2 MagnetsAbout three thousand years ago, the Greeks discovered rocks which would attract iron or similar rocks (a mineral ore we call magnetite). They were found in Magnesia, an area in Asia Minor
3 LodestonesThe Chinese later used these naturally occurring magnets, called lodestones, for ocean navigation.The first recorded description of a compass was in the Chinese Book Dream Pool Essays (1086) by Shen Kuo in the Song Dynasty, about 100 years earlier than its first record in Europe by Alexander Neekam in 1190.Source:
4 MagnetsWilliam Gilbert (a physician to Queen Elizabeth I) made many discoveries about magnets – including that the Earth itself is a giant magnetic sphere!He also discovered that he could make his own magnets, and coined the term “magnetic pole”.
5 Magnets Magnetism is caused by the MagnetsMagnetism is caused by themovement of electrons within an atom.Magnets are surrounded by magnetic fieldsElectrons produce magnetic fields because theyorbit the nucleusspin on their own axis.
6 !!! Chemistry Flashback !!!Electrons pair up two per orbital – one spins clockwise, the other counter clockwise.Direction of spin determines the “pole” of the electron.Diamagnetic materials – have paired electrons where the fields cancel out because all the electrons are in pairs and have opposite spins.Material will be repelled by a magnetic field (weak effect).(1/1,000,000 weaker than iron).The electric fields required to levitatethese materials are extremely large.Source:http://www.hfml.sci.kun.nl/froglev.htmlMagnetic Frog
7 Paramagnetic materials - have unpaired electrons. !!! Chemistry Flashback !!!Paramagnetic materials - have unpaired electrons.Iron (Fe) electron configuration 4 s2 3 d6In d cloud electrons occupy 5 orbitals.Auf bau principle – electrons must enter an empty orbital before they pair up.The magnetic fields of the unpaired electrons combine to make each Fe atom a tiny magnet.
8 But not all iron is magnetic…right? Why not? The unpaired electrons give areas in these elements small magnetic fields.When the individual areas or domains all line up, the piece of metal has a BIG magnetic field
9 Magnetic Materials Ferromagnetic – an element which is Magnetic MaterialsFerromagnetic – an element which isattracted to magnets and can be made into temporary magnets.Iron, nickel and cobalt.All are paramagnetic elements
10 http://www. physics. carleton Magnetic MaterialsHard magnetic materials - require a strong external magnetic field to orient their domains.Once oriented the domains stay aligned.Permanent magnetsAlnico, an alloy of aluminum, nickel, cobalt,iron and copper common permanent magnet.Heating or hitting can move the domains out of alignmentSoft magnetic materials (nails & paper clips) are easily magnetized but demagnetized when the external field is removed.Domains become random again whenthe magnet is removed.Temporary magnetism
11 Magnetic PolesMagnets have polarity (different parts of a magnet experience different forces)Poles of a magnet are called north and southOpposite poles attract, like poles repel.Magnetic poles always come in pairs (northand south) not possible to have only one poleMagnetic dipole.Breaking a magnet in half forms two new magnets.
12 Cutnell & Johnson, Wiley Publishing, Physics 5th Ed. Magnetic FieldThe space around a magnet has an invisible magnetic field that exerts magnetic forcesThis field is represented by drawing magnetic field lines or lines of magnetic fluxGreater magnetic flux density (stronger field) is shown with more flux linescloser lines stronger the magnetic field.the flux density is the greatest at the POLES!arrows show the direction (out of the north pole and into the south pole)pass through the magnet to form loops.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Earth’s Field
13 Drawing Magnetic Fields Compass MethodIf we could scatter tiny compass needles over a piece of paper and bring a bar magnet underneath them, the needles would line up in the bar magnet’s magnetic fieldIron Filing MethodSprinkling iron files near a magnet will cause the filings to line up along the magnetic flux linesCutnell & Johnson, Wiley Publishing, Physics 5th Ed.
14 Magnetic Fields Bar Magnet Two Like Magnets Two Unlike Magnets
19 Earth’s Magnetism The earth has a magnetic field! Earth’s MagnetismThe earth has a magnetic field!Scientists theorize it is caused by electric currents circulating in the liquid outer core.The earth has both a north and a south magnetic pole, like a magnet.Notice the earth’s magnetic field lines!Same shape as a bar magnetIs the Earth’s North Pole a Northor a South magnetic pole?Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
20 CompassIf suspended, a magnet’s north pole will point toward the earth’s geographic north.A compass is a magnetic needle on a pivot.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
21 North Pole FallacyIs the Earth’s North Pole a North or South magnetic pole?You already know that like poles_______and that unlike poles _______.But think about this…The north end of a magnet is attracted to the south end of a second magnet.The north end of a compass needle points to the geographic NORTH pole of the earth….So…the earth’s geographic NORTH pole must be a magnetic SOUTH pole.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
22 Earth’s Magnetic Field Since the earth is tilted, the magnetic poles of the earth don’t line up exactly with the geographic poles.This discrepancy is called magnetic declination.Angle of declinationCopywrited by Holt, Rinehart, & Winston
23 Importance of Earth’s Magnetic Field NavigationAnimal migrationNavigational systemsProtects the earth from solar windsCharged particles from the sunAurora Borealis – Northern LightAurora Australis – Southern LightsEarth’s Core
24 Earth’s Magnetic Field Earth’s Magnetic FieldOver the past 150 years, the main component of the Earth's magnetic field has decayed by nearly 10%, a rate ten times faster than expectedThis is centered around an area in the south Atlantic Ocean that has a field 35% weaker than expected.source:Earth’s MagneticField
25 Are Magnetism and Electricity Connected? Until 1820 everyone thought electricity and magnetism were completely separate.Hans Oersted discovered that a compass needle is deflected by an electric current.Electricity and Magnetism are just different aspects of the same thing!Oersted – Dutch teacher. Demonstrating that magnetism and electricity not connected. Student after class switched direction of the wire.
26 Magnetic Field Generation Moving charges create magnetic fields.The magnetic field of a current through a straight wire makes circles perpendicular to the current.
27 Magnetic Field Generation Copywrited by Holt, Rinehart, & WinstonCutnell & Johnson, Wiley Publishing, Physics 5th Ed.
28 Right Hand Rule (Grip Rule) Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Copywrited by Holt, Rinehart, & WinstonTo calculate the direction of the magnetic field produced by a current carrying wire:Point your right thumb in the direction of the conventional current flow.Your fingers curl in the direction of the magnetic field.Current Convention:
29 RHR PracticeWhat direction would the magnetic field be around a current coming out of the screen?A. ClockwiseB. CounterclockwiseC. Into the screenD. Out of the screen
30 Checking Understanding The magnetic field of a straight, current- carrying wire isparallel to the wire.perpendicular to the wire.around the wire.inside the wire.zero.Answer: CSlide 24-4
31 Checking Understanding Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P?Answer: DSlide 24-19
32 Checking Understanding Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P?Answer: DSlide 24-20
33 Magnetic Force A charge moving in a magnetic field feels a force. The force on the charge is a “sideways” force - perpendicular to the field line and to the charge’s velocity.
34 Magnetic Force Charge not moving? Charge moving with field line? Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Magnetic ForceCharge not moving?Charge moving with field line?The charge must move ACROSS the field lines to feel a forceNO FORCE
35 Magnetic Force Experiments show that: F ~ the current, I Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Magnetic ForceExperiments show that:F ~ the current, IF ~ the length of conductor in the field,F = (a constant) I xthe constant is called the magnetic flux density (B) when current flows at 90° to the field.B is a measure of the strength of the magnetic fieldB units are NA-1m-1 or Teslas (T)
36 Magnetic Force Flux density is the force per unit Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Magnetic ForceFlux density is the force per unitlength acting on a conductorplaced at 90° to the field.If the conductor is placed at an angle θ to the field, then the force is given by:
38 Magnetic Force on a Wire Checking UnderstandingMagnetic Force on a WireA horizontal wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?1) left2) right3) zero4) into the page5) out of the pageIB
39 Magnetic Force on a Wire Checking UnderstandingMagnetic Force on a Wire1) left2) right3) zero4) into the page5) out of the pageA horizontal wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?BI
40 Magnetic Force on a Charge On average, the charges must be moving with speed v = /t.Therefore,If the direction of the velocity is not at 90° to the flux lines, we use the component of the velocity which acts at 90° to the field.and the direction of the force is at 90° (perpendicular) to both the velocity and the magnetic field.Consider a conductor of length, having n free electrons per unit volume. A current, I, is flowing through it.Recall, andThis is the sum of the forces acting on all the free charges as they move through the piece of conductor.Therefore, force per charge, F, is given byCharged Particle in aMagnetic Field
41 Right Hand Rule (Slap Rule) The direction of the magnetic field can be determined using the right hand rule.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Force direction calculationThumb direction of (+) chargePoint fingers in the directionof the magnetic fieldThe palm indicates the direction of forceAlternative methodIs there a left hand rule?Yes, when a (–) charge is involvedCopywrited by Holt, Rinehart, & Winston
42 What direction?A positive charge moving with a constant velocity enters a uniform magnetic field pointing out of the paper. What way will the charge move?Continue straightCurve upwardCurve downwardGo into the paperWhat would have happened if it was a negative charge moving into a magnetic field pointing into the paper?Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
43 Checking Understanding Magnetic ForceA positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?1) out of the page2) into the page3) downward4) to the right5) to the leftx x x x x xvq
44 Checking Understanding Magnetic ForceA positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?1) out of the page2) into the page3) downward4) upward5) to the leftx x x x x xvq
45 Checking Understanding Magnetic ForceA positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?1) out of the page2) into the page3) zero4) to the right5) to the left® ® ® ® ®vq
46 Charge Paths in a Magnetic Field Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Three possible paths followed by a charged particle moving through a uniform magnetic field:if q = zero the path is a straight lineif q = 90° the path is circularif 0 < q < 90° the path is a helix.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
47 Flux Density due to Current Flowing in a Long, Straight Wire The flux density, B, at point p is directed out of the plane of the diagram.The magnitude of B depends onThe current, IThe perpendicular distance, rThe medium in the space around the wireAssumption: if r is small compared with the length of wire, then B does not depend on the length of the wire.Therefore,where µ is the permeability of the mediumµo represents air or a vacuum and has units of NA-2 or Henrys per meter (Hm-1).
48 Force per Unit Length between Two Long Parallel Conductors Carrying Current Flux density, B, near conductor 2 due to I1 isSo, the force (F=I B) which acts on length of conductor 2 is given byTherefore, the force per unit length is given byAlso, by Newton’s third law we can say that there is an equal but opposite force acting on conductor 1.Now, if F/ .= 2 × 10-7 Nm-1 and r = 1m and I1 = I2, then the current in each conductor is 1 Amp.Derivation source:
49 Formal Amp DefinitionOne Amp is that current which, when flowing in each of two straight, parallel, infinitely long wires, separated by 1m, in a vacuum, produces a force per unit of 2 ×10-7Nm-1.
50 Attraction or Repulsion What will happen if two long parallel wires are carrying currents, I1 and I2, flowing in the same direction are placed next to each other?They attract each otherThey repel each otherNo interactionCopywrited by Holt, Rinehart, & WinstonCopywrited by Holt, Rinehart, & WinstonCutnell & Johnson, Wiley Publishing, Physics 5th Ed.
51 Attraction or Repulsion What will happen if two long parallel wires are carrying currents, I1 and I2, flowing in the opposite direction are placed next to each other?They attract each otherThey repel each otherNo interactionCopywrited by Holt, Rinehart, & WinstonCutnell & Johnson, Wiley Publishing, Physics 5th Ed.
52 Flux Density inside a Long Coil (Solenoid) Current flowing through a conductor produces a magnetic field.For a long straight wire, then the field is distributed over a large region of space.If the wire is used to make a coil, the magnetic field is concentrated into a smaller space and is therefore stronger.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
53 Wire LoopBending a current carrying wire into a circle gives a magnetic field like this:Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
54 SolenoidCutnell & Johnson, Wiley Publishing, Physics 5th Ed.Winding many turns makes a solenoid coil with a magnetic field like a bar magnet.
56 Checking Understanding Current LoopWhat is the direction of the magnetic field at the center (point P) of the square loop of current?1) left2) right3) zero4) into the page5) out of the pagePI
57 Magnetic Strength of a Coil Theory suggests that the flux density, Bc, at the center of a long coil, isWhere N = # of turns= lengthMeasurements shows that if the solenoid’s length ≥ 10 times its diameter, the flux density inside is uniform over most of its length.The graph shows the variation of B along the axis of a long solenoid.
58 ElectromagnetA coil of wire with a current passing through it creates a magnetic field just like a bar magnet.Can be turned on/off or reversed by controlling the current flow.
59 Electromagnet How can you strengthen an electromagnet? Putting an iron core in the center of the coil strengthens the magnetic field.Adding more coils makes the magnetic field stronger.Increasing the current through the wire strengthens the magnetic field.
60 Simple Electric Motors A coil, with current flowing through it, placed in a magnetic field, can experience a torque.When a current-carrying loop is placed in a magnetic field, the loop tends to rotate such that its normal becomes alignedwith the magnetic field.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
61 Simple Electric Motors Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Simple Electric MotorsTorque (τ):magnitude of the torque ~ Idepends on the angle, θ, between the field and the coil.Torque ~ sin θτ =F x d for a loop of wired = w/2 sinΦwhere w = width of the loopΦ is the angle between the normal to the plane of the loop and the direction of the magnetic field.Net torque = τ = ILB(1/2 w sin Φ) + ILB(1/2 w sin Φ) = IAB sin ΦWire is wrapped to form a loop of N loopst = NIABsinf
62 Simple Electric Motors A simple d.c. electric motor consists of a coil of wire placed in a magnetic field.When current flows through the coil, a torque is produced.The brushes and commutator conduct the current from the supply to the coil.Each of the carbon brushes makes contact with one half of the commutator.The commutator rotates with the coil.This arrangement ensures that the torque produces a constant sense of rotation.Copywrited by Holt, Rinehart, & Winston
63 Simple Electric Motors In the diagram below, the force on side a – b of the coil will be directed downwards so the rotation is counter-clockwise (viewed from the front).When the coil has rotated 180°, side d – c is on the left but, as the commutator has also rotated, the torque is still in the same sense.DC Motors
69 Magnetic FluxIf B is at 90° to the area, A, then the total magnetic flux, Φ "passing through" A is defined to beΦ greek letter phiThe units of flux are Tm² 1 Tm² = 1 WeberIf B is not at 90° to the area: the component of B which acts at 90° to A is B cos α.So, the flux passing through the area isf = AB
70 Flux Linkagea flux, Φ, "passes through" a coil of N turns then the coil is said to be linked to the flux so we define the quantity "flux linkage" asN = # of turns,B = magnetic field strengthA = cross sectional area of coilθ = angle to normal of coilAssociated with a multiple turned coil or solenoidFlux linkage = # of turns x magnetic fluxΦ = NBA cosθ
71 Can a Magnetic Field produce a Current? For 12 years after Oersted’s discovery that electric current creates a magnetic field, scientists looked for a way for magnetic fields to create a current.In 1832, Michael Faraday made a suggestion: “Move the Magnet!”Doing so “induced” an electric current!!!! The result of Faraday’s work became known as electromagnetic induction.
72 Electromagnetic Induction Thrusting a magnet into a loopof wire induces current.Holding the magnet still does not!It doesn’t matter whether the magnetic field moves or the wire moves. It works either way!Faraday described this by saying that electromotive forces are generated in the wire whenever field lines cut across the wire.When the magnet is thrust into the loop,its field lines cut across the wiregenerating EMF that produces current.Ditto when the loop is moved over themagnet.
73 EMF Clarification Warning: The term EMF can be misleading!!!!! The electromotive forces that are generated are not really “forces”.They are actually increases in electrical potential (voltage) and are therefore measured in VOLTS!IB defines EMF – work done per unit chargeCircuit EMF –in moving charge from one terminal of the battery to the other.Motional EMF – induced as a result of the motion of a conductor in the magnetic fieldBut WHY??!?!?!?!
74 EMF GenerationCopywrited by Holt, Rinehart, & WinstonNo relative motion between the conductor and the magnetic field no emf.
75 EMF Induced in a Conductor Moving through a Magnetic Field A conductor moves a distance, Δs, at 90° to a magnetic field of flux density B, in time Δ t.The free electrons in the conductor will experience a force causing them to move through the conductor.Suppose that a total charge Δ Q moves past any point in the conductor in time Δ t.The work done by the force F is given byThis work is equal to the energy given to the charge Δ Q.Therefore the work done per unit charge isand, work done per unit charge is the induced emf .F Δ s/ Δ QW = FDs
76 EMF Induced in a Conductor Moving through a Magnetic Field If the conductor moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current, I, induced in it.Therefore,So,Derivation source:
78 EMF generationIn the case of TWO wire loops, when current is first turned on in one loop, magnetic field lines build up, cutting across the other loop – producing EMF.When the current is switched off, the field lines collapse, again cutting across the loop.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Electrical Induction
79 Faraday’s Law of Electro-Magnetic Induction The induced emf is directly proportional to the rate of change of magnetic flux linking the conductor.and, if the conductor is a coil having N turns, we have:In the case of a straight conductor moving at 90° to a uniform field, we foundIf the conductor moves a distance Δs in time Δt, then the speed, v, is given by v = Δ s/ Δ t.So, in this case, the two statements are equivalent.Derivation source:
80 GeneratorsCutnell & Johnson, Wiley Publishing, Physics 5th Ed.Generator action requires a conductor, a magnetic field, and relative motion.Generators and motors are almost identical in construction.Both consist of wire loops wrapped around an iron form - the armature - placed in a strong magnetic field.Convert energy in opposite directions.Electric generators convert mechanical energy to electric energy.Electric motors convert electrical energy into mechanical energy.
81 Generator vs MotorIn a generator, as the armature turns, current is induced in the wire. This current cuts across the magnetic field lines and produces an EMF (voltage).In a motor, a voltage is placed across an armature coil that is in a magnetic field. The voltage causes current to flow in the coil creating a magnetic force which causes the armature to turns (torque)Copywrited by Holt, Rinehart, & Winston
83 The Laws of Electro-Magnetic Induction No current No effectShort circuitedcurrent flows due to induced emfcoil is repelled from the magnetSimilarly, if the magnet is moved the opposite way, the coil "tries" to follow it.
84 Lenz’s LawWhen an induced current flows in a wire, it creates a magnetic field. This magnetic field must resist the magnet’s motion, so work is done in moving it.When the north pole of a magnet is thrust into the loop, the current must flow in a direction to make a north pole repelling the magnet.Copywrited by Holt, Rinehart, & Winston
85 Lenz’s LawInduced current flows in a direction to oppose the change that produced it.law of conservation of energy electro-magnetic induction.
88 Eddy Currents in Motors As DC motor begins to rotate, an emf (back emf) will be induced in the loop due to the changing magnetic flux in the loop.Lenz’s law states that this emf will oppose the change in the flux that created it.The induced current will flow in the loop in the opposite direction to the direction of the current fed by the battery.The current in the loop when it is rotating will be lower than initially before the loop has started to rotate.Lights dimming when the refrigerator motor turns on
89 AC GenerationCopywrited by Holt, Rinehart, & WinstonCopywrited by Holt, Rinehart, & WinstonAC Generator – coil of wire is made to rotate in a magnetic field causing the magnetic flux in the wire to change with its rotation producing an alternating EMF.
90 AC Generation Flux Linkage = Copywrited by Holt, Rinehart, & WinstonIf the coil turns at a constant angular speed,Therefore,Faraday’s LawSubstituting,Flux Linkage =where N is number of coils, B is magnetic field, and θ is the angle between the magnetic field and the normal of the coil.
91 AC Generation where represents the slope of a graph of cos (ωt) against t.Slope is (calculus)EMF becomes(max EMF)Note: EMF is zero when the flux is a max or min and flux is zero when the EMF is a max or min----- Meeting Notes (9/15/15 14:16) -----
92 AC GenerationHow does the speed of the coil rotation in a generator effect the output power?P=ε IIf the speed is doubled what will be the change in output power?
93 AC GenerationIf an identical light was burning with the same intensity in the DC and AC circuits shown below, would the average current be the same?
94 AC Generation From Ohm’s Law: So, or But, average IAC is zero Average or mean ACPower must be thesame as the DC Powerfor the light to have thesame intensity.Physics for the IB Diploma 5th Edition (Tsokos) 2008
95 Root Mean Square Since P = I2R, then Where, or This is called the root mean square (rms)The r.m.s. value of an a.c. supply is analogous to the steady d.c.value which would convert heat at the same rate in a given resistance.
96 AC NotationCopywrited by Holt, Rinehart, & Winston
98 The Ideal Transformer Assumptions of an ideal transformer: the coils have zero resistanceall the magnetic flux, Φ, produced by the primary current, Ip, is linked with the secondary coilWhen Ip changes, Φ changes.From Faraday’s law, we have:Combining these two statements givesCopywrited by Holt, Rinehart, & WinstonTransformers
99 TransformerPower in both the primary and secondary circuit of the transformer is the same.Transformer EquationsP = primary quantitiesS = secondary quantitiesChallenges:Eddy currents are produced in the iron core because the electrons in the iron move due to the magnetic field.These cause the material to heat up.By laminating the core into thin sandwiches of iron these are eliminated.
100 Transformer ExampleA TV contains a transformer with primary windings of 200 turns and a secondary winding of 50 turns. If 120 V is supplied to the primary winding what is the secondary output voltage?What is the secondary output current?TransformerExamplesCutnell & Johnson, Wiley Publishing, Physics 5th Ed.
102 AC vs DC Power – Current Wars DC – Thomas EdisonAC – Nikola TeslaInvented the light bulbOwned the patents for DC Power DistributionProvided DC Power to 59 customers in NYC, September 4, 1882Company became General ElectricInvented the AC Motor, radio (Marconi given credit), radio control.Owned the patents for AC Power DistributionWorked for Edison then went to work for George WestinghouseWon contract to provide electricity to Chicago World Fair in 1893
103 What if Edison had won the current wars? If soHomes powered with DC Power.Power plants needed to be within a few miles of home.Currently, power plants are far from homes. Why?Long power linesFeasibility?power planthomeappliancelong transmission linelooks like:RloadRwireX
104 DC Power Distribution – Feasibility? AC Electricity02/07/2008DC Power Distribution – Feasibility?120 WattLight bulb12 VoltConnection BoxPower Planton Colorado River150 milesEstimate resistance of power lines:~ Ohms per meterlength 200 kmCalculate current required by a single bulb120 W light bulb12 Volt connection box usingCalculate power lost in transmission lineRecall, Plost = I2R0.001 W/m 2105 m = 20 OhmsP = VI so I = P/VI = 120 W/12 V = 10 APlost = I2R = (10A)2 x 20Ω = 2000 WLecture 7
105 DC Power Distribution – Feasibility? AC Electricity02/07/2008DC Power Distribution – Feasibility?150 miles120 WattLight bulbPower Planton Colorado River12 VoltConnection BoxRwireCalculate Total Power RequiredTotal Power = Power Lost + Power RequiredCalculate the efficiency (e)? e = Pout/PinWhat could we change in order to do better?RloadTotal Power = 2 (2000) = 4120 WXRwiree = Po/Pi= 120 W/4120 W = 0.3%Lecture 7
106 AC Electricity02/07/2008The TradeoffMajor Problem: high current through the (fixed resistance) transmission linesNeed less currentPower Loss is I2R I2 increases exponentially with currentAppliances require minimum amount of powerP = VI so less current demands higher voltageSolution: High Voltage transmissionRepeat the power calculation for a 120 W light bulb with 12,000 Volts or 12kV delivered to the house.Lecture 7
107 DC Power Distribution – Feasibility? AC Electricity02/07/2008DC Power Distribution – Feasibility?150 miles120 WattLight bulbPower Planton Colorado River12,000 VoltConnection BoxCalculateCurrentPower Lost in Transmission LineTotal Power RequiredEfficiency (e)? e = Pout/PinMore Power Delivered More Profit!I = P/V = I = 120 W/12,000 V = 0.01 APlost = I2R = (0.01A)2 x 20Ω = WTotal Power = 2 (0.002W) + 120W = We = Po/Pi= 120 W/ W = %Lecture 7
108 AC Electricity02/07/2008DANGER High Voltage!High voltage in each household is a recipe for disastersparks every time you plug something inrisk of firenot cat or kid friendlyNeed a way to step-up/step-down voltageTransformernot possible with DC, Why?Works only with AC (Tesla wins)Lecture 7
109 A way to provide high efficiency, safe low voltage: AC Electricity02/07/2008Power TransmissionA way to provide high efficiency, safe low voltage:step-up to 500,000 Vstep-down,back to 5,000 Vstep-down to 120 V~5,000 VoltsHigh Voltage Transmission LinesLow Voltage to ConsumersLecture 7
111 How electricity gets to your home…. Power TransmissionHow electricity gets to your home….Power stationStep-up transformerNational GridStep-down transformerHomes, businesses and factories etc
112 Power Transmission Power Generated at Power Plant Power stepped up in voltage and sent to high voltage transmission linesPower stepped down in voltage through transformers prior to sending it to your home.Example: 480kW PlantTransmission Lines transmit electricity at 240kVWhat is the current in the line?If the resistance of the cable is 100 Ω what is the power lost in the transmission?What would be the power lost if the lines transmitted power at 120kV?Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
113 120 VAC is a root-mean-square number: peak-to-peak is 340 Volts! AC Electricity04/25/2006= 170 Volts= -170 VoltsSpring 2006UCSD: Physics 8; 2006120 VAC is a root-mean-square number: peak-to-peak is 340 Volts!Lecture 8
114 Power TransmissionMost U.S. voltages are 120 V. It used to be 110-V because early light bulbs couldn’t handle higher voltages.Most other countries have switched to 220 V, which transmits power more efficiently.
115 AC Receptacle Receptacles have three holes each AC Electricity04/25/2006AC ReceptacleReceptacles have three holes eachLower (rounded) hole is earth groundconnected to pipes.green wireLarger slot is “neutral”for current “return”never far from groundwhite wireif wired correctlySmaller slot is “hot”swings to +170 and 170black wiredangerous oneCutnell & Johnson, Wiley Publishing, Physics 5th Ed.Lecture 8
116 AC DC - Rectification Half-wave Rectification A single diode convert AC into a pulsating DCDiodeElectrical gateAllows only positive current through (forward biased)Blocks negative current (reverse biased)Output limitationElectrical energy in AC negative cycle not used.
117 AC DC - Rectification Full-wave Rectification A diode bridge convertsAC into a pulsating DC signal using all the energy of the AC signal
118 AC DC - Rectification Full-wave Rectification Positive half cycle, current flows A-CNegative half cycle, current flows B-D
119 AC DC - Rectification Full-wave Rectification Drawing the circuit Diodes on parallel sides point in the same directionAC signal is fed to the point where opposite ends of two diodes join.Positive output comes from the junction of the negative side of two diodesNegative output comes from the junction of the negative side of two diodes
120 AC DC – Smoothing Circuit Turns the pulsating output of a rectifying circuit into a more steady DC output.Uses a capacitor in parallel with the output of rectifying circuit.Smoothed half-wave Rectification
121 AC DC – Smoothing Circuit Turns the pulsating output of a rectifying circuit into a more steady DC output.Smoothed full-wave Rectification
122 AC DC – Smoothing Circuit Output ripple – slight fluctuationCapacitorShort term energy storageConstantly charging and dischargingSlow discharge requires a large capacitance C so the time constantτ is significantly largeτ=RC where R = resistance
123 Wheatstone Bridge Arrangement used to estimate an unknown resistor Used primarily with DC circuitsFour resistorsTwo fixed resistorsOne variable resistorOne unknown resistor (RX)Variable resistor always paired with unknown resistor.Galvanometer (Ammeter) bridges pair of resistorsAdjust variable resistor so galvanometerreads 0 A
124 Wheatstone BridgeWhen galvanometer reads 0 A, no potential difference across BD.Therefore, the potential difference across R1 and R3 are identical and the same is true for R2 and RX.V1=I1R1=I3R3 and V2=I1R2=I3RXSo,
125 Wien BridgeModification of Wheatstone bridge allow identification of resistance and capacitance values for an unknown componentUsed with AC power supplyCurrent in center arm adjusted to zero.Adjusting R2, C2 and the frequency of the supply to minimize current.Unknown values of RX and CX canbe calculated.
126 Sources:Homer, D. and Bowen-Jones, M.,(2014) Physics: Course Companion, Oxford University PressTsokos, K.A.,(2014) Physics for the IB Diploma,6th edition, Cambridge University PressUniversity of California at San Diego (2008). AC Electricity: Why AC Distribution? Retrieved from
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