Lecture 11 Inductance and Capacitance
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1 ecure Inducance and apacance EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
2 Goals. Fnd he curren olage for a capacance or nducance gen he olage curren as a funcon of me.. ompue he capacances of parallel-plae capacors. EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
3 Goals. ompue he sored energes n capacances or nducances. 4. Descrbe ypcal physcal consrucon of capacors and nducors and denfy parasc effecs. 5. Fnd he olages across muually coupled nducances n erms of he currens. EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
4 apacor Energy s sored n he elecrc feld ha exss beween he plaes when he capacor s charged. q EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
5 q q apacance d q d q EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
6 apacance Does D curren flow hrough a capacor? No! Only A curren flows hrough a capacor! EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
7 Deermnng urren for a apacance Gen Volage Fnd gen : q 6 d d 6 d d EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
8 Deermnng urren for a apacance Gen Volage From o μs: from o 4 μs: from 4 o 5 μs: d V 6 5x V 6 d x s s d 6 6 x5x 5A d d d d V 7 V 6 d x s s d 6 d 7 A EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
9 Deermnng Volage for a apacance Gen urren.5sn q 4 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
10 Deermnng Volage for a apacance Gen urren q d.5sn.5x.5x q d cos 4 [ ] 4 cos EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
11 Deermnng Volage for a apacance Gen urren q q 7 5 [ ] 4 cos EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
12 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. Sored Energy q q d d d d d p w d d p q q
13 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. urren, Power and Energy for a apacance x for x d d for μf
14 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc for p urren, Power and Energy for a apacance
15 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. urren, Power and Energy for a apacance for w
16 Exercse. The curren hrough a. μf capacor s shown below. Fnd he charge, olage, power and sored energy as funcons of me and plo hem o scale ersus me. EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
17 harge, Volage, Power and Sored Energy q d q x x d x ms x x d x x d x 4x 6 ms 4ms EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
18 harge, Volage, Power and Sored Energy q q.μf 4 ms 4 4 ms 4ms EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
19 harge, Volage, Power and Sored Energy p 4x ms ms 4ms EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
20 harge, Volage, Power and Sored Energy w 5 p d.5x ms ms 4ms EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
21 apacances n Parallel eq dv d dv d dv d dv d dv d EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. dv d dv d eq dv d
22 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. apacances n Seres d d d d d Q d d d eq eq eq
23 apacance of he Parallel- Plae apacor εa A d W ε 8.85 F m ε ε ε r EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
24 apacance of he Parallel-Plae apacor A W cmcm 4 d.mm x m A ε d x m x mx m m.m F.m 8.854x 77x F.77nF 4 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
25 Desgn a μf apacor μf x 6 F ε r ε A d ε r ε W d W cm.m d 5μm 5x m ε r.4 polyeser 6 6 d x F5x m ε ε W x F / m.m r 6 4.9m Impraccal! EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
26 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
27 Parasc Elemens R s Ressy of he capacor plaes S nducance due o curren flow no and ou of he capacor R P eakage ressance of he delecrc EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
28 Parasc Elemens A s charged up o V, s dscharged The oal energy w oal : w w 6 woal w w 5mJ FV 5mJ EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
29 Parasc Elemens A he swch s closed, and he charge q on he capacor plaes redsrbues: q q q oal q x q 6 FV μ μ EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
30 Parasc Elemens w w w eq eq q 5V 6 eq F5V 6 eq F5V w w.5mj oal eq μf μ μf.5mj.5mj EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. Where dd he mssng energy go?
31 Inducance EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
32 Joseph Henry Wres Henry: "I may howeer menon one fac whch I hae no seen noced n any work...when a small baery s moderaely exced... f a wre hry or fory fee long be used nsead of he shor wre, hough no spark wll be percepble when he connecon s made, ye when s broken by drawng one end of he wre from s cup of mercury, a d spark s produced." EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
33 Inducance The polary of he olage s such as o oppose he change n curren enz s law. EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
34 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. d d d d d p d d d w Inducance p d d
35 Inducor urren wh onsan Appled Volage d H V d 5A Wha happens f we open he swch a sec? EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. d d
36 Waer Hammer EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
37 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. Fnd he urren gen he Volage A d s for A H x s V x d x s for d μ μ
38 Seres Inducances eq d d d d d d d d d d eq EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
39 EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. Parallel Inducances d d d d d eq eq
40 Equalen Inducance 5H 5H 5H eq. 5H 5H 5H H eq H H 5H eq H.5H. 5H EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
41 R S Ressance of connecng wres P apacance beween he col wndngs R P Ressance of he col wndngs EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
42 Muual Inducance Felds are adng Felds are opposng Magnec flux produced by one col lnks he oher col EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc.
A capacitor consists of two conducting plates, separated by an insulator. Conduction plates: e.g., Aluminum foil Insulator: air, mica, ceramic, etc
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