Capacitors & Inductors

Transcription

1 apaciors & Inducors EEE5 Elecric ircuis Anawach Sangswang Dep. of Elecrical Engineering KMUTT Elecric Field Elecric flux densiy Elecric field srengh E Elecric flux lines always exend from a posiively charged body o a negaively charged body, always exend or erminae perpendicular o he charged surfaces, and never inersec. apaciors A capacior is a passive elemen designed o sore energy in is elecric field A capaciorconsiss of wo conducing plaes separaed by an insulaor (or dielecric) apaciance A capacior consruced simply of wo parallel conducing plaes Separaed by an insulaing maerial (in his case, air). apaciance is a measure of a capacior s abiliy o sore charge on is plaes (is sorage capaciy). A capacior has a capaciance of farad if coulomb of charge is deposied on he plaes by a poenial difference of vol across he plaes Variables Q V Unis Farads (F) oulombs () Vols (V) 3 4

2 apaciors A cross-secional view of he parallel plaes Field disribuion apaciors Permiiviy () of he dielecric (F/m) E The greaer, he greaer he amoun of charge deposied on he plaes he greaer he flux densiy For vacuum, permiiviy ( ) is 8.85x - Relaive permiiviy ( ) E The capaciance E / / 5 6 Dielecric Srengh Fixed apaciors Mica mil. in. 7 Applicaions wih emperaure variaion and high volage, small leakage curren, ranges: picofaradso. uf, wih V or more 8

3 Fixed apaciors eramic Fixed apaciors Elecrolyic capaciors Low breakdown volage, high leakage curren, ranges: few ufo +, uf, wih +5V Tanalum capaciors Low leakage curren, works wih boh dc and ac, ranges: few pf uf, wih 5V or more 9 Fixed apaciors Polyeaser(mylar) Works wih boh D & A neworks, low leakage curren, ranges:. ufo + uf, wih up o,v apaciors Variable capaciors urren-volage relaionship dq d v i i d d v i d v( ) +

4 haracerisics urren and volage haracerisics Sored energy dv p v i v d d v i d dv w pd v d v d v( ) w v v() Terminal characerisics An open circui o dc Volage canno change abruply Ideal capacior does no dissipae energy 3 4 Example 6.4 Deermine curren hrough a uf capacior 5 < < 5 < < 3 v( ) < < 4 oherwise Example 6.5 Obain he energy sored in each capacior Pracice prob. i( ) 6 5 < < 5 < < 3 5 3< < 4 oherwise alculae he volage across an uncharged mf capacior a ms and 5 ms 5 Ex w 6mJ, w 8 mj Pracice: mv, 4mV 6

5 Series and Parallel apaciors Parallel connecion Series and Parallel apaciors Series connecion dv dv dv dv i i + i+ i3+ L+ i L+ d d d d dv k i d dv d 7 v v + v + L+ v i( ) d+ v ( ) + i( ) d+ v ( ) + + L+ i( ) d+ v ( ) + v ( ) + L+ v ( ) i( ) d v( ) + + L+ i( ) d+ v ( ) Example Find he uivalen capaciance seen a he erminals of he circui in he circui shown below: Faraday s Law 4µF Example Find he volage across each of he capaciors in he circui shown below: v 3V v 3V v 3 V v 4 V 9 If a conducor is moved hrough a magneic field so ha i cus magneic lines of flux, a volage will be induced across he conducor If a coil of urns is placed in he region of a changing flux, a volage will be induced across he coil

6 Lenz s Law An induced effec is always such as o oppose he cause ha produced i. An induced volage is developed across he coil due o he change in curren hrough he coil. hoking : The insan he curren begins o increase, here will be an opposing effec rying o limi he change in curren. Self inducance: he abiliy of a coil o oppose any change in curren, measured in Henry (H) Inducors An inducor is a passive elemen designed o sore energy in is magneic field. An inducor consiss of a coil of conducing wire. L µ A l Inducors d i v L and i v( ) d i( ) d L + An inducor acs like a shor circui o dc (di/d ) and is curren canno change abruply urren canno change insananeously di p v i L i d w di w pd L id L idi L i d Li 3 Example The erminal volage of a -H inducor is v (-) V Find he curren flowing hrough i a 4 s and he energy sored in i wihin < < 4 s. Assume i() A. i(4s) -8A w(4s) 3J 4

7 Example Deermine v c,i L,and he energy sored in he capacior and inducor in he circui of circui shown below under dc condiions. Series and Parallel Inducors Series connecion i L 3A v 3V w L.5J w 9J di di di di v v+ v+ v3+ L+ v L + L + L3 + L+ L d d d d di Lk L i d L L + L L di d 5 6 Series and Parallel Inducors Parallel connecion i i + i + L+ i v( ) d+ i ( ) + v( ) d+ i ( ) L L + + L+ v( ) d+ i ( ) + i ( ) + L+ i ( ) L L L v( ) d i( ) L + + L+ v( ) d+ i ( ) L L L L L 7 Example alculae he uivalen inducance for he inducive ladder nework in he circui shown below: L 5mH 8

8 Example 6. Find i (), v( ), v ( ), v( ), i ( ), i ( ) given ha i( ) 4( e ) ma, i () ma i () i() i () 4 ( ) 5 ma di v ( 4)( ) e 8 e mv d v e mv di v 3 e mv d i ( ) v ( ) d i () e d 5mA 8 3e ma 4H i ( ) v ( ) d i () e d ma e ma H + 9 3