Apostila De Eletricidade

CK m J \ e]S N
TŽ
 {SIE dpQ GIGKE O Qbd NTS \ N O E d JMS d e]J H E DŽ C E O QGQ  ETLMe d_f NTh E   N Q VH NTCRN @‹jH Q W  G Q E6G d JlS d e]JlHKE6G Q  e]J kTN_L QYX H Q G O N m J \ e]S N
6Ž
!]‹ O Q E X O Q F QGdSQkQS  e Q          ;"= ? TS ;"U ? TS ;"V ? @ = ? SW@ U ? TSYXZ@ V A?   ; U \[ TS^]N_a` i 2= i C + iR + i 2= i C + iR + R R vR v2 = vC vR - - v2 = vC C - C - - vC (0 ) = V0 vC (0 ) = V0 m J \ e@S N
6Ž
!  ‚JlS d e@JlH ETG  Q  e@Jlk_NTL QpX H Q G X E H Q WoCgE QpX H S N O N X e]LMN  Ž ByC]LMJ d N X O E G Q NbH SKN X G ETSKW N O N O Q "cN_C]L`N dpQyX E6G d JMS d e]J H E6G QjQ  eRNgd_f Eh Q G‚N d JlW N@‹ E@H Q  W  G Q E d JMS d e]JlHKE O N m J \ e]SKN
6Ž
D Q N_GjG QY\ e@J X H Q G Q  e]NgdTf Eh Q G           ] = A TS^] U A TSb] V A c = A SWc U A SYXZc V A   ; U \[ TS^]N_a` B Ž Ž Ž  
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   iR i 2= i C + + I R (s) I C (s) = I 2 (s) R + v2 = vC vR - Z R (s) = R + C - VC (s) = V2 (s) VR (s) vC (0- ) = V0 - Z C (s) = 1 sC Vo s - m J \ e@S N
6Ž
D ‚JlS d e@JlH E  Q  e]J k_NTL QpX H QbX N S Q  e Qp X]d JMN QYX H SKN O N X e]L`N  Ž PAQ k Q  G Q X ETH NTS  e Q Q GIH Qbd JMS d e]J H E Qb Q  e]J kTN_L QYX H Q NTE O E Z 9Q WoC]LlE
TŽ%"E \ E]‹  c = A TS ' X ]N_ A V U  ( *!  ]N_  ] = A S

A ) V U  ! ` ByC]LMJ d N X O E G Q N)H S N X G E6SIW N O N O Q c" N_C]L`N dpQ J X k Q SKGKN Q W
6Ž Œ
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6Ž ŒTŒ  ‹   X ]N_ ;"=A ? TS ]N_  @ = ? S a Z{a  yi m m  # + !,+ [ [ ! 0/21  . -  . - / 1 ?  A? (`
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‹ d NTL d e]L`N_S<;"= A? ‚Q*@ = ?  C]NTS NoN Q HVN_CRN @ Ž " i 2 (t) on on + v2 (t) R L off i 2 (t) on on L on - B%C6EMFNHOC,I>CJ'K R B L"E FNH C'I>C

CK m J \ e]SKN
6Ž
  SKE dYQ GKGKE O Qbd NTS \ N O E d JlS d e@JlH E " Ž  ETLMe d_f NTh E   N Q VH NTCRN @‹jH Q W  G Q E6G d JlS d e]JlHKE6G Q  e]J kTN_L QYX H Q G O N m J \ e]S N
6Ž
9‹ O Q E X O Q CFE O Q  G Q QGdSQkQS  e Q          ;>= ? TS ; ? TS ;"V ? @ = A? S @ ? TS XZ@ V A? @  [ SWc_a` i 2= i L + iR + i 2= i L + iR + R R vR v2 = vL vR - - v2 = vL L - L - - i L (0 ) = I 0 i L (0 ) = I 0 m J \ e]S N
TŽ
 ‚JMS d e]JlHKE6G " Q  e]J k_NTL QpX H Q G X E H Q W CFE QYX HKS N O N X e]L`N  Ž ByC]LMJ d N X O E G Q NbH SKN X G ETSKW N O N O Q "cN_C]L`N dpQyX E6G d JMS d e]J H E6G QjQ  eRNgd_f Eh Q G‚N d JlW N@‹ E@H Q  W  G Q E d JMS d e]JlHKE O N m J \ e]SKN
6Ž
 Q N_GjG QY\ e@J X H Q G Q  e]NgdTf Eh Q G  A Sb] V A   A TS ] = A Sb] c = A S c @  XZc V A  [ SWc_a` B Ž Ž Ž  
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    iR i 2= i L + + I R (s) I L (s) = I 2 (s) R + v2 = vL vR - L - i L ( 0- ) = I 0 Z R (s) = R + VL (s) = V2 (s) VR (s) - L I0 Z L (s) = sL - m J \ e]S N
TŽ
  ‚JMS d e]JlHKE " Q  e]Jlk_NTL QYX H Q~X N S Q e  QY X]d J`N QpX H S N O N X e]LMN  Ž PAQ k Q  G Q X ETH NTS  e Q Q GIH Qbd JMS d e]J H E Qb Q  e]J kTN_L QYX H Q NTE O E Z 9Q WoC]LlE 9Ž%"E \ E]‹  c6_   X ] = A S c6_ 
c = A S A V # 
A V  #  ` ByC]LMJ d N X O E G Q N)H S N X G E6SIW N O N O Q c" N_C]L`N dpQ J X k Q SKGKN Q W
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6Ž Œ  ‹  c_  [   ?  ;"= ? TS X c6_  [  A ? (` @ = ? TS . .  + a Z{a  yi m m / 1 + / 1
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d JMS d e]J H E6G G NTh EoN X NTLlJMG N O E6G 
6Ž ‚JMS d e]JlHKE  G Q  SIJ Q Ž Œ9Ž ‚JMS d e]JlHKE  G Q  SKJ Q Ž @Ž ‚JMS d e]JlHKE "ˆG Q  SKJ Q Ž !]Ž ‚JMS d e]JlHKE " G Q  SKJ Q Ž D9Ž ‚JMS d e]JlHKE  C]NTS NTL Q LlE]Ž Ž ‚JMS d e]JlHKE "ˆCRNTSKNTL Q LME]Ž NTS N d N O Nˆe]W O Q L Q G Q  G Qp\ e]J O E E=W Q GIW E H JlCgE O Q S Q GIE6LMe d_f NTh E J  Q  NTC]S Q G QpX HVN O Ee@W W E O Q LlE Q  e]Jlk_NTL QYX H Q X E O E6W  X JlE O N S Q e  QY X]d J`N@‹ JlJ  Q  d NTL d e]LMN O N7N7S Q GICgE6GUHVN X E O ETW  X JME O N S Q e Qp X]d JMN Q JlJMJ  N S Q GKCFE6GIH N X E O E6W  X JME O E H Q WoCgE Q  E@HKJ O N N CRNTSUH JlS O N S Q GICgETGIHVN X E O E6W  X JlE O N S Q e QY X]d J`N@Ž  P N O EE d JlS d e@JlH E  O N m J \ e]SKN
6Ž
@‹ d E6W d E X O JUdTf Eh Q G+J X J d JMNTJMGoJ \ e]NTJMG+N  Q SIE]‹ d NTL d  e]L`N_= ? S ]  @ = A? TS  '   P N O EE d JMS d e]J H E d NTL d e]LMNTS<;>= ? ‚Q*@ = A?  Ž !  #"%$
: " # [ + ! + [ ! 0/ 1 . - 0/ 1 . -
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6Ž !   A?  ? ` O N m J \ e]S N
6Ž Œ@‹ d E6W d E X O JId_f Eh Q G J X J d J`NTJlG J \ eRNTJlG+N  Q SIE]‹ i 2 (t) + v2 (t) R VD u(t) L - i L (0- ) = 0 m J \ e]SKN 6
Ž Œ %‚JlS d e@JlH E " d E6W d E X O JId_f NTh E J X J d JMNTL X e]LMN@Ž  E6LMe d_f NTh E yBDC]LlJ d N X O E  G Q N HKS N X G E6SIW N O N O Q "NTC]LMN dYQ[X E d JMS d e]J H E ETSKJ \ J X NTL ‹nE@H Q  W  G Q E d JMS d e]J H E Q  e]Jlk_NTL QYX H Q O N m J \ e]SKN
6Ž Œ !]‹ O Q E X O Q CFE O Q  G QbQ G d S Q k Q S  e Q   ] = A Sb] A S   vR R VD u(t) L VD s i L (0 ) = 0 m J \ e]SKN 6
Ž Œ! %‚JMS d e]J H E - " ` VR (s) I L (s) = I 2 (s) Z R (s) = R + - - a Z{a  yi m m + I R (s) i 2= i L + v2 = vL iR A X ] V A   A SWc V A  c = A SWc + ] + VL (s) = V2 (s) - Z L (s) = sL Q  e]J k_NTL QpX H QbX N S Q  e Qp X]d JMN d E X O JId_f NTh E J X J d J`N_L X e]LMN  Ž 
      
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NTL d e]LMN X O E G Qa] = A  Q*c = A  ‹ Q W e X d_f NTh E O Q ‹
Q ‹           c= A c A S c V A S   S    S A   ] S  A ! ] S V ! S   A !  ]  ] = A TS A A 
V A  V  #
X V  #
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A V (   `  ByC]LMJ d N X O E G Q N HKS N X G E6SIW N O N O Q " NTC@L`N dpQ J X k Q SKG N Q W
6Ž !  ‚Q
TŽ !D  ‹   @ = ? S ' ]   !  ]  ;>= ? TS  X
[  . + [  . + / 1 / A? (` 1
6Ž !

6Ž ! Œ   X V A  ` !  ( %  ]   # ! c= A % ] V  A   A  ] V A TS JlW C@LMJ ]d N X O E G Q
6Ž !
 Q
6Ž ! Œ  ‹ c= A
# S  , A ]   A ! ] = A  
S S V  A? 
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 P N O E E d JMS d e]J H E#" O N m J \ e]SKN 6
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: i 2 (t) + v2 (t) L VD u(t) R - i L (0- ) = 0 m J \ e]SKN
6Ž Œ D%‚JlS d e@JlH E " d E6W d E X O JId_f NTh E J X J d JMNTL X e]LMN@Ž  E6LMe d_f NTh E yBDC]LlJ d N X O E  G Q N HKS N X G E6SIW N O N O Q "TN C]LMN dYQ[X E d JMS d e]J H E ETSKJ \ J X NTL ‹nE@H Q  W  G Q E d JMS d e]J H E O N m J \ e@S N
6Ž Œ ‹ O Q E X O Q CgE O Q  G Q~Q G d S Q k Q S  e Q    ] ] = A Sb] V A TS   vL - ` VL (s) + I L (s) i 2= i R R Z L (s) = sL + - I R (s) = I 2 (s) + v2 = vR L VD u(t) A X ] A SWc V A  c = A SWc + iL A   VD s - i L (0 ) = 0 Z R (s) = R - + VR (s) = V2 (s) - m J \ e]SKN
6Ž Œ %‚JMS d e]J H E " Q  e]J k_NTL QpX H QbX N S Q  e Qp X]d JMN d E X O JId_f NTh E J X J d J`N_L X e]LMN  Ž  N_L d e@L`N X O E G Qa] = A  Q*c = A  ‹ Q W e X d_f NTh E O Q ‹
Q ‹          c = A c A SWc V A S  
A ! S  ! A (  A   % V  ] V c = A
  V # ] V A S S
 ] = A a Z{a  yi m m    V S A  S    S  ! ] A
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TŽ DT  ‹   ] ;"=  ? TS ]   @ = ? S !  P= ? Ž N O E E d JMS d e]J H E   0"%$   : d NTL d e]L`N_S<;"= A? ‚Q*@  X
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Ž Œ  ‚JMS d e]JlHKE  d E6W d E X O JUdTf NTh E J X J d JMNTL X e]LMN@Ž  ETLMe d_f NTh E yBDC]LlJ d N X O E  G Q N HKS N X G E6SKW N O N O Q "NTC]L`N dYQ)X E d JMS d e]J H E E6SIJ \ J X NTL ‹FE@H Q  W  G Q E d JMS d e]JlHKE Q  e]Jlk_NTL QYX H Q O N m J \ e]S N
TŽ Œ 9‹ O Q E X O Q CFE O Q  G QbQ G d S Q k Q S  e Q      ] = A TS^] U A TSb] V A     c A X c V A  NTL d e]LMN X O E G Qa] =  A  Q*c = A  ‹ Q W e X d_f NTh E O Q ‹
Q ‹  c = A SWc U A TS     `   ] = A     ] U A S^] V A U  V c  S S S    A
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 I D u(t) i 2= i C iR + vR - I R (s) + v2 = vC C R + - ID s - vC ( 0 ) = 0 + VC (s) = V2 (s) - -     c c c U A TS X c V A TS A A X

c c X A A A VU
c
X c= A S S  S S  A # JMWoC]LMJ Rd N X O E G Q
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#  # # c ] = A ! A  A A  S V U  !  . - /   ` ByC]LMJ d N X O E G Q N)H S N X G E6SIW N O N O Q c" N_C]L`N dpQ J X k Q SKGKN Q W
6Ž D D ‚Q
6Ž D  ‹ #   c 
X @ = ?   S c  [ ;>= ? S    a Z{a  yi m m 1 sC Q  e]Jlk_NTL QYX H QbX N S Q e Qp X]d JMN d E X O JId_f NTh E J X J d JMNTL X e]LMN  Ž   Z C (s) = VR (s) - m J \ e]S N T
Ž Œ  ‚JMS d e]JlHKE  Z R (s) = R + I C (s) = I 2 (s) + +  . - [ / 1 ? (` 1 A? 
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Ž Œ %‚JMS d e]J H E " d ETW d E X O JId_f NTh E J X J d J`N_L X e]LMN@Ž  ETLMe d_f NTh E yBDC]LlJ d N X O E  G Q N HKS N X G E6SKW N O N O Q "NTC]L`N dYQ)X E d JMS d e]J H E E6SIJ \ J X NTL ‹FE@H Q  W  G Q E d JMS d e]JlHKE Q  e]Jlk_NTL QYX H Q O N m J \ e]S N
TŽ 69‹ O Q E X O Q CFE O Q  G QbQ G d S Q k Q S  e Q  A Sb] V A  ] = A Sb]    c c = A TS c A S A X c V A I D u(t) i 2= i L iR + vR ` + v2 = vL R L - I R (s) Z R (s) = R + + - ID s - i L (0 ) = 0 + VL (s) = V2 (s) - VR (s) - I L (s) = I 2 (s) - Z L (s) = sL m J \ e]S N
TŽ 6 %‚JMS d e]J H E " Q  e]J kTN_L QYX H Q X N S Q e QY X@d J`N d E X O JIdTf N_h EoJ X J d J`NTL X e]L`N  Ž  NTL d e]LMN X O E G Qa] = A  Q*c = A  ‹ Q W e X d_f NTh E O Q
‹ Q
‹     ] = A S ] S A TS^] V A   V  c A  
S  V      c  !  c c A S c= A S S c A  X A A # A  !    S A   V c    A c   . A  c X c V A S  S !
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T‹ d NTL d e]LMNTS<;>= ?  Q*@ = A?  Ž  i 2 (t) + v2 (t) R VD u(t) C - vC (0- ) = V0 m J \ e@S N 6
Ž 
 ‚JlS d e@JlH E  d ETW QYX H SKN O N bQ d E X O JIdTf N_h EoJ X J d J`NTL Ž  ETLMe d_f NTh E yBDC]LlJ d N X O E G Q N HKS N X G E6SKW N O N O Q "NTC]L`N dYQ)X E d MJ S d e]J H E E6SIJ \ J X NTL ‹FE@H Q  W  G Q E d JMS d e]JlHKE Q  e]Jlk_NTL QYX H Q O N m J \ e]S N
TŽ Œ Ž + + I R (s) vR - iR i 2= i C + v2 = vC R VD u(t) C VR (s) I C (s) = I 2 (s) + Z R (s) = R + - VD s - vC (0 ) = V0 Z C (s) = VC (s) = V2 (s) 1 sC Vo s - m J \ e]SKN
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Q 9‹@E6G GKJ X NTJMG O Q GKN  O N G NTh E O N O E6G CFE6S  ;>= ? ;>= S S ?  ]N_  [ A?  ]  ]N_  [ ] 
X ]  ]_TX ]  [   / ?  ;>=  0/ . - + S    @ = ? @= S  S A?  ]N_ ] X        @=  ! X ]_ A?    / + [ ! 0/ 1 . - + [ + /21 . - [
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6Ž !]Ž + vC i 2= i R + v2 = vR iC C VD u(t) + I C (s) + - R - VC (s) I R (s) = I 2 (s) Vo s 1 sC Z C (s) = VD s - vC (0 ) = V0 Z R (s) = R - + VR (s) = V2 (s) - m J \ e]S N
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 ‚JlS d e]JlHKE  d E6W d E X O JId_f NTh E J X J d JMNTL X e]LMN@Ž  ETLMe d_f NTh E yBDC]LlJ d N X O E  G Q N HKS N X G E6SKW N O N O Q "NTC]L`N dYQ)X E d JMS d e]J H E E6SIJ \ J X NTL ‹FE@H Q  W  G Q E d JMS d e]JlHKE Q  e]Jlk_NTL QYX H Q O N m J \ e]S N 9Ž Œ9‹ O Q E X O Q CFE O Q  G Q Q G d S Q k Q S  e Q    A X ] V A  c = A TS c U A TS c V A  ` ] = A TSb] U A Sb] + iR  vR R v1 (t) u(t) + I R (s) i 2= i C + v2 = vC C VR (s) I C (s) = I 2 (s) Z R (s) = R + - + VC (s) = V2 (s) - V1 (s) - vC ( 0 ) = 0 - Z C (s) = 1 sC m J \ e]S N @Ž Œ  ‚JlS d e@JlH E  Q  e]J k_NTL QpX H QbX N S Q  e Qp X]d JMN d E X O JId_f NTh E J X J d J`N_L X e]L`N  Ž  NTL d e]LMN X O E  G Qa] = A  Q*c = A  ‹ Q W e X d_f NTh E O Q ‹ Q ] A  ‹    c = A S S      A  c U A S c V A ] A ] S U V U      S  A V U  % A ! A    V U  A (
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