ELEG 205 Fall Lecture #10. Mark Mirotznik, Ph.D. Professor The University of Delaware Tel: (302)
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1 EEG 05 Fall 07 ecure #0 Mark Mirznik, Ph.D. Prfessr The Universiy f Delaware Tel: ( mirzni@ece.udel.edu
2 haper 7: apacirs and Inducrs
3 The apacir Symbl Wha hey really lk like
4 The apacir Wha is cmmn amngs all capacirs? Meal surfaces separaed by dielecric (i.e. insulaing maerial such as air, glass, paper, plasic
5 The apacir When a vlage is applied acrss he w meal plaes he plaes accumulae elecrical charge (psiive n ne plae and negaive n he her plae Sme Physics Q A capacir sres energy in an elecric field. I des n absrb r dissipae any energy
6 The apacir Sme Physics The amun f charge ha is sred n he capacir depends n w hings ( The size f he vlage ( The size f he capacir and is maerials Q, V Farads Q
7 The apacir Sme Physics: Parallel Plae Equain Fr his gemery he capaciance is deermined be: ε ε r A εε r, d Farads F / m Relaive permiiviy (depends n he maerial beween he plaes
8 The apacir Sme Physics: Parallel Plae Equain Example: Hw big d he plaes need be ge a F capacir? A ε ε d r ε ε d ε ε.0.0 r r A d cm, Farads F / m A m 00 miles n a side square plaes!
9 The apacir Sme Physics Quesin: Is here curren flwing in he wires and inside he capacir? Q
10 The apacir Quesin: Is here curren flwing in he wires and inside he capacir? Sme Physics Q Answer Yes: As lng as he charge is changing in ime here is curren i dq d
11 The apacir Quesin: Is here hen a relainship i dq d Q, V Farads beween he vlage and curren ( V d i d dv d fr a capacir? i( dv ( d
12 The apacir i( V ( i( dv ( d
13 The apacir dv ( i( d i( V ( V ( i( d V (
14 The apacir: Sred Energy ( ( ( ( ( ( ( ( ( ( ( ( v v dv v E d d dv v d P E d dv v i v P ( ( ( v v E
15 The Inducr Symbl Wha hey really lk like
16 A wire ha is usually wund arund a cre. The cre culd be magneic (i.e. ferrie r nn-magneic (air, plasic. I wrks by building up and sring energy in he way f magneic fields.. The Inducr Wha is cmmn amngs all capacirs? Magneic fields An inducr sres energy in a magneic field. I des n absrb r dissipae any energy
17 The Inducr Wha deermines hw much energy is sred in he magneic field? Tw hings: ( The amun f curren ha flws hrugh he inducr and is range f change. ( The shape and maerial f he inducr (i.e. hw many wire urns, diameer, cre maerial. All f hese parameers are wha we call he inducance, Magneic fields Wha are he unis fr inducance?
18 The Inducr Quesin: Is here hen a relainship di( beween he vlage and curren v( d fr an inducr?
19 The Inducr v ( i( v( di( d
20 The Inducr di( v( ( d v i( i( v( d i(
21 The Inducr: Sred Energy E ( i( i (
22 Summary Symbl Unis Vlage urren relainship Inegral frm Sred Energy apacir Farads (F i( dv( d v( i( d v( E ( v( Inducr Henry (H v( di( d i( v( d i( E ( i(
23 Wha d capacirs and inducrs lk like a D? Symbl Unis Vlage urren relainship Inegral frm Sred Energy I V D D dv d di d D D Fr D all vlages and currens DO NOT vary in ime 0 0 N curren flws hrugh a capacir fr D (i.e. OPEN IRUIT N vlage acrss an inducr fr D (i.e. shr IRUIT
24 Summary Symbl Unis Vlage urren relainship Inegral frm Sred Energy Wha des i lk like a D apacir Farads (F i( dv( d v( i( d v( E ( v( pen circui Inducr Henry (H v( di( d i( v( d i( E ( i( shr circui
25 an vlages and currens change insananeusly? ( Resisr Symbl v( R i( Unis Vlage Wha wuld happen if we ried urren change Inegral he vlage frmr curren Sred relainship insananeusly Energy hms law permis insananeus changes bh vlage and curren
26 an vlages and currens change insananeusly? ( Inducr di( v( d If he curren ries change insananeusly hen he vlage ges infiniy! N pssible Unis URRENT ANNOT HANGE INSTANTANEOUSY FOR AN INDUTOR Vlage Wha wuld happen if we ried urren change Inegral he vlage frmr curren Sred relainship insananeusly Energy
27 an vlages and currens change insananeusly? (3 apacir i( dv( d If he vlage ries change insananeusly hen he curren ges infiniy! N pssible VOTAGE ANNOT HANGE INSTANTANEOUSY FOR A APAITOR Unis Vlage Wha wuld happen if we ried urren change Inegral he vlage frmr curren Sred relainship insananeusly Energy
28 Summary Symbl Unis Vlage urren relainship Inegral frm Sred Energy Wha des i lk like a D an vlage r curren change insananeusly apacir Farads (F i( dv( d v( i( d v( E ( v( Open circui Vlage N urren - Yes Inducr Henry (H v( di( d i( v( d i( E ( i( Shr circui Vlage Yes urren - N
29 mbinain f apacirs apacirs in Series v s i v - v - KV: v s v v Take derivaive f bh sides wih respec ime dv s d dv d dv d Use law f he capacir relae vlage curren 0 0 i( dv ( d dv s d i i 0 dv s d i
30 mbinain f apacirs apacirs in Series v s i v - v - v s i eq dv s d i i dv d s i( dv ( d apacirs in series add like resisrs in parallel eq
31 mbinain f apacirs apacirs in parallel i s v - i i i s v eq - K: i s i i Use law f he capacir relae vlage curren dv dv i s 0 d d 0 dv ( d i s eq apacirs in parallel add like resisrs in series
32 mbinain f apacirs Inducrs in Series v s i v - v - KV: v s v v Use law f he inducr relae vlage curren di di 0 d d 0 v s ( d eq v s di v ( di d Inducrs in series add like resisrs in series
33 mbinain f apacirs Inducrs in Parallel i s i i v - i s v eq - K: i s i i 0 Take derivaive f bh sides wih respec ime Use law f he capacir relae vlage curren di s d di d di s d di d v 0 v 0 di s d v
34 mbinain f apacirs Inducrs in Parallel i s i i v - di s d i s v eq - v v di d s eq Inducrs in parallel add like resisrs in parallel
35 Summary Symbl mbinain in Series mbinain in Parallel apacir Adds like resisrs in parallel Adds like resisrs in series Inducr Adds like resisrs in series Adds like resisrs in parallel
36 Elecrical Symbls ibrary fr Drawing Schemaics in PwerPin Fr bes resuls: Turn snap--grid-n D n scale he symbls library. Draw enire schemaic firs, hen scale desired size. Afer rain, press up/dwn and sideways arrw keys realign he cmpnen wih he grid. Acives Passives Surces Discrees
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