# 1 Magnetic Circuits and Transformers Discussion D10.1 Chapter 6.

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1 Magnetic Circuits and Transformers Discussion D10.1 Chapter 6

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

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).

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)

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”

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

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

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

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

10 Mutual Inductance Linear media Let

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

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

13 Ideal Transformer - Impedance Input impedance Load impedance Turns ratio

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.

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

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