CHAPTER· 25 Electromagnetic Induction · 2019-08-25 · CHAPTER· 25 Electromagnetic...

CHAPTER·

25 ElectromagneticInduction

.....................~ Go With the Flow

Aluminum is classified as a non-magnetic substance. Twoaluminum rings, one with a slit and one a continuous ring,are placed over a magnetic field generator that is produc-ing a constantly-changing magnetic field. Why does onering float but the other one does not?

•

Levitation? There is no superconductor or permanent mag-net in this photograph. The ring is made of aluminum, a

non-magnetic conductor. The coil of wire around the cen-tral rod produces a continually changing magnetic field.You may never have seen such a floating ring, but the phys-ical principle that explains why it is levitated also explainshow the modern electrical distribution system works.

-

Chapter Outline25.1 CREATING ELECTRIC

CURRENT FROMCHANGING MAGNETICFIELDS

· Faraday's Discovery· Electromotive Force· Electric Generators· Alternating Current Generator

25.2 EFFECTS OF CHANGINGMAGNETIC FIELDS:INDUCED EMF

· Lenz's Law· Self-Inductance· Transformers

VConcept CheckThe following terms or

concepts from earl ier chaptersare important for a goodunderstanding of this chapter. Ifyou are not familiar with them,you should review them beforestudying this chapter.. potential difference, electron

pump, current, resistance,Chapter 22

. right-hand rules, electricmotor, Chapter 24

515

Objectives· explain how a changing magnetic

field produces an electric current.· define EMF; show an ability to

calculate EMF of wires moving in amagnetic field and know thelimitations of the equation.

· explain how an electric generatorworks and how it differs from amotor.

· explain the difference betweenpeak and effective voltage andcurrent; use both in solvingproblems.

To induce current, there must berelative motion of a wire and themagnetic field.

F. Y. I.Michael Faraday left school at

age 14 to become an apprenticeto a bookbinder. He read most ofthe books in the shop. JosephHenry left school at age 13 towork for a watch maker. Later inlife, Faraday became director ofthe Royal Institution in London,founded by the American Benja-min Thomson (Count Rumford).Henry became the director of theSmithsonian Institution in Wash-ington DC, founded by the En-glishman James Smithson.

FIGURE 25-1. When a wire is movedin a magnetic field, an electriccurrent flows in the wire, but onlywhile the wire is moving. Thedirection of the current flow dependson the direction the wire is movingthrough the field. The arrowsindicate the direction of conventionalcurrent flow.

516 Electromagnetic Induction

25.1 ..........................................CREATING ELECTRIC CURRENTFROM CHANGING MAGNETICFIELDS

In1822, Michael Faraday wrote a goal in his notebook: "ConvertMagnetism into Electricity." After nearly ten years of unsuccessful ex-

periments, he was able to show that a changing magnetic field couldproduce electric current. In the same year, Joseph Henry, an Americanhigh school teacher, made the same discovery.

Faraday's DiscoveryOersted had discovered that an electric current produces a magnetic

field. Faraday tried all combinations of field and wire without successuntil he found he could induce current by moving the wire in a mag-netic field. Figure 25-1 shows one of Faraday's experiments. A wireloop that is part of a closed circuit is placed in a magnetic field. If thewire moves up through the field, the current moves in one direction.When the wire moves down through the field, the current moves in theopposite direction. If the wire is held stationary or is moved parallel tothe field, no current flows. An electric current is generated in a wireonly when the wire cuts magnetic field lines.

To generate current, either the conductor can move through a mag-netic field, or the magnetic field can move past a conductor. It is therelative motion between the wire and the magnetic field that producesthe current. The process of generating a current through a circuit in thisway is called electromagnetic induction.

In what direction does the current move? To find the force on thecharges in the wire, use the third right-hand rule described in Chapter24. Hold your right hand so that your thumb points in the direction inwhich the wire is moving and your fingers point in the direction of themagnetic field. The palm of your hand will point in the direction of theconventional (positive) current flow, Figure 25-2.

Wiremoving up

(Current

B

s F

~/IB_V_N Motion of the wire

Electromotive ForceWhen we studied electric circuits, we learned that a charge pump is

needed to produce a continuous current flow. The potential increase,or voltage, given to the charges by the pump is called the electromotiveforce, or EMF. Electromotive force, however, is not a force; it is a po-tential increase and is measured in volts. Thus the term EMF is mislead-ing. Like many other historical terms still in use, it originated beforeelectricity was well understood.

What creates the increase in potential that can cause an induced cur-rent to flow? When a wire is moved through a magnetic field, a forceacts on the charges and they move in the direction of the force. Workis done on the charges. Their electrical potential energy, and thus theirpotential, is increased. The increase in potential is called the inducedEMF. The EMF, measured in volts, depends on the magnetic fieldstrength, B, the length of the wire in the magnetic field, L, and thevelocity of the wire in the field, v. If B, v, and the direction of the lengthof the wire are mutually perpendicular,

I EMF = BLv·1

If the moving wire is part of a closed circuit, the EMF will cause acurrent to flow in the circuit in the direction of the EMF.

If a wire moves through a magnetic field at an angle to the field, onlythe component of the wire's velocity that is perpendicular to the direc-tion of the field generates EMF.

A microphone is a simple application that depends on an inducedEMF. The "dynamic" microphone is similar in construction to a loud-speaker. The microphone in Figure 25-3 has a diaphragm attached toa coil of wire that is free to move in a magnetic field. Sound wavesvibrate the diaphragm, which moves the coil in the magnetic field. Themotion of the coil, in turn, induces an EMF across the ends of the coil.The voltage generated is small, typically 10-3 V, but it can be in-creased, or amplified, by electronic devices.

FIGURE 25-2. The right-hand rulecan be used to find the direction ofthe forces on the charges in aconductor that is moving in amagnetic field.

v••

Electromotive force is measuredvolts.

The EMF depends on magnetic fieldstrength, the length of the Wire, and itsvelocity perpendicular to the field.

sCoil

Magnet(also serves asthe supporting

frame)

C .~onnectlng Air vent

wires

FIGURE 25-3. Schematic of amoving coil microphone. Thealuminum diaphragm is connected toa coil in a magnetic field. Whensound waves vibrate the diaphragm,the coil moves in the magnetic field,generating a current proportional tothe sound wave.

25.1 Creating Electric Current from Changing Magnetic Fields 517

POCKETLAB

MAKING CURRENTSHook the ends of a 1 m length

of wire to the binding posts of agalvanometer (or microamme-ter). Make several overlappingloops in the wire. Watch thereadings on the wire as youmove a pair of neodymiummag-nets (or a strong horseshoemagnet) near the loops. Recordyour observations.What can youdo to increase the current? Re-place the 1 m lengthof wire witha pre-formed coil and see howmuch current you can produce.Describeyour results.


Example ProblemInduced EMF

A straight wire 0.20 m long moves perpendicularly through a mag-netic field of magnetic induction 8.0 x 10-2 T at a speed of7.0 m/s. a. What EMF is induced in the wire? b. The wire is part of acircuit that has a resistance of 0.50 D. What current flows in thecircuit?Given: L = 0.20 m

8 = 8.0 X 10-2 Tv = 7.0 mlsR = 0.500

Solution: a. EMF = 8Lv= (8.0 x 10-2 T)(0.20 m)(7.0 m/s)= (8.0 x 10-2 N/A·m)(0.20 m)(7.0 m/s)

EMF = 0.11 (_N_)(m)(m) = 0.11 W = 0.11 VA'm s A

b. I = ~ = 0.11 V 0.22 AR 0.500

Unknowns: a. EMF b. IBasicequations: a. EMF = 8Lv

b. I = VIR

Practice Problems1. A straight wire, 0.5 m long, is moved straight up through a O.4-T

magnetic field pointed in the horizontal direction at a speed of20 m/s.a. What EMF is induced in the wire?b. The wire is part of a circuit of total resistance of 6.0 D. What is

the current in the circuit?2. A straight wire, 25 m long, is mounted on an airplane flying at

125 m/s. The wire moves perpendicularly through Earth's magneticfield (8 = 5.0 x 10-5 T). What EMF is induced in the wire?

3. A permanent horseshoemagnet is mounted so that the magnetic fieldlines are vertical. If a student passesa straight wire between the polesand pulls it toward herself, the current flow through the wire is fromright to left. Which is the N-pole of the magnet?

~ 4. A straight wire, 30.0 m long, moves at 2.0 mls perpendicularlythrough a 1.0-T magnetic field.a. What EMF is induced in the wire?b. The total resistance of the circuit of which the wire is a part is

15.0 D. What is the current?

Electric GeneratorsThe electric generator, invented by Michael Faraday, converts me-

chanical energy to electric energy. An electric generator consists of anumber of wire loops placed in a strong magnetic field. The wire iswound around an iron form to increase the strength of the field. Theiron and wires are called the armature, similar to that of an electricmotor.

2

N

4 1=0

a b

The armature is mounted so that it can rotate freely in the field. Asthe armature turns, the wire loops cut through the magnetic field lines,inducing an EMF. The EMF, commonly called the voltage, developedby the generator depends on the magnetic induction, B, the length ofwire rotating in the field, L, and v, the speed of the loops perpendicularto the magnetic field. Increasing the number of loops in the armatureincreases the wire length, L, increasing the induced EMF.

When a generator is connected in a closed circuit, current flows thatis proportional to the induced EMF. Figure 25-4 shows a single loopgenerator. The direction of the induced current can be found from thethird right-hand rule. As the loop rotates, the strength and direction ofthe current change. The current is greatest when the component of theloop's velocity perpendicular to the field is largest. This occurs whenthe motion of the loop is perpendicular to the magnetic field-when theloop is in the horizontal position. As the loop rotates from the horizontalto the vertical position, it moves through the magnetic field lines at anever-increasing angle and current decreases. When the loop is in thevertical position, the wire segments move parallel to the field and thecurrent is zero. As the loop continues to turn, the segment that wasmoving up begins to move down, reversing the direction of the currentin the loop. This change in direction takes place each time the loopturns through 180°. The current changes smoothly from zero to somemaximum value and back to zero during each half-turn of the loop.Then it reverses direction. The graph of current versus time is shown inFigure 25-5.

FIGURE 25-4. An electric current isgenerated in a wire loop as the looprotates (a). The cross-sectional view(b) shows the position of the loopwhen maximum current is generated.The numbered positions correspondto the numbered points on the graphin Figure 25-5.

The strength and direction of theinduced current change as thearmature rotates.

FIGURE 25-5. This graph shows thevariation of current with time as theloop in Figure 25-4b rotates. Thevariation of EMF with time is givenby a similar graph.


FIGURE 25-6. Alternating currentgenerators transmit current to anexternal circuit by way of a brush-slip-ring arrangement (a). Thealternating current varies withtime (b).

The direction of current produced bygenerators in electric utility companiesalternates from one direction to theother and back 60 times each second.

HELP WANTEDELECTRICIAN

Electrical contractor needs electri-cians who have successfully com-pleted a 5-year apprenticeship pro-gram conducted by a union orprofessional builder'S association.You must be a high school grad, bein good physical condition, have ex-cellent dexterity and color vision, andbe willing to work when and wherethere is work. You will do all aspectsof the job, including reading blue-prints, dealing with all types of wires,conduits, and equipment. Safety andquality work must be your highestpriori' . . ct:nternational Brotherhood of Electri-

cal Workers, 1125 15th Street,.w., Washington, DC 20005


i:

o JL---\.---I---\--f-

-/max

Brushes

a b

Generators and motors are almost identical in construction but con-vert energy in opposite directions. A generator converts mechanical en-ergy to electric energy while a motor converts electric energy to me-chanical energy. In a generator, mechanical energy turns an armaturein a magnetic field. The induced voltage causes current to flow. In amotor, a voltage is placed across an armature coil in a magnetic field.The voltage causes current to flow in the coil and the armature turns,producing mechanical energy from electrical energy.

Alternating Current GeneratorAn energy source turns the armature of a generator in a magnetic field

at a fixed number of revolutions per second. In the United States,elec-tric utilities use a 60-Hz frequency. The current goes from one direc-tion, to the other, and back to the first, 60 times a second.

Figure 25-6 shows how an alternating current in an armature is trans-mitted to the rest of the circuit. The brush-slip-ring arrangement permitsthe armature to turn freely while still allowing the current to pass intothe external circuit. As the armature turns, the alternating current variesbetween some maximum value and zero. If the armature is turning rap-idly, the light in the circuit does not appear to dim or brighten becausethe changes are too fast for the eye to detect.

The power produced by a generator is the product of the current andthe voltage. Power is always positive because either / and V are bothpositive or both negative. Because / and V vary, however, the powerassociatedwith an alternating current varies and its average value is lessthan the power suppl ied by a direct current with the same /max and Vrnax-

In fact, the average AC power is

PAC =1/2P ACmax = 1/2PDC'

It is common to describe alternating currents and voltages in terms ofeffective currents and voltages. Recall that P = /2R. Thus, the averageAC power can be written in terms of the effective current,

PAC = PeffR.

PAC = 1i2PDcPeffR = 1i2(pmaxlR

Jeff = y1/2J2max

Jeff = 0.707Jmax

Veff = 0.707Vmax

The voltage generally available at wall outlets is described as 120 V,where 120 is the magnitude of the effective voltage, not the maximumvoltage.

Example ProblemEffective Voltage and Effective Current

An AC generator develops a maximum voltage of 34 V and deliversa maximum current of 0.17 A to a circuit. a. What is the effectivevoltage of the generator? b. What effective current is delivered to thecircuit? c. What is the resistance of the circuit?

Given: Vmax= 34 V Unknowns: a. Veffb. Jeffc. RJmax= 0.17 A Basic equations: a. Veff = 0.707 Vmax

b. Jefl = 0.707 Jmax

c. R = VeflJefl

Solution: a. Veff = o.707(Vmax)= 0.707(34 V) = 24 V

b. Jeff= 0.707(1max)= 0.707(0.17 A) = 0.12 A

Veff 24 Vc R = - = -- = 2000= 2.0 X 1020• Jeff 0.12 A

Practice Problems5. A generator in a power plant develops a maximum voltage of 170 V.

a. What is the effective voltage?b. A 60-W light bulb is placed across the generator. A maximum

current of 0.70 A flows through the bulb. What effective currentflows through the bulb?

c. What is the resistance of the light bulb when it is working?6. The effective voltage of a particular AC household outlet is 117 V.

a. What is the maximum voltage across a lamp connected to theoutlet?

b. The effective current through the lamp is 5.5 A. What is the max-imum current in the lamp?

7. An AC generator delivers a peak voltage of 425 V.a. What is the effective voltage in a circuit placed across the gener-

ator?b. The resistance of the circuit is 5.0 x 102 O. What is the effective

current?~ 8. If the average power dissipated by an electric light is 100 W, what is

the peak power?

F. Y. I.In an incandescent bulb, the

filament temperature cannotchange fast enough to keep upwith the changing voltage. How-ever, a fluorescent lamp can.Look at the blades of a fan in thelight of a fluorescent lamp. Youwill see blue-looking blades fromthe 120-Hz blue flashes of ex-cited mercury vapor. The overallyellowish light is from the phos-phors on the inner surface of thetube, which emit a more slowlychanging light.

POCKETLAB

MOTOR AND GENERATORMake a series circuit with a

Genecon (or efficient DC motor),a miniature lamp, and ammeter.Rotate the handle (or motorshaft) to try to light the lamp. De-scribe your results. Predict whatmight happen if you connectyour Genecon to the Geneconfrom another lab group andcrank yours. Try it. Describewhat happens. Can more thantwo be connected?


PHYSICSLABo: The Pick Up

PurposeTo investigate changing magnetic fields with a tele-phone pickup coil.

Materials· telephone pickup coil (Radio Shack #44-533 orsimilar)

· mini audio amplifier (Radio Shack #277-1008 orsimilar)

· strong permanent magnet· iron or air core solenoid coil· 9-V battery· low-voltage AC power supply· battery-powered car· 1 meter of string· masking tape

Procedure1. Put the 9-V battery into the amplifier and plug

in the telephone pickup coil.2. Place the strong permanent magnet on the table.

Slowly bring the pickup coil near the magnet.

Mini audioamplifier

Pickup coil


3. Use the suction cup to stick the pickup coil onthe table. Attach the magnet to a string so that ithangs just above the pickup coil.

4. Swing the magnet like a pendulum. Twist thestring so that as it untwists it will spin the mag-net.

5. Attach the low-voltage AC power supply to thesolenoid coil. Turn the power supply to about2-3 V.

6. Hold the pickup coil near the solenoid coil tofind where the sound is loudest. Listen to theamplifier as the pickup coil is rotated.

Observations and Data1. When does the pickup coil and amplifier make

a sound in Procedure 2-4?2. Describe the sound as the pickup coil and am-

plifier approaches the solenoid coil.

Analysis1. The pickup coil produces no signal when it is

held stationary near the permanent magnet. Ex-plain this.

2. Explain why rotating the pickup coil (Procedure6) changes the loudness of the signal.

3. Predict the sound that you would hear if the so-lenoid coil was connected to a battery. Explainyour prediction.

Applications1. Turn the battery-powered car on low speed and

bring the pickup coil near to "hear" the chang-ing magnetic fields. Predict how the sound willbe different when the battery-powered car is onhigh speed. Try it. What happened? Why?

........................CONCEPT REVIEW1.1 Could you make a generator by mounting permanent magnets on

the rotating shaft and having the coil stationary? Explain.1.2 A bike generator lights the headlamp. What is the source of the

energy for the bulb when the rider travels along a flat road?1.3 Consider the microphone shown in Figure 25-3. When the dia-

phragm is pushed in, what is the direction of the current in the coil?1.4 Critical Thinking: A student asks: "Why doesn't AC dissipate any

power? The energy going into the lamp when the current is positiveis removed when the current is negative. The net is zero." Explainwhy this argument is wrong .

25.2.......................................EFFECTS OF CHANGINGMAGNETIC FIELDS: INDUCEDEMF

Ina generator, current flows when the armature turns through a mag-netic field. We learned in Chapter 24 that when current flows through

a wire in a magnetic field, a force is exerted on the wire. Thus, a forceis exerted on the wires in the armature. In a sense, then, a generator is,at the same time, a motor.

Lenis LawIn what direction is the force on the wires of the armature? The direc-

tion of the force on the wires opposes the original motion of the wires.That is, the force acts to slow down the rotation of the armature. Thedirection of the force was first determined in 1834 by H. F. E. Lenz andis called Lenz's law.

Lenz's law states: The direction of the induced current is such thatthe magnetic field resulting from the induced current opposes thechange in the field that caused the induced current. Note that it is thechange in the field and not the field itself that is opposed by the inducedmagnetic effects.

Figure 25-7 is a simple example of how Lenz's law works. The N-pole of a magnet is moved toward the right end of a coil. To opposethe approach of the N-pole, the right end of the coil must also become

Objectives· state Lenz's law; explain back-EMF

and how it affects the operation ofmotors and generators.

· explain the nature of self-inductance and its effects incircuits.

· describe the transformer; explainthe connection of turns ratio tovoltage ratio; solve transformerproblems.

According to Lenz's law, the direction ofthe induced current is such that thecurrent's magnetic effects oppose thechanges that produced the current.

FIGURE 25-7. The magnetapproaching the coil causes aninduced current to flow. Lenz's lawpredicts the direction of flow shown.

N s

25.2 Effects of Changing Magnetic Fields: Induced EMF 523

POCKETLAB

SLOW MAGNETSLay the 1 m length of copper

tube on the lab table. Try to pullthe copper with a pair of neo-dymium magnets. Can you feelany force on the copper? Holdthe tube by one end so that ithangs straight down. Drop asmall steel marble through thetube. Use a stopwatch to mea-sure the time needed for themarble and then for the pair ofmagnetsto fall through the tube.Catch the magnetsin your hand.If they hit the table or floor theywill break. Devise a hypothesisthat would explain the strangebehavior and suggest a methodof testing your hypothesis.

FIGURE 25-8. Sensitive balancesuse eddy current damping to controloscillations of the balance beam (a).As the metal plate on the end of thebeam moves through the magneticfield, a current is generated in themetal. This current, in turn, producesa magnetic field that opposes themotion that caused it, and themotion of the beam is dampened (b).

>

Pivot .;...-~""""


an N-pole. In other words, the magnetic field lines must emerge fromthe right end of the coil. Use the second right-hand rule you learned inChapter 24. You will see that if Lenz's law is correct, the induced cur-rent must flow in a counterclockwise direction. Experiments haveshown that this is so. If the magnet is turned so an S-pole approachesthe coil, the induced current will be in a clockwise direction.

If a generator produces only a small current, then the opposing forceon the armature will be small, and the armature will be easy to turn. Ifthe generator produces a larger current, the force on the larger currentwill be larger, and the armature will be more difficult to turn. A gener-ator supplying a large current is producing a large amount of electricalenergy. The opposing force on the armature means that an armature ofmechanical energy must be supplied to the generator to produce theelectrical energy, consistent with the law of conservation of energy.

Lenz's law also applies to motors. When a current-carrying wiremoves in a magnetic field, an EMF is generated. This EMF, called theback-EMF, is in a direction that opposes the current flow. When a motoris first turned on, a large current flows because of the low resistance ofthe motor. As the motor begins to turn, the motion of the wires acrossthe magnetic field induces the back-EMF that opposes the current flow.Therefore, the net current flowing through the motor is reduced. If amechanical load is placed on the motor, slowing it down, the back-EMF is reduced and more current flows. If the load stops the motor,current flow can be so high that wires overheat.

The heavy current required when a motor is started can cause voltagedrops across the resistance of the wires that carry current to the motor.The voltage drop across the wires reduces the voltage across the motor.If a second device, such as a light bulb, is near the motor in a parallelcircuit with it, the voltage at the bulb will also drop when the motor isstarted. The bulb will dim. As the motor picks up speed, the voltagewill rise again and the bulb will brighten.

When the current to the motor is interrupted by turning off a switchin the circuit or by pulling the motor's plug from a wall outlet, thesudden change in the magnetic field generatesa back-EMF that can belarge enough to cause a spark across the switch or between the plugand the wall outlet.

A sensitive balance, Figure 25-8, such as the kind used in chemistrylaboratories, uses Lenz's law to stop its oscillation when an object isplaced on the pan. A piece of metal attached to the balance arm is

Wire coil Wire coil Wire coil

located between the poles of a horseshoe magnet. When the balancearm swings, the metal moves through the magnetic field. Currents,called eddy-currents, are generated in the metal. These currents pro-duce a magnetic field that acts to oppose the motion that caused thecurrents. Thus the metal piece is slowed down. The force opposes themotion of the metal in either direction, but does not act if the metal isstill. Thus it does not change the mass read by the balance. This effectis called "eddy-current damping."

The magnetic field caused by the induced EMF causes the ring in thechapter-opening photo to float. The coil is driven by AC, so the mag-netic field is constantly changing, and this change induces an EMF inthe ring. The resulting ring current produces a magnetic field that op-poses the change in the generating field, the ring is pushed away. Thelower ring has been sawed through. There is an EMF generated, but nocurrent flow, and hence no magnetic field is produced by the ring.

Wire coil

FIGURE 25-9. As the current in thecoil increases from left to right, theEMF generated by the current alsoincreases.

F . Y. I.

~ .Go With The Flow

Self-InductanceBack-EMF can be explained another way. As Faraday showed, EMF

is induced whenever a wire cuts magnetic field lines. Consider the coilof wire shown in Figure 25-9. The current through the wire increasesas we move from left to right. Current generates a magnetic field, shownby magnetic field lines. As the current and magnetic field increase, newlines are created. As the lines expand, they cut through the coil wires,generating an EMF to oppose the current changes. This induction ofEMF in a wire carrying changing current is called self-inductance. Thesize of the EMF is proportional to the rate at which field lines cutthrough the wires. The faster you try to change the current, the largerthe opposing EMF, and the slower the current change. If the currentreaches a steady value, the magnetic field is constant, and the EMF iszero. When the current is decreased, an EMF is generated that tends toprevent the reduction in magnetic field and current.

Because of self-inductance, work has to be done to increase the cur-rent flowing through the coil. Energy is stored in the magnetic field. Thisis similar to the way a charged capacitor stores energy in the electricfield between its plates.

Many modern automobileshave an electronic ignition sys-tem that varies the magneticfield. An aluminum armature with4, 6, or 8 protrusions (dependingon the number of spark plugs)spins. Each protrusion in turnpasses through the magneticfield, causing it to vary.


L I 400 V100V ~ __ --

- 5 turnslOA ~3 - 2.5A-------r-rl I 20 turns -'I'

1000W. Core .

POCKETLAB

SLOW MOTORMake a series circuit with a

miniature DC motor, an amme-ter, and a DC power supply.Hook up a voltmeter in parallelacross the motor. Adjust the set-ting on the power supply so thatthe motor is running at mediumspeed. Make a data table toshow the readings on the am-meter and voltmeter. Predictwhat will happen to the readingson the circuit when you hold theshaft and keep it from turning.Try it. Explain the results.

A transformer uses two coupled coils toincrease or decrease the voltage in anAC circuit.

FIGURE 25-10. For a transformer,the ratio of input voltage to outputvoltage depends upon the ratio ofthe number of turns on the primaryto the number of turns on thesecondary.

Primary

a Step-up transformer


TransformersInductance between coils is the basis for the operation of a transfor-

mer. A transformer is a device used to increase or decrease AC volt-ages. Transformers are widely used because they change voltages withessentially no loss of energy.

Self-inductance produces an EMF when current changes in a singlecoil. A transformer has two coils, electrically insulated from each other,but wound around the same iron core. One coil is called the primarycoil. The other coil is called the secondary coil. When the primary coilis connected to a source of AC voltage, the changing current creates avarying magnetic field. The varying magnetic field is carried through thecore to the secondary coil. In the secondary coil, the varying field in-duces a varying EMF. This effect is called mutual inductance.

The EMF induced in the secondary coil, called the secondary voltage,is proportional to the primary voltage. The secondary voltage also de-pends on the ratio of turns on the secondary to turns on the primary.

secondary voltage number of turns on secondaryprimary voltage number of turns on primary

I~; ~ z;1Ns

Vs = -VpNp

If the secondary voltage is larger than the primary voltage, the transfor-mer is called a step-up transformer. If the voltage out of the transformeris smaller than the voltage put in, then it is called a step-down transfor-mer.

In an ideal transformer, the electric power delivered to the secondarycircuit equals the power supplied to the primary. An ideal transformerdissipates no power itself. Since P = VI,

Vp Ip = v, Is.The current that flows in the primary depends on how much current

is required by the secondary circuit.

Is = Vp _ NpIp v, Ns

Secondary Primary Secondary

1000V200V

2A lOA

---1000W 2000W2000W

b Step-down transformer

A step-up transformer increases voltage; the current in the primary cir-cuit is greater than that in the secondary. In a step-down transformer,the current is greater in the secondary circuit than it is in the primary.

Example ProblemStep-Up Transformer

A certain step-up transformer has 2.00 x 102 turns on its primarycoil and 3.00 x 103 turns on its secondary coil. a. The primary coilis supplied with an alternating current at an effective voltage of90.0 V. What is the voltage in the secondary circuit? b. The currentflowing in the secondary circuit is 2.00 A. What current flows in theprimary circuit? c. What is the power in the primary circuit? in thesecondary circuit?

Given: Np = 2.00 x 102

Ns = 3.00 X 103

Vp = 90.0 VIs = 2.00 A

Unknowns: a. v, b. Ip c. PBasicequations:

v, Nsa.-=-v, Np

b. Vp/p = Vs/sSolution:

V Na. -E = -'2 or Vv, Ns= VpNs

Np(90.0 V)(3.00 x 103

) _ 32.00 X 102 - 1.35 x 10 V

b V I = V I or I = Vs/s = (1350 V)(2.00 A) -. p p ssp Vp 90.0 V - 30.0 A

c. Pp = Vp Ip = (90.0 V)(30.0 A) 2.70 x 103 Wr, = v, Is = (1350 V)(2.00 A) = 2.70 x 103 W

Practice ProblemsIn all problems, effective currents and voltages are indicated.9. A step-down transformer has 7500 turns on its primary and 125

turns on its secondary. The voltage across the primary is 7200 V.a. What voltage is across the secondary?b. The current in the secondary is 36 A. What current flows in the

primary?10. The secondary of a step-down transformer has 500 turns. The pri-

mary has 15 000 turns.a. The EMF of the primary is 3600 V. What is the EMF of the sec-

ondary?b. The current in the primary is 3.0 A. What current flows in the

secondary?

FIGURE25-11. If the input voltage isconnected to the coils on the left,with the larger number of turns, thetransformer functions as a step-down transformer. If the inputvoltage is connected at the right, it isa step-up transformer.

F.Y.I.The transformerswith the larg-

est power rating in the worldchanges765 kV to 345 kV. Theirpowerhandlingcapacity is 1 500OOOW.

25.2 Effectsof Changing Magnetic Fields: Induced EMF 527

FIGURE 25-12. Transformers areused to reduce voltages to consumerlevels at the points of use.

HISTORYCONNECTION

In the late 1800s, there wasmuch debate in the UnitedStates over the best way totransmit power from powerplants to consumers. The exist-ing plants transmitted direct cur-rent (DC), but DC had seriouslimitations. A key decision wasmade to use alternating current(AC) in the new hydroelectricpower plant at Niagara Falls.With the first successful trans-mission of AC to Buffalo, NewYork in 1896, the Niagara Fallsplant paved the way for the de-velopment of AC power plantsacross the country. It literallyprovided the spark for the rapidgrowth of United States citiesand industries that followed.


11. An ideal step-up transformer's primary circuit has 500 turns. Its sec-ondary circuit has 15 000 turns. The primary is connected to an ACgenerator having an EMF of 120 V.a. Calculate the EMF of the secondary.b. Find the current in the primary if the current in the secondary is

3.0 A.c. What power is drawn by the primary? What power is supplied

by the secondary?~ 12. A step-up transformer has 300 turns on its primary and 90 000

(9.000 X 104) turns on its secondary. The EMF of the generator to

which the primary is attached is 60.0 V.a. What is the EMF in the secondary?b. The current flowing in the secondary is 0.50 A. What current

flows in the primary?

As was discussed in Chapter 23, long-distance transmission of electricenergy is economical only if low currents and very high voltages areused. Step-up transformers are used at power sources to develop volt-ages as high as 480 000 V. The high voltage reduces the current flowrequired in the transmission lines, keeping /2R losses low. When theenergy reaches the consumer, step-down transformers provide appropri-ately low voltages for consumer use.

There are many other important uses of transformers. Television pic-ture tubes require up to 25 kV, developed by a transformer within theset. The spark or ignition coil in an automobile is a transformer designedto step up the 12 V from the battery to thousands of volts. The "points"interrupt the DC current from the battery to produce the changing mag-netic field needed to induce EMF in the secondary coil. Some arc weld-ers require currents of 104 A. Large step-down transformers are used toprovide these currents, which can heat metals to 3000°C or more.

CONCEPT REVIEW2.1 You hang a coil of wire with its ends joined so it can swing easily.

If you now plunge a magnet into the coil, the coil will swing.Which way will it swing with respect to the magnet and why?

2.2 If you unplug a running vacuum cleaner from the wall outlet, youare much more likely to see a spark than if you unplug a lightedlamp from the wall. Why?

2.3 Frequently, transformer windings that have only a few turns aremade of very thick (low-resistance) wire, while those with manyturns are made of thin wire. Why is this true?

2.4 Critical Thinking; Would permanent magnets make good transfor-mer cores? Explain.

Physics andsociety

WEAK ELECTROMAGNETICFIELDS-A HEALTHCONCERN?

Alternating currents, such asthose in household wiring,

produce electric and magneticfields. The very low AC fre-quency is call Extremely LowFrequency, or ELF. The manysources of ELF electric andmagnetic fields include powerlines, home wiring, electricclocks, electric blankets, televi-sions and computer terminals.Twenty years ago, most scien-tists would have claimed thatvery weak electric and magneticfields produced by ELFs couldnot affect living systems. Electricfields do exert forces on the ionsin cellular fluids, and changingmagnetic fields can induce suchelectric fields. Fields normallypresent in cells, however, aremuch larger than fields inducedby ELFs, and, unlike ultravioletradiation, ELFs can't breakchemical bonds.

Recently, however, experi-ments have shown that cells aresensitive to even very weak ELFfields. They can affect flow ofions across cell membranes,synthesis of DNA, and the re-sponse of cells to hormones.Abnormal development ofchick embryos has been seen.The experimental results, how-ever, are very complex. Someeffects of ELFs occur only atcertain frequencies or ampli-tudes. Others occur only if thefields are turned on or offabruptly. Finally, for most en-vironmental health hazards thelarger the exposure, or dose,the larger the effect. For ELFs,there is no clear way to defineor measure dose.

Some action has alreadybeen taken to reduce ELFfields.Electric blankets producingmuch lower magnetic fields arenow sold. Several computermanufacturers sell terminalsthat produce smaller fields.Without knowing how to mea-sure dose, however, it is notclear if such changes areenough to solve the problem.

Is there an association be-tween cancer and exposure to

ELF?Some studies found smallincreases in leukemia, breastcancer, and brain cancer. Stud-ies of users of electric blanketshave shown no effects on men,but increases in cancers andbrain tumors in children whosemothers slept under electricblankets while pregnant. Stud-ies to find the causes will takeyears and may not have conclu-sive results. In the meantime,what should be done?

DEVELOPING AVIEWPOINTRead articles about ELFs andcome to class ready to discussthe following questions.1. What do you think should bedone? Should no action betaken until there is conclusiveevidence of health hazards ofELFs?Or, is there enough rea-son for concern to take mea-sures to limit exposure to ELFs?2. Suppose a study finds manycancer cases among peoplewho live near power lines.Would this prove that ELFfieldsfrom power lines cause cancer?3. What steps could you take toreduce exposure to ELF?4. What could utility compa-nies do to reduce ELF fields?

SUGGESTED READINGSNoland, David. "Power Play."Discover 10 (12), 62-68, De-cember, 1989.Pool, Robert. "ElectromagneticFields: The Biological Evi-dence." Science 249, 1378-1381, September 21, 1990.Raloff, Janet. "EPA Suspects ELFFields Can Cause Cancer." Sci-ence News 137, 404-405,June 30, 1990.


CHAPTER 25 REVIEW····························------------~~=---~~~~~~~~~

SUMMARY25.1 Creating Electric Current from Changing

Magnetic Fields

· Michael Faraday and Joseph Henry discoveredthat if a wire moves through a magnetic field, anelectric current can be induced in the wire.

· The direction that current flows in a wire movingthrough a magnetic field depends upon the di-rection of the motion of the wire and the direc-tion of the magnetic field.

· The current produced depends upon the anglebetween the velocity of the wire and the mag-netic field. Maximum current occurs when thewire is moving at right angles to the field.

· Electromotive force, EMF, is the increased po-tential of charges in the moving wire. EMF ismeasured in volts.

· The EMF in a straight length of wire movingthrough a uniform magnetic field is the productof the magnetic induction, B, the length of thewire, L, and the component of the velocity of themoving wire, v, perpendicular to the field.

· An electric generator consists of a number ofwire loops placed in a magnetic field. Becauseeach side of the coil moves alternately up anddown through the field, the current alternates di-rection in the loops. The generator develops al-ternating voltage and current.

· A generator and a motor are similar devices. Agenerator converts mechanical energy to electricenergy; a motor converts electric energy to me-chanical energy.

25.2 Effects of Changing MagnetiC Fields:Induced EMF

· Lenz's law states: An induced current is alwaysproduced in a direction such that the magneticfield resulting from the induced current opposesthe change in the field that is causing the in-duced current.

· A transformer has two coils wound about thesame core. An AC current through the primarycoil induces an alternating EMF in the secondarycoil. The voltages in alternating current circuitsmay be increased or decreased by transformers.


KEY TERMSelectromagnetic inductionelectromotive forceelectric generatorLenz's lawself-inductancetransformer

primary coilsecondary coilmutual inductancestep-up transformerstep-down

transformer

REVIEWING CONCEPTS1. How are Oersted's and Faraday's results sim-

ilar? How are they different?2. Matt has a coil of wire and a bar magnet. De-

scribe how Matt could use them to generatean electric current.

3. What does EMF stand for? Why is the nameinaccurate?

4. What is the armature of an electric generator?5. Why is iron used in an armature?6. What is the difference between a generator

and a motor?7. List the major parts of an AC generator.8. Why is the effective value of an AC current

less than the maximum value?9. Water trapped behind Hoover Dam turns tur-

bines that rotate generators. List the forms ofenergy between the stored water and the finalelectricity produced.

10. State Lenz's law.11. What produces the back-EMF of an electric

motor?12. Why is there no spark when you close a

switch, putting current through an inductor,but there is a spark when you open theswitch?

13. Why is the self-inductance of a coil a majorfactor when the coil is in an AC circuit but aminor factor when the coil is in a DC circuit?

14. Explain why the word "change" appears sooften in this chapter.

15. Upon what does the ratio of the EMF in theprimary of a transformer to the EMF in thesecondary of the transformer depend?

APPLYING CONCEPTS1. What is the difference between the current

generated in a wire when the wire is movedup through a horizontal magnetic field and thecurrent generated when the wire is moveddown through the same field?

2. Substitute units to show that the unit of BLv isvolts.

3. If the strength of a magnetic field is fixed, inwhat three ways can you vary the size of theEMF you can generate?

4. When a wire is moved through a magneticfield, resistance of the closed circuit affectsa. current only. c. both.b. EMF only. d. neither.

5. As Logan slows his bike, what happens to theEMF produced by his bike's generator?

6. A hand-cranked generator is dropped, weak-ening the permanent magnet. How does thisaffect the speed at which the generator mustbe cranked to keep the same EMF?

7. The direction of AC voltage changes 120times each second. Does that mean a deviceconnected to an AC voltage alternately deliv-ers and accepts energy?

8. A wire segment is moved horizontally be-tween the poles of a magnet as shown in Fig-ure 25-13. What is the direction of the in-duced current?

FIGURE 25-13. Use with ApplyingConcept S.

9. M.artha makes an electromagnet by windingwire around a large nail. If she connects themagnet to a battery, is the current larger justafter she makes the connection or severaltenths of seconds after the connection ismade? Or is it always the same? Explain.

10. A wire segment is moving downward throughthe poles of a magnet as shown in Figure 25-14. What is the direction of the induced cur-rent?

11. Thomas Edison proposed distributing electri-cal energy using constant voltages (DC).George Westinghouse proposed using the

present AC system. What are the reasons theWestinghouse system was adopted?

12. A transformer is connected to a batterythrough a switch. The secondary circuit con-tains a light bulb. Which of these statementsbest describes when the lamp will be lighted?a. as long as the switch is closedb. only the moment the switch is closedc. only the moment the switch is openedExplain.

13. An inventor claims that a very efficient trans-former will step up power as well as voltage.Should we believe this? Explain.

14. Suppose a magnetic field is directed verticallydownward. You move a wire at constantspeed, first horizontally, then downward at45°, then directly down.a. Compare the induced EMF for the three

motions.b. Explain the variations in voltage.

15. The direction of Earth's magnetic field in thenorthern hemisphere is downward and to thenorth. If an east-west wire moves from northto south, in which direction does the currentflow?

16. Steve is moving a loop of copper wire downthrough a magnetic field B, as shown in Fig-ure 25-16.a. Will the induced current move to the right

or left in the wire segment in the diagram?b. As soon as the wire is moved in the field,

a current appears in it. Thus, the wire seg-ment is a current-carrying wire located in amagnetic field. A force must act on thewire. What will be the direction of the forceacting on the wire due to the induced cur-rent?

DownFIGURE 25-14. Use with ApplyingConcepts 10 and 16.

17. Steve, a physics instructor, drops a magnetthrough a copper pipe, Figure 25-15. Themagnet falls very slowly and the class con-cludes that there must be some force oppos-ing gravity.

Chapter 25 Review 531

a. What is the direction of the current inducedin the pipe by the falling magnet if theS-pole is toward the bottom?

b. The induced current produces a magneticfield. What is the direction of the field?

c. How does this field reduce the accelerationof the falling magnet?

FIGURE 25-15. Use with ApplyingConcepts 17.

18. Why is a generator more difficult to rotatewhen it is connected to a circuit and supplyingcurrent than it is when it is standing alone?

PROBLEMS

25.1 Creating Electric Current From ChangingMagnetic Fields

1. A wire segment, 31 m long, moves straight upthrough a 4.0 x 1O-2-T magnetic field at aspeed of 15.0 m/s. What EMF is induced inthe wire?

2. A wire, 20.0 m long, moves at 4.0 m/s perpen-dicularly through a 0.50-T magnetic field.What EMF is induced in the wire?

FIGURE 25-16. Use with Problem 2.

3. An airplane traveling at 950 km/h passes overa region where Earth's magnetic field is 4.5 x10-5 T and is nearly vertical. What voltage isinduced between the plane's wing tips, whichare 75 m apart?


4. A straight wire, 0.75 m long, moves upwardthrough a horizontal 0.30- T magnetic field ata speed of 16 m/s.a. What EMF is induced in the wire?b. The wire is a part of a circuit with a total

resistance of 11 D. What current flows inthe circuit?

~ 5. A 40-cm wire is moved perpendicularlythrough a magnetic field of 0.32 T with a ve-locity of 1.3 m/s. If this wire is connected intoa circuit of 10-D resistance, how much currentis flowing?

~ 6. Jennifer connects both ends of a copper wire,total resistance 0.10 D, to the terminals of agalvanometer. The galvanometer has a resis-tance of 875 D. Jennifer then moves a10.0-cm segment of the wire upward at1.0 m/s through a 2.0 x 1O-2-T magneticfield. What current will the galvanometer indi-cate?

~ 7. The direction of a 0.045-T magnetic field is60° above the horizontal. A wire, 2.5 m long,moves horizontally at 2.4 m/s.a. What is the vertical component of the mag-

netic field?b. What EMF is induced in the wire?

8. An EMF of 0.0020 V is induced in a 10-cmwire when it is moving perpendicularly acrossa uniform magnetic field at a speed of4.0 m/s. What is the size of the magneticfield?

9. At what speed would a 0.2-m length of wirehave to move across a 2.5- T magnetic field toinduce an EMF of 10 V?

10. An AC generator develops a maximum EMFof 565 V. What effective EMF does the gen-erator deliver to an external circuit?

11. An AC generator develops a maximum volt-age of 150 V. It delivers a maximum currentof 30.0 A to an external circuit.a. What is the effective voltage of the gener-

ator?b. What effective current does it deliver to the

external circuit?c. What is the effective power dissipated in

the circuit?12. An electric stove is connected to an AC

source with effective voltage of 240 V.a. Find the maximum voltage across one of

the stove's elements when it is operating?

b. The resistance of the operating element is11 n. What effective current flows throughit?

~ 13. A generator at Hoover Dam can supply375 MW (375 x 106 W) of electrical power.Assume that the turbine and generator are85% efficient.a. Find the rate which falling water must sup-

ply energy to the turbine.b. The energy of the water comes from a

change in potential energy, mgh. What isthe needed change in potential energyeach second?

c. If the water falls 22 m, what is the mass ofthe water that must pass through the tur-bine each second to supply this power?

25.2 Effects of Changing Magnetic Fields:Induced EMF

14. The primary of a transformer has 150 turns. Itis connected to a 120-V source. Calculate thenumber of turns on the secondary needed tosupply these voltages.a. 625 V b. 35 V c. 6.0 V

15. A step-up transformer has 80 turns on its pri-mary. It has 1200 turns on its secondary. Theprimary is supplied with an alternating currentat 120 V.a. What voltage is across the secondary?b. The current in the secondary is 2.0 A.

What current flows in the primary circuit?c. What is the power input and output of the

transformer?16. A portable computer requires an effective

voltage of 9.0 volts from the 120 -V line.a. If the primary of the transformer has 475

turns, how many does the secondaryhave?

b. A 125-mA current flows through the com-puter. What current flows through thetransformer's primary?

17. In a hydroelectric plant, electricity is gener-ated at 1200 V. It is transmitted at 240 000 V.a. What is the ratio of the turns on the pri-

mary to the turns on the secondary of atransformer connected to one of the gen-erators?

b. One of the plant generators can deliver40.0 A to the primary of its transformer.What current is flowing in the secondary?

18. A hair dryer uses 10 A at 120 V. It is usedwith a transformer in England, where the linevoltage is 240 V.a. What should be the ratio of the turns of the

transformer?b. What current will it draw from the 240-V

line?19. A step-up transformer is connected to a gen-

erator that is delivering 125 V and 95 A. Theratio of the turns on the secondary to theturns on the primary is 1000 to 1.a. What voltage is across the secondary?b. What current flows in the secondary?

~ 20. A 150-W transformer has an input voltage of9.0 V and an output current of 5.0 A.a. Is this a step-up or step-down transformer?b. What is the ratio of output voltage to input

voltage?~ 21. A transformer has input voltage and current of

12 V and 3.0 A respectively, and an outputcurrent of 0.75 A. If there are 1200 turns onthe secondary side of the transformer, howmany turns are on the primary side?

~ 22. Scott connects a transformer to a 24-Vsource and measures 8.0 V at the secondary.If the primary and secondary were reversed,what would the new output voltage be?

USING LAB SKILLS1. After doinq the Pocket Lab on page 518, pre-

dict what will happen if the magnet is kept sta-tionary and the coil moves. Try it. What hap-pens if the coil and magnet move together? Tryit.

THINKING PHYSIC-LY1. A bike's headlamp is powered by a generator

that rubs against a wheel. Why is it harder topedal when the generator is lighting the lamp?

2. Suppose an "anti-Lenz's law" existed thatmeant a force was exerted to increase thechange in magnetic field. Thus, when moreelectrical energy was demanded from a gener-ator, the force needed to turn it would be re-duced. What conservation law would be vio-lated by this new "law"? Explain.

Chapter 25 Review 533

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