UNIT 6 INDUCTOR AND INDUCTANCE

Transcription

1 UNIT 6 INDUCTOR AND INDUCTANCE 6.1 Inductor and nductance Assocated quanttes - Inductor, also called a choke, s another passve type electrcal component desgned to take advantage of ths relatonshp by producng a much stronger magnetc feld than one that would be produced by a smple col. - Symbol of nductance s L. - Unt of nductance s Henry. - Inductance the property of an electrc crcut by whch an electromotve force s nduced n t as the result of changng magnetc flux. - Electromagnet temporary magnet producton due to flow of electrc current. - Electromagnetc nducton - producton process electrc form magnet Types of nductor Ar core Fxed Iron core Ferrte core Varable Core loss Constructon of nductor An nductor s usually constructed as a col of conductng materal, typcally copper wre, wrapped around a core ether of ar or ferrous materal. Core materals wth hgher permeablty than ar confne the magnetc feld closely to the nductor, thereby ncreasng the nductance. Inductors come n many shapes. Most are constructed as enamel coated wre wrapped around a ferrte wth wre exposed on the outsde, whle some enclose the wre completely n ferrte and are called shelded. 1

2 Some nductors have an adjustable core, whch enables changng of the nductance. Small nductors can be etched drectly onto a prnted board by layng out the trace n a spral pattern. 6.2 Inductance equvalents crcut for seres and parallel connecton Inductors connected n seres Fgure 1 E T I L 1 e 1 e 2 Fgure 2: Inductor n seres L 2 Total voltage, E T = e 1 + e 2 Total nductance, L T = L 1 + L 2 It follows that for n seres connected nductors L T = L 1 + L L n Current, I = I L1 = I L Inductors connected n parallel E T I T I 1 I 2 L 1 e 1 L 2 e 2 Total voltage, E T = e 1 = e 2 Total current, I T = I 1 + I 2 Total nductance Fgure 3: Inductor n parallel It follows that for n parallel connected nductors 2

3 6.2.3 Inductors connected n seres-parallel E T I T L 1 I 1 I 2 L 2 L 3 Total current, I T = I 1 +I 2 Total nductance, L T = L 1 + L 2 // L 3 Fgure 5: Inductor n seresparallel connecton Example 1 Calculate the equvalent nductance of two nductors of 3H and 5H connected: (a) n seres (b) n parallel. Soluton: a) Total nductance n seres, b) Total nductance n parallel, Example 2 Fnd the nductance to be connected n parallel wth a 10H capactor for the equvalent capactance to be 6H. Soluton:,, For two capactance n seres: Example 3 Fnd the total nductance for the crcut below I T L 1 Total nductance, L T = L 1 + L 2 // L 3 5H I 1 I 2 E T L 2 2H L 3 3H 3

4 TUTORIAL 1 Fnd the total nductance of the crcut. 1. 2H E T 1H 3H 4H [Ans: 0.788H] 2. A 2mH 3mH 5mH B 4mH 6mH [Ans: 8.33mH] 3. A 2H 4H 6H 2H 2H 5H 3H 5H 3H B [Ans: 3.54H] 4. 12mH 5.2mH 4mH 2mH 40mH 12mH 12mH 4mH [Ans: 20mH] 4

5 6.3 Crcut wth nductve load Electromagnetc nducton When a conductor s moved across a magnetc feld so as to cut through the lnes of force (or flux, an electromotve force (e.m.f) s produced n the conductor. If the conductor forms part of a closed crcut then the e.m.f produced causes an electrc current to flow round the crcut. Hence an e.m.f s nduced n the conductor as a result of ts movement across the magnetc feld. Ths effect s known a electromagnetc nducton Faraday s Law Faraday s laws of electromagnetc nducton state: ) An nduced e.m.f s setup whenever the magnetc feld lnkng that crcut changes ) The magntude of the nduced e.m.f n any crcut s proportonal to the rate of change of the magnetc flux lnkng the crcut Mathematcal relatonshp between the nduced e.m.f and the network Faraday noted that the e.m.f nduced n a loop s proportonal to the rate of change of magnetc flux through t: Where; e s the electromotve force nduced (n volts) N s the number of turns of the col dφ s the change of flux n Weber, Wb dt s the tme taken for the flux to change n seconds. *Notce the negatve sgn s the nduced current wll now produce an nduced magnetc fled. The drecton of that magnetc feld wll be opposte to the drecton the flux s changng Self-nductance and the nduced e.m.f Inductance s the name gven to the property of a crcut whereby there s an e.m.f nduced nto the crcut by change of flux lnkages produced by a current change. When the e.m.f s nduced n the same crcut as that n whch the current s changng, the property s called self-nductance, L. Induced e.m.f s the product of self-nductance and the rate of change n current Where; e s nduced e.m.f (n volts) L s self-nductance n Henry d s the change of current n Amperes dt s the tme taken for the current to change n seconds. 5

6 6.3.5 The mathematcal of self-nductance Where; N s number of turns of col L s length of col A s surface area µ s permeablty The factors that nfluence nductance A component called an nductor s used when the property of nductance s requred n a crcut. The basc form of an nductor s smply a col of wre. Factors whch affect the nductance of an nductor nclude: ) The number of turns of wre (N) more turns the hgher the nductance ) The cross-sectonal area of the col of wre (A) the greater the cross-sectonal area the hgher the nductance ) The presence of magnetc core - when the col s wound on an ron core, the same current sets up a more concentrated magnetc feld and the nductance s ncreased v) The way turns are arranged a short tck col of wre has a hgher nductance than the along thn one. 6.4 Rse and decay of current goes through an nductor n the dc crcut Rse and decay of current b R L a S V Fgure 5: Inductor crcut Refer to Fgure 5, when swtch n a poston, nductor connected to DC supply. The current had not acheved maxmum value mmedately. The current are gong to reach maxmum value n a perod of tme that certan caused by producton e.m.f nduced by nductor whch always aganst the supply voltage. In other words, the currant of the crcut s rse delayed. When swtch s beng transformed to poston b, nductor crcut had short crcut (no supply voltage). The current s not decrease contnue to zero but take a tme that certan from maxmum value untl zero value. Refer to fgure 6 whch s shown the exponental graph changng of current n nductor crcut. 6

7 Rse of current Decay of current I M I M Rt I ( 1 L M e ) I M e Rt L t t Fgure 6: Graph changng of current n nductor crcut Tme constant Tme constant, defnes as tme for current acheve maxmum (I M ) f ths mantan the early promoton rate current. ) Tme constant at rse of current Practcally, the current dd not rse by regular. By graphcally, t acheves 63.2% from maxmum value (pont B n fgure 7) n tme constant. In other words, tme constant, also defnes as tme for current of nductor acheve 63.2% from the maxmum value. I M 63.2% A C 5 B D I ( 1 L M e ) Fgure 7: Graph rse of current through an nductor From RL crcut, tme constant,, gven by equaton: t Rt From the graph: Current wll be rsng from mnmum value (0) by exponent headed for maxmum value, I M (steady state). Tme for value of acheve 63.2% from maxmum value s tme constant,. Tme for value of I acheve maxmum value s 5 7

8 ) Tme constant at decay of current In decay of current through an nductor, a method to fnd values of tme constant same as n rse of current through an nductor. The dfferences are value of current decay from maxmum value (I M ) to mnmum (0), and value 63.2% replaced wth 36.8% whch s 100% %. Fgure 8 shown clear pctures for decay of current n nductor. I M 36.8% 0 Fgure 8: Graph decay of current through an nductor Energy stored n an nductor 5 I M e Rt L t From the graph: Current wll reduce from maxmum value (I M ) by exponentally untl mnmum value (0). Tme for to reach 36.8% from maxmum value (reducng of 63.2% from orgn value, I M ) s tme constant: Tme for to reach fnal value (zero) s 5. An nductor possesses an ablty to store energy. The energy stored, W n the magnetc feld of an nductor s gven by: Example 1 One nductor 0.5H connected n seres wth resstor 20Ω and dc voltage 120V. Determne: ) Tme constant ) Energy stored n nductor ) Current at tme 0.025s Soluton ) Tme constant ) ) Energy store, 8

9 Example 2 b a S R=10Ω L=7.5H When swtch connected to a, calculate: ) Tme constant ) Tme taken for current acheve maxmum value ) Maxmum current f the current s 2.5A n 0.38s. 100V Soluton ) Tme constant, ) ) Example 3 One crcut has resstor 40Ω connected n seres wth nductor 15H and dc voltage 220V. Calculate: ) Tme constant ) Current at tme () ) Current at tme 0.05s v) Energy stored n nductor Soluton ) Tme constant ) t = 0.05s ) v) 9

10 TUTORIAL 2 1. A col of nductance 0.04 H and resstance 10Ω s connected to a 120 V, d.c. supply. Determne (a) the fnal value of current (b) the tme constant of the crcut (c) the value of current after a tme equal to the tme constant from the nstant the supply voltage s connected. [12A,4ms,7.58A] 2. The wndng of an electromagnet has an nductance of 3H and a resstance of 15Ω. When t s connected to a 120 V d.c. supply, calculate: (a) the steady state value of current flowng n the wndng (b) the tme constant of the crcut (c) the value of the nduced e.m.f. after 0.1s (d) the tme for the current to rse to 85% of ts fnal value (e) the value of the current after 0.3 s [8A,0.2s,72.78V,0.379s,6.215A] 3. A col has an nductance of 1.2H and a resstance of 40Ω and s connected to a 200 V, d.c. supply. Determne the approxmate value of the current flowng 60 ms after connectng the col to the supply. [4.3 A] 4. A 25 V d.c. supply s connected to a col of nductance 1H and resstance 5Ω. Determne the approxmate value of the current flowng 100 ms after beng connected to the supply. [2 A] 5. The feld wndng of a 200 V d.c. machne has a resstance of 20Ω and an nductance of 500mH. Calculate: (a) the tme constant of the feld wndng (b) the value of current flow one tme constant after beng connected to the supply (c) the current flowng 50 ms after the supply has been swtched on. [(a) 25 ms (b) 6.32 A (c) 8.65 A] 10