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1 Magnetic Circuits and Transformers Discussion D10.1 Chapter 6

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2 Hans Christian Oersted (1777 – 1851) Ref: http://chem.ch.huji.ac.il/~eugeniik/history/oersted.htmhttp://chem.ch.huji.ac.il/~eugeniik/history/oersted.htm 1822 In 1820 he showed that a current produces a magnetic field. X

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3 André-Marie Ampère (1775 – 1836) French mathematics professor who only a week after learning of Oersted’s discoveries in Sept. 1820 demonstrated that parallel wires carrying currents attract and repel each other. attract repel A moving charge of 1 coulomb per second is a current of 1 ampere (amp).

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4 Michael Faraday (1791 – 1867) Self-taught English chemist and physicist discovered electromagnetic induction in 1831 by which a changing magnetic field induces an electric field. Faraday’s electromagnetic induction ring A capacitance of 1 coulomb per volt is called a farad (F)

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5 Joseph Henry (1797 – 1878) American scientist, Princeton University professor, and first Secretary of the Smithsonian Institution. Discovered self- induction Built the largest electromagnets of his day Unit of inductance, L, is the “Henry”

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6 Magnetic Fields and Circuits A current i through a coil produces a magnetic flux, , in webers, Wb. H = magnetic field intensity in A/m. B = magnetic flux density in Wb/m 2. = magnetic permeability Ampere's Law: Magnetomotive force reluctance

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7 Magnetic Flux Magnetic flux, , in webers, Wb. Current entering "dots" produce fluxes that add.

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8 Faraday's Law Faraday's Law: induced voltage in coil 1 is Sign of induced voltage v 1 is such that the current i through an external resistor would be opposite to the current i 1 that produces the flux 1. Total flux linking coil 1: i Example of Lenz's law Symbol L of inductance from Lenz

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9 Mutual Inductance Faraday's Law In linear range, flux is proportional to current self-inductance mutual inductance

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10 Mutual Inductance Linear media Let

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11 Ideal Transformer - Voltage The input AC voltage, v 1, produces a flux This changing flux through coil 2 induces a voltage, v 2 across coil 2

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12 Ideal Transformer - Current The total mmf applied to core is Magnetomotive force, mmf For ideal transformer, the reluctance R is zero.

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13 Ideal Transformer - Impedance Input impedance Load impedance Turns ratio

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14 Ideal Transformer - Power Power delivered to primary Power delivered to load Power delivered to an ideal transformer by the source is transferred to the load.

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15 L.V.D.T. Linear Variable Differential Transformer http://www.rdpelectronics.com/displacement/lvdt/lvdt-principles.htm Position transducer http://www.efunda.com/DesignStandards/sensors/lvdt/lvdt_theory.cfm

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16 LVDT's are often used on clutch actuation and for monitoring brake disc wear LVDT's are also used for sensors in an automotive active suspension system

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