Slide #1.

Energy Storage Devices
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Slide #2.

Objective of Lecture Describe The construction of an inductor How energy is stored in an inductor The electrical properties of an inductor  Relationship between voltage, current, and inductance; power; and energy Equivalent inductance when a set of inductors are in series and in parallel
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Slide #3.

Inductors Generally - coil of conducting wire Usually wrapped around a solid core. If no core is used, then the inductor is said to have an ‘air core’. http://bzupages.com/f231/energy-stored-inductor-uzma-noreen-group6-
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Slide #4.

Symbols http://www.allaboutcircuits.com/vol_1/chpt_15/1. html
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Slide #5.

Alternative Names for Inductors Reactor- inductor in a power grid Choke - designed to block a particular frequency while allowing currents at lower frequencies or d.c. currents through  Commonly used in RF (radio frequency) circuitry Coil - often coated with varnish and/or wrapped with insulating tape to provide additional insulation and secure them in place  A winding is a coil with taps (terminals). Solenoid – a three dimensional coil.  Also used to denote an electromagnet where the magnetic field is generated by current flowing through a toroidal inductor.
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Slide #6.

Energy Storage The flow of current through an inductor creates a magnetic field (right hand rule). B field http://en.wikibooks.org/wiki/Circuit_Theory/Mutual_Ind Ifuctance the current flowing through the inductor drops, the magnetic field will also decrease and energy is released through the generation of a current.
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Slide #7.

Sign Convention • The sign convention used with an inductor is the same as for a power dissipating device. • When current flows into the positive side of the voltage across the inductor, it is positive and the inductor is dissipating power. • When the inductor releases energy back into the circuit, the sign of the current will be negative.
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Slide #8.

Current and Voltage Relationships L , inductance, has the units of Henries (H) 1 H = 1 V-s/A di vL L dt t1 1 iL  vL dt L to
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Slide #9.

Power and Energy t1 pL vL iL LiL iL dt to t1 t1 diL w L iL dt L iL diL dt to to
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Slide #10.

Inductors Stores energy in an magnetic field created by the electric current flowing through it. Inductor opposes change in current flowing through it.  Current through an inductor is continuous; voltage can be discontinuous. http://www.rfcafe.com/references/electrical/Electricity%20-%20Basic%20Navy%20Training %20Courses/electricity%20-%20basic%20navy%20training%20courses%20-%20chapter
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Slide #11.

Calculations of L For a solenoid (toroidal inductor) 2 2 N A N  r  o A L    N is the number of turns of wire A is the cross-sectional area of the toroid in m2. r is the relative permeability of the core material o is the vacuum permeability (4π × 10-7 H/m) l is the length of the wire used to wrap the toroid in meters
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Slide #12.

Wire Unfortunately, even bare wire has inductance.     7 L  ln 4   1 2 x10 H   d   d is the diameter of the wire in meters. 
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Slide #13.

Properties of an Inductor Acts like an short circuit at steady state when connected to a d.c. voltage or current source. Current through an inductor must be continuous  There are no abrupt changes to the current, but there can be abrupt changes in the voltage across an inductor. An ideal inductor does not dissipate energy, it takes power from the circuit when storing energy and returns it when discharging.
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Slide #14.

Properties of a Real Inductor Real inductors do dissipate energy due resistive losses in the length of wire and capacitive coupling between turns of the wire.
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Slide #15.

Inductors in Series
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Slide #16.

Leq for Inductors in Series vin v1  v2  v3  v4 di di v1 L1 v2 L2 dt dt i di di v3 L3 v4 L4 dt dt di di di di vin L1  L2  L3  L4 dt dt dt dt di vin Leq dt L eq L1  L2  L3  L4
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Slide #17.

Inductors in Parallel
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Slide #18.

Leq for Inductors in Parallel iin i1  i2  i3  i4 1 i1  L1 i3  1 L3 1 iin  L1 t1 1 i2  L2 vdt to t1 i vdt i4  to t1 1 vdt   L2 to 1 iin  Leq t1 1 L4 1 vdt   L3 to t1 vdt to t1 vdt to t1 1 vdt   L4 to t1 vdt to L eq  1 L1   1 L2   1 L3   1 L4   1 t1 vdt to
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Slide #19.

General Equations for Leq Series Combination Parallel Combination If S inductors are in If P inductors are in series, then parallel, then: S Leq  Ls s 1  P 1  Leq     p 1 L p  1
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Slide #20.

Summary Inductors are energy storage devices. An ideal inductor act like a short circuit at steady state when a DC voltage or current has been applied. The current through an inductor must be a continuous function; the voltage across an inductor can be discontinuous. The equation for equivalent inductance for inductors S in series parallel Leq  Ls  s 1 1 inductors P   in Leq    p 1 1  L p 
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