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UT Arlington PHYS 1444 - Lecture Notes

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PHYS 1444 – Section 003 Lecture #19AnnouncementsElectric GeneratorsHow does an Electric Generator work?Slide 5Example 29 – 5A DC GeneratorEddy Currents (read more in 29-5)TransformerHow does a transformer work?Transformer EquationExample 29 – 8Example 29 – 9: Power TransmissionElectric Field due to Magnetic Flux ChangeGeneralized Form of Faraday’s LawInductanceMutual InductanceSlide 18Example 30 – 1Monday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu1PHYS 1444 – Section 003Lecture #19Monday, Nov. 14, 2005Dr. Jaehoon Yu•Electric Generators•DC Generator•Eddy Currents•Transformer•Mutual InductanceToday’s homework is homework #10, due noon, next Tuesday!!Monday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu2Announcements•Instructor evaluation today•A colloquium at 4pm this Wednesday–Dr. P. Nordlander from Rice University–About nano material and magnetic field they generate–Extra credit opportunityMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu3Electric Generators•What does a generator do?–Transforms mechanical energy into the electrical energy–What does this look like?•An inverse of an electric motor which transforms electrical energy to mechanical energy–An electric generator is also called a dynamo•Whose law does the generator based on?–Faraday’s law of inductionMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu4How does an Electric Generator work?•An electric generator consists of–Many coils of wires wound on an armature that can rotate by mechanical means in a magnetic field•An emf is induced in the rotating coil•Electric current is the output of a generator•Which direction does the output current flow when the armature rotates counterclockwise?–The conventional current flows outward on wire A toward the brush–After half the revolution the wire A will be where the wire C is and the current flow on A is reversed•Thus the current produced is alternating its directionMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu5How does an Electric Generator work?•Let’s assume the loop is rotating in a uniform B field w/ constant angular velocity  The induced emf is• •What is the variable that changes above?–The angle . So what is d/dt?•The angular speed .–So 0t–If we choose 0=0, we obtain– –If the coil contains N loops:–What is the shape of the output?•Sinusoidal w/ amplitude 0=NBA•US ac frequency is 60Hz. Europe is at 50Hz–Most the U.S. power is generated at steam plantse =e =e =BddtF- =dB dAdt- � =�rr[ ]cosdBAdtq-[ ]cosdBA tdtv- =sinBA tv vBdNdtF- =sinNBA tv v =0sin te vMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu6Example 29 – 5 An AC generator. The armature of a 60-Hz ac generator rotates in a 0.15-T magnetic field. If the area of the coil is 2.0x10-2m2, how many loops must the coil contain if the peak output is to be 0=170V?The maximum emf of a generator is Solving for NSince2 fv p=0NBAe v=0NBAev=We obtainN =02 BAfep=( )( ) ( )2 2 11701502 0.15 2.0 10 60VturnsT m sp- -=�״�Monday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu7A DC Generator•A DC generator is almost the same as an ac generator except the slip rings are replaced by split-ring commutators•Output can be smoothed out by placing a capacitor on the output–More commonly done using many armature windingsSmooth output using many windingsMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu8Eddy Currents (read more in 29-5)•Induced currents are not always confined to well-defined path•In some cases where a conductor is moving in and out of the magnetic field, the Lenz’s law causes flow of electrons that opposes the change in magnetic flux–This change is in the direction that impedes the production of emf–And thus causes energy losses•These currents are called eddy currents–Just like the eddy currents in the water that pulls the boat in the opposite direction of the movementMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu9Transformer•What is a transformer?–A device for increasing or decreasing an ac voltage–A few examples?•TV sets to provide HV to picture tubes, portable electronic device converters, transformers on the pole, etc •A transformer consists of two coils of wires known as primary and secondary–The two coils can be interwoven or linked by a laminated soft iron core to reduce eddy current losses•Transformers are designed so that all magnetic flux produced by the primary coil pass through the secondaryMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu10How does a transformer work?•When an ac voltage is applied to the primary, the changing B it produces will induce voltage of the same frequency in the secondary•So how would we make the voltage different?–By varying the number of loops in each coil–From Faraday’s law, the induced emf in the secondary is – –The input primary voltage is– –Since dB/dt is the same, we obtain– SV =PV =S SP PV NV N=Transformer Equation BSdNdtFBPdNdtFMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu11Transformer Equation•The transformer equation does not work for dc current since there is no change of magnetic flux•If NS>NP, the output voltage is greater than the input so it is called a step-up transformer while NS<NP is called step-down transformer•Now, it looks like energy conservation is violated since we can get more emf from smaller ones, right?–Wrong! Wrong! Wrong! Energy is always conserved!–A well designed transformer can be more than 99% efficient–The power output is the same as the input: – – P PV I =SP PP S SIV NI V N= =S SV IMonday, Nov. 14, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu12Example 29 – 8 Portable radio transformer. A transformer for home use of a portable radio reduces 120-V ac to 9.0V ac. The secondary contains 30 turns, and the radio draws 400mA. Calculate (a) the number of turns in the primary; (b) the current in the primary; and (c) the power transformed. (a) What kind of a transformer is this?P =A step-down x-formerPSVV=Since We obtain PN =(b) Also from the transformer equation SPII=We obtain PI =(c) Thus the power transformed isHow about the input power? The same assuming 100% efficiency.PSNNPSSVNV=12030 4009VturnsV=PSVVSSPVIV=90.4 0.03120VA AV=S SI V =( ) ( )0.4 9 3.6A V W� =Monday, Nov. 14, 2005 PHYS 1444-003, Fall


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UT Arlington PHYS 1444 - Lecture Notes

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