PHYS 1444 – Section 004 Lecture #18EMF Induced on a Moving ConductorElectric Generator (Dynamo)How does an Electric Generator work?Example 29 – 5A DC GeneratorTransformerHow does a transformer work?Transformer EquationExample 29 – 8Example 29 – 9: Power TransmissionElectric Field due to Magnetic Flux ChangeGeneralized Form of Faraday’s LawInductanceWednesday, April 11, 2007 1 PHYS 1444-004, Spring 2007Dr. Andrew BrandtPHYS 1444 – Section 004Lecture #18Wednesday, April 11 2007Dr. Andrew Brandt•Generator•Transformer•InductanceHW8 due Mon 4/16 at 11pm on CH 28+29Start Ch. 30/Review on 4/16Test on ch 26-29 Weds 4/18Wednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt2EMF Induced on a Moving Conductor•Another way of inducing emf is using a U shaped conductor with a movable rod resting on it.•As the rod moves at a speed v, it travels vdt in time dt, changing the area of the loop by dA=lvdt.e =BddtF=BdAdt=dtBlvBlvdt=•Using Faraday’s law, the induced emf for this loop is–This equation is valid as long as B, l and v are perpendicular to each other. •An emf induced on a conductor moving in a magnetic field is called a motional emfmotional emfWednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt3Electric Generator (Dynamo)•An electric generator transforms mechanical energy into electrical energy•It consists of many coils of wires wound on an armature that can be rotated 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?–Initially the current flows as shown in figure to reduce flux through the loop–After half a revolution, the current flow is reversed•Thus a generator produces alternating currentWednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt4How does an Electric Generator work?•Let’s assume the loop is rotating in a uniform B field with constant angular velocity The induced emf is• e =e =e =BddtF- =dB dAdt- � =�rr[ ]cosdBAdtq-[ ]cosdBA tdtv- =sinBA tv vBdNdtF- =sinNBA tv v =0sin te v• What is the variable that changes above?–The angle . What is d/dt?•The angular speed .–So 0t–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 uses 50HzWednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt5Example 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- -=�״�Wednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt6A DC Generator•A DC generator is almost the same as an ac generator except the slip rings are replaced by split-ring commutatorsSmooth output using many windings• Dips in output voltage can be reduced by using a capacitor, or more commonly, by using many armature windingsWednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt7Transformer•What is a transformer?–A device for increasing or decreasing an AC voltage–Examples, the complete power chain from generator to your house, high voltage electronics –A transformer consists of two coils of wires known as the 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 secondaryWednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt8How 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 wire•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 – SV =PV =S SP PV NV N=Transformer Equation BSdNdtFBPdNdtF–The input primary voltage is– –Since dB/dt is the same, we obtain–Wednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt9Transformer 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 a larger emf from a 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 IThe output current for step-up transformer will be lower than the input, while it is larger for a step-down transformer than the input.Wednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt10Example 29 – 8 Portable radio transformer. A transformer for use with 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 transformerPSVV=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� =Wednesday, April 11, 2007 PHYS 1444-004, Spring 2007Dr. Andrew Brandt11Example 29 – 9: Power Transmission Transmission lines. An average of 120kW of electric power is sent to a small town from a power plant 10km away. The transmission lines have a total resistance of 0.4. Calculate the power loss if the power is transmitted at (a) 240V and (b) 24,000V.We cannot use P=V2/R since we do not know the voltage along the transmission line. We, however, can use P=I2R.(a) If 120kW is sent at 240V, the total current isI =Thus the power loss due to the transmission line isP =(b) If 120kW is sent at 24,000V, the total current is.I =Thus the power loss due
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