Inductors. An inductor, is an electrical component which resists changes in electric current passing through it.

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1 Inductors An inductor, is an eectrica component which resists changes in eectric current passing through it. It consists of a conductor such as a wire, usuay wound into a coi. When a current fows through it, energy is stored temporariy in a magnetic fied in the coi. When the current fowing through an inductor changes, the time-varying magnetic fied induces a votage in the conductor, according to Faraday s aw of eectromagnetic induction, which opposes the change in current that created it. Most references in this presentation are summarized from Wikipedia entry Inductor

2 Michae Faraday (UK) *Discovered eectromagnetic induction *Invented precursor devices which became eectric motors (and generators) *Major contributions to fieds of eectromagnetism and eectrochemistry Joseph Henry (US) A diagram of Faraday's iron ring-coi apparatus *Discovered sef inductance *Invented the eectromagnet *Work on eectromagnetic reay basis of the eectrica teegraph system

3 Mathematica definition of Inductance L votage induced d L d V dt d V V L dt magnetic fux inked by coi current Faraday s (&Lenz s) aw of eectromagnetic induction dt A ferrite core inductor with two 47 mh windings. chain rue Potentia difference across an inductor An inductor with an inductance of Henry produces an EMF of vot when the current through the inductor changes at the rate of ampere per second. The poarity (direction) of the induced votage is given by Lenz's aw, which states that it wi be such as to oppose the change in current. For exampe, if the current through an inductor is increasing, the induced votage wi be positive at the termina through which the current enters and negative at the termina through which it eaves.

4 Cacuating the Inductance of a coi L 0 KN A 0 40 Hm 7-0 Permeabiity of free space Reative permeabiity of core materia within coi K Nagaoka coefficient N Number of coi turns A Cross sectiona area of coi Length of coi L Inductance (in Henries (H) if a other units are SI) If radius of a (circuar) coi is r K r Materia Air, wood, water, copper Nicke, carbon stee 00 Ferrite (Fe O 3, usuay combined with Nicke, Zinc...) Reative permeabiity > 640 Pure iron > 5,000

5 Toroida inductor diameter of coi windings number of cois L dn D diameter of torus Ony vaid when d 0.D Toroida inductor in the power suppy of a wireess router

6 Energy stored in the magnetic fied of an inductor The instantaneous power which must be suppied to manifest current I in an inductor is P IV By considering the magnetic fied strength B in a soenoid of N turns ength and cross section A, this energy expression aows us to derive a more genera resut for the energy per unit voume stored in a magnetic fied u Where V is the votage induced by the inductor V E L dt If it takes time t to manifest current I, the tota energy stored in the inductor is t 0 Pdt t I E LI dt L I 0 dt 0 E LI E LI NI B 0 L LI u A B u 0N A 0 magnetic fied of a soenoid coi inductance energy per unit voume ref

7 Combining inductors in series V L dt So L is proportiona to potentia difference V The current through inductors in series stays the same, but the votage across each inductor can be different. The sum of the potentia differences (votage) is equa to the tota votage. L L L... L n True ony when there is no mutua couping of magnetic fieds between individua inductors

8 Combining inductors in parae V L dt So L is proportiona to potentia difference V Inductors in a parae configuration each have the same potentia difference (votage). L... L L L n True ony when there is no mutua couping of magnetic fieds between individua inductors

9 Signa fitering using inductors In this configuration, the inductor bocks AC current, whie aowing DC current to pass. Vin I Inductor Vout In this configuration, the inductor decoupes DC current, whie aowing AC current to pass. Vin I Inductor Vout