloud, they have the potential to do work if released,i.e., they pos-sess potential energy.Definitionof Voltage:TheVoltIn electrical terms,a difference in potential energy is defined as voltage.Ingeneral, the amount of energy required to separate charges depends on thevoltage developed and the amount of charge moved. By definition, the volt-age between two points is one volt if it requires one joule of energy to moveone coulomb of charge from one point to the other: In equation form,W[volts, V](22)V=Qwhere Wis energy in joules,Q is charge in coulombs,and Vis the resultingvoltage in volts.Note carefully that voltage is defined between points. For the case of thebattery, for example, voltage appears between its terminals. Thus, voltagedoes not exist at a point by itself; it is always determined with respect tosome other point. (For this reason, voltage is also called potential differ-ence.We often use the terms interchangeably.)Note also that, although weconsidered static electricityindevelopingthe energy argument,the sameconclusion results regardless of how you separate the charges;this may beby chemical means as in abattery,bymechanical meansas in agenerator,byphotoelectric means as in a solar cell, and so on
trons; hence, the zinc carries a negative charge. An alternate reaction leaves the carbon rod with a deficiency of electrons, causing it to be positively charged. These separated charges create a voltage (1.5 V in this case) between the two electrodes. The battery is useful as a source since its chemical action creates a continuous supply of energy that is able to do useful work, such as light a lamp or run a motor. Potential Energy The concept of voltage is tied into the concept of potential energy. We therefore look briefly at energy. In mechanics, potential energy is the energy that a body possesses because of its position. For example, a bag of sand hoisted by a rope over a pulley has the potential to do work when it is released. The amount of work that went into giving it this potential energy is equal to the product of force times the distance through which the bag was lifted (i.e., work equals force times distance). In a similar fashion, work is required to move positive and negative charges apart. This gives them potential energy. To understand why, consider again the cloud of Figure 2–7. Assume the cloud is initially uncharged. Now assume a charge of Q electrons is moved from the top of the cloud to the bottom. The positive charge left at the top of the cloud exerts a force on the electrons that tries to pull them back as they are being moved away. Since the electrons are being moved against this force, work (force times distance) is required. Since the separated charges experience a force to return to the top of the cloud, they have the potential to do work if released, i.e., they possess potential energy. Definition of Voltage: The Volt In electrical terms, a difference in potential energy is defined as voltage. In general, the amount of energy required to separate charges depends on the voltage developed and the amount of charge moved. By definition, the voltage between two points is one volt if it requires one joule of energy to move one coulomb of charge from one point to the other. In equation form, V W Q [volts, V] (2–2) where W is energy in joules, Q is charge in coulombs, and V is the resulting voltage in volts. Note carefully that voltage is defined between points. For the case of the battery, for example, voltage appears between its terminals. Thus, voltage does not exist at a point by itself; it is always determined with respect to some other point. (For this reason, voltage is also called potential difference. We often use the terms interchangeably.) Note also that, although we considered static electricity in developing the energy argument, the same conclusion results regardless of how you separate the charges; this may be by chemical means as in a battery, by mechanical means as in a generator, by photoelectric means as in a solar cell, and so on. Section 2.3 ■ Voltage 37
38Chapter2Voltageand CurrentAlternatearrangementsofEquation2-2areuseful:W=QV[joules, J](2-3)W(2-4)[coulombs, C]0VEXAMPLE2-2If it takes35Jof energy tomoveachargeof 5Cfromonepoint to another, what is the voltage between the two points?SolutionW-35JV==7J/C=7V5CQPRACTICE1. The voltage between two points is 19 V. How much energy is required toPROBLEMS2move67×10lselectrons from one point to the other?2. The potential difference between two points is 140mV.If 280 μJ of work arerequired to move a charge Qfrom one point to the other, what is Q2. 2 mCAnswers: 1. 204JAlthoughEquation 2-2 is the formal definition of voltage,it is a bitabstract.Amore satisfying waytolook atvoltage isto viewit as theforceor“push"that moves electrons around a circuit.This view is looked at in greatdetail, starting in Chapter 4 where we consider Ohm's law.For the moment,however,wewill staywithEquation2-2,whichisimportantbecauseitpro-vides thetheoretical foundationfor many of theimportant circuit relation-(a) Symbol for a cellships that you will soon encounterSymbolfor DCVoltage SourcesConsider again Figure 2-1. The battery is the source of electrical energy thatmoves charges around the circuit.This movement of charges, as we will soonsee, is called an electric current.Because one of the battery's terminals is(b) Symbol for a batteryalways positive and theotheris always negative,current is always in the samedirection.Suchaunidirectional currentiscalleddcordirectcurrentandthebattery is called a dc source. Symbols for dc sources are shown in Figure 2-9.1.5 VThelong bar denotes thepositive terminal.On actual batteries,thepositiveterminal is usuallymarkedPOS(+)and thenegativeterminalNEG(-).(c) A 1.5 volt battery2.4CurrentFIGURE2-9Battery symbol. Thelong bar denotes the positive terminalEarlier, you learned that there are large numbers of free electrons in metalsand the short bar the negative terminal.likecopper.Theseelectronsmoverandomlythroughoutthematerial (FigureThus, it is not necessary to put + and2-6), but their net movement in any given direction is zero.signs on the diagram.For simplicity.we use the symbol shown in (a)Assume now that abattery is connected as in Figure 2-10.Since elec-throughoutthis book.trons areattracted bythepositivepole of thebatteryand repelled bythe neg
Although Equation 2–2 is the formal definition of voltage, it is a bit abstract. A more satisfying way to look at voltage is to view it as the force or “push” that moves electrons around a circuit. This view is looked at in great detail, starting in Chapter 4 where we consider Ohm’s law. For the moment, however, we will stay with Equation 2–2, which is important because it provides the theoretical foundation for many of the important circuit relationships that you will soon encounter. Symbol for DC Voltage Sources Consider again Figure 2–1. The battery is the source of electrical energy that moves charges around the circuit. This movement of charges, as we will soon see, is called an electric current. Because one of the battery’s terminals is always positive and the other is always negative, current is always in the same direction. Such a unidirectional current is called dc or direct current, and the battery is called a dc source. Symbols for dc sources are shown in Figure 2–9. The long bar denotes the positive terminal. On actual batteries, the positive terminal is usually marked POS () and the negative terminal NEG (). 2.4 Current Earlier, you learned that there are large numbers of free electrons in metals like copper. These electrons move randomly throughout the material (Figure 2–6), but their net movement in any given direction is zero. Assume now that a battery is connected as in Figure 2–10. Since electrons are attracted by the positive pole of the battery and repelled by the neg- 38 Chapter 2 ■ Voltage and Current EXAMPLE 2–2 If it takes 35 J of energy to move a charge of 5 C from one point to another, what is the voltage between the two points? Solution V W Q 3 5 5 C J 7 J/C 7 V PRACTICE PROBLEMS 2 1. The voltage between two points is 19 V. How much energy is required to move 67 1018 electrons from one point to the other? 2. The potential difference between two points is 140 mV. If 280 mJ of work are required to move a charge Q from one point to the other, what is Q? Answers: 1. 204 J 2. 2 mC E E 1.5 V (a) Symbol for a cell (b) Symbol for a battery (c) A 1.5 volt battery FIGURE 2–9 Battery symbol. The long bar denotes the positive terminal and the short bar the negative terminal. Thus, it is not necessary to put and signs on the diagram. For simplicity, we use the symbol shown in (a) throughout this book. Alternate arrangements of Equation 2–2 are useful: W QV [joules, J] (2–3) Q W V [coulombs, C] (2–4)
39Section2.4CurrentWhentheamountof chargethatpasses a point in one second isonecoulomb,thecurrentisone ampereLampImaginaryPlaneMovement ofelectrons throughthewireFIGURE2-10Electronflowinaconductor.Electrons(-)areattractedtothepositive(+) pole of the battery. As electrons move around the circuit, they are replenished at thenegative pole of the battery.This flow of charge is called an electric current.ative pole,they move around the circuit,passingthrough the wire,thelampand the battery. This movement of charge is called an electric current. Themore electrons per second that pass through the circuit, thegreater is the cur-rent. Thus, current is the rate of flow (or rate of movement) of charge.TheAmpereSince charge is measured in coulombs, its rate of flow is coulombs per sec-ond.IntheSI system,onecoulombpersecondisdefinedasoneampere(commonlyabbreviated A).Fromthis,weget that oneampere is thecurrentin a circuit when one coulomb of charge passes a given point in one second(Figure2-10).The symbol for current is I.Expressed mathematically.0I =(2-5)[amperes, A]1where Q is the charge (in coulombs) and t is the time interval (in seconds)overwhich it ismeasured.InEquation2-5,it is importantto notethattdoesnot represent a discrete point in time but is the interval of time during whichthe transfer of charge occurs. Alternate forms of Equation 2-5 are(2-6)Q = It[coulombs, C]and0[seconds, s](2-7)EXAMPLE2-3If 840 coulombsof chargepassthroughtheimaginaryplane of Figure 2-10 during a time interval of 2 minutes, what is the current?SolutionConverttto seconds.Thus.1=2840C7C/s=7A1(2 X 60)s
ative pole, they move around the circuit, passing through the wire, the lamp, and the battery. This movement of charge is called an electric current. The more electrons per second that pass through the circuit, the greater is the current. Thus, current is the rate of flow (or rate of movement) of charge. The Ampere Since charge is measured in coulombs, its rate of flow is coulombs per second. In the SI system, one coulomb per second is defined as one ampere (commonly abbreviated A). From this, we get that one ampere is the current in a circuit when one coulomb of charge passes a given point in one second (Figure 2–10). The symbol for current is I. Expressed mathematically, I Q t [amperes, A] (2–5) where Q is the charge (in coulombs) and t is the time interval (in seconds) over which it is measured. In Equation 2–5, it is important to note that t does not represent a discrete point in time but is the interval of time during which the transfer of charge occurs. Alternate forms of Equation 2–5 are Q It [coulombs, C] (2–6) and t Q I [seconds, s] (2–7) Section 2.4 ■ Current 39 When the amount of charge that passes a point in one second is one coulomb, the current is one ampere Lamp Imaginary Plane Movement of electrons through the wire FIGURE 2–10 Electron flow in a conductor. Electrons () are attracted to the positive () pole of the battery. As electrons move around the circuit, they are replenished at the negative pole of the battery. This flow of charge is called an electric current. EXAMPLE 2–3 If 840 coulombs of charge pass through the imaginary plane of Figure 2–10 during a time interval of 2 minutes, what is the current? Solution Convert t to seconds. Thus, I Q t (2 8 40 6 C 0)s 7 C/s 7 A
40Chapter2Voltage andCurrentPRACTICE1.Between t=1 ms and t=14ms,8μC of chargepass through a wire.WhatPROBLEMS3is the current?2.After the switch of Figure 2-1 is closed, current / =4 A.How much chargepasses through thelamp between the time the switch is closed and the timethat it is opened 3 minutes later?Answers: 1. 0.615 mA2.720CAlthough Equation 2-5 is the theoretical definition of current, we neveractuallyuseittomeasurecurrent.Inpractice,weusean instrumentcalledanammeter(Section 2.6).However,it is an extremely importantequation thatwe will soon use to develop other relationships.CurrentDirectionIn the early days of electricity, it was believed that current was a movementof positive charge and that these charges moved around the circuit from thepositive terminal of the battery to the negative as depicted in Figure 2-11(a)Based on this, all the laws, formulas, and symbols of circuit theory weredeveloped.(We now refer to this direction as the conventional currentdirection.) After the discovery of the atomic nature of matter, it was learnedthatwhat actuallymoves in metallic conductors are electrons and that theymove through the circuit as in Figure 2-ll(b).This direction is called theelectron flow direction.However,because the conventional currentdirec-tion was so well established, most users stayed with it.We do likewise.Thus.inthisbook,theconventionaldirectionforcurrentisused11L(a)Conventional current direction(b)ElectronflowdirectionFIGURE2-11Conventional currentversus electron flow.In thisbook,we use conven-tional current.AlternatingCurrent (AC)So far, we have considered only dc. Before we move on, we will brieflymention ac or alternating current. Alternating current is current thatchanges direction cyclically,i.e, charges alternatelyflow in one directionthen in the otherin a circuit.Themost common ac sourceisthe commercialac power system that supplies energy to your home.We mention it herebecauseyou will encounteritbrieflyinSection2.5.It iscovered in detail inChapter 15
Although Equation 2–5 is the theoretical definition of current, we never actually use it to measure current. In practice, we use an instrument called an ammeter (Section 2.6). However, it is an extremely important equation that we will soon use to develop other relationships. Current Direction In the early days of electricity, it was believed that current was a movement of positive charge and that these charges moved around the circuit from the positive terminal of the battery to the negative as depicted in Figure 2–11(a). Based on this, all the laws, formulas, and symbols of circuit theory were developed. (We now refer to this direction as the conventional current direction.) After the discovery of the atomic nature of matter, it was learned that what actually moves in metallic conductors are electrons and that they move through the circuit as in Figure 2–11(b). This direction is called the electron flow direction. However, because the conventional current direction was so well established, most users stayed with it. We do likewise. Thus, in this book, the conventional direction for current is used. 40 Chapter 2 ■ Voltage and Current PRACTICE PROBLEMS 3 1. Between t 1 ms and t 14 ms, 8 mC of charge pass through a wire. What is the current? 2. After the switch of Figure 2–1 is closed, current I 4 A. How much charge passes through the lamp between the time the switch is closed and the time that it is opened 3 minutes later? Answers: 1. 0.615 mA 2. 720 C (a) Conventional current direction E I (b) Electron flow direction E I FIGURE 2–11 Conventional current versus electron flow. In this book, we use conventional current. Alternating Current (AC) So far, we have considered only dc. Before we move on, we will briefly mention ac or alternating current. Alternating current is current that changes direction cyclically, i.e., charges alternately flow in one direction, then in the other in a circuit. The most common ac source is the commercial ac power system that supplies energy to your home. We mention it here because you will encounter it briefly in Section 2.5. It is covered in detail in Chapter 15.