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Elétrica

apostila de elétricidade básica

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2401 Eletricidade D ELETRICIDADE !" # %&&7(1 ! "$%& ' ( )!*+,)+ %-$*+! . ! "$%& ( %/0$& 1& +*+$& '2 ! "$%& ( +*+$& *+$+)& '3 ! "$%& ( $-0+! 1 !0,%+ 1 +*+$& . ! "$%& . ( +01$&* ! !+$&* ! "$%& 4 ( !0,%+ 1 +*+$& 0&+1!+ .. ! "$%& 3 ( &$50+! / +*+$& 0&+1!+ 47 ! "$%& 7 ( +*+$& $*+8,+& 72 9: ; < ! " $ % )*+ !,+) $ %"" %!%&!" % !% #!" ' -! ))*+( %! ) " "%"!%!" " !" "%"! + . -! ))*+ • !* %! " " " + # "' • %* " , " !"' • ", " %#!"" & % %' • -* " .0" "! # *%! "2)' &!'()*+, '-+ / 01 +2 +)! • 4 5 "%%!" %" "! #! %! ! %" • 325! % 76 : 4 ) ;! !" !" <+=? <". 6 " !5," "!? 6 #! "! #!" !? #! " !J #! !J < K" %6#!" !J • %!" + "6% 6 " %8 :) 2 ( 325! !A B AC F!" BC H" BHC I!! BIC " "%5 BC -"! B-C ,% BΩC % BC < B2< 01 +=) !,+) " %! % .0" "! " *%! .0" 6' = ] !? B Ω C ρ D !) " %! B Ω ⋅ C D "%%!" BC ] .0" !) B C ρ ⋅ +( %!" " !" + " !? #!' 325! K%" B!" 0" C( )!" B = CQ !%!" B = C' %1 >2 !5 % .0" 6#5 ! !0" "! % % !"' % !" # !A" ").0" )Q ! " ! 6 ! *"%( * = + ∗ *+#) = ∗ = − = = Y = B" !J % " B C C +=) *2 + = ⋅ Q = ' Q = − ' !0"Q = ⋅ = !0"Q = − − ⋅ = ! KZ ( = ∗ = = ' 5"7? !"D !" ⇔ !? ⇔ !0" ! "!' = = = Y ∀ !" 5!" ⇔ !? *! ⇔ "! Q ! !0"' = ∞ = = Y ∀ = − ⋅ 1 @)>> 01 7? 6( "!" !"K0" ! " % %!" " !"' 7( %," *," " % )A % R !%" " R !' A!>( ." + 0" "!#% , % " !" " !"' K%"( E E %1 @)>> . )+ ;@< ^ "% 6#5 "! % + + R % !" # % _ ∑ = = ⇔ Σ "! !" " R $ Σ "! " " R' "79 "! + " RQ !5 B "! " RQ !5 C • • • R ." %, D1 @)>> . +? ^ "% 6#5 !Z % + + ." % !" # % _' ∑ = = "79 " " %," *," " !" >-Q )" !0" "% " %" "!"' K%"( E E − + + − = &!'(2*+!( +( 01 + 2 , ".0" # ⇔ %% "! % !"" " %!"' ⇔ = + + + = = + + + = + + + = + + + %1 + 2 .!! 3" ⇔ 5 6 " % ⇔ = = + + + = + + + ⎛ ⎞ ⎟ = ⎜⎜ + + + ⎟⎠ ⎝ = = + + + = + + + 5).0"( " + ⇔ 7` + D1 )79 + 'E' <"! !0" % # ⇔ + + '' <"! 0" % " <"! !0" % " R "% " !% " %%" )"' '' <"! "! % # <"! "! % # R "% " !% " %%" )"' '' <"! "! % " ⇔ + − E1 "9 +9 = = ⇒ = + = % 6 = F1 ))*+ " )+ + + + + " = + = + = = = = + = + + " = + = + A G! = + " = + + + * Υ→Δ 279 Δ→Υ ⇔ ⇔ !? + )! ! \ + = + BEC + + !? + )! ! \ + = + BC + + !? + )! ! + = + BC + + 279 Δ → Υ = + + = + + = 279 Υ → Δ = + + = + + = + + + + &!'(8*-0 10,'1 +!( %1 39 + !"#$ % ! &!$!%&!$!& $! !& $% $&! % '! : )*+ .! !" 0" %/ 9 ;< = !"!!!#$ %&& ! !% "'%=() +> "*?) ","> -0 > ( ' ) + (!% !%$%!$$ )$! > + , -$ !% #&! . %, & /! " = − + = − − = − 0$$ % &#!1! #&!%!2!%). ! ! !$3 !$3 #" !$3 &!#+ & 0%56!&#!1! #&! %!2!%) $&!%& &$$ %%! !$$& & = = − # % (!73 + ! 9!$ (!% $$ !&!! 7:!$ )%? ; % ; .Ω .Ω 0;) .Ω 0;. − @% @ .%? " < = % " " $ ; .Ω .Ω − − .Ω ⎧ = ⎨ = − ⎩ 0;) − − + + − = ⇒ ⎧ + = ⇔ ⎡ ⎤ ⎡ ⎤ = ⎡ ⎤ 0;. ⎨ ⎢ ⎥⎢ ⎥ ⎢ ⎥ 0;. − − + − = ⇒ ⎧ ⎩ = + = − ⎣ ⎦ ⎣ ⎦ ⎣ − ⎦ ⎨ − + + − = ⎩ = !! "* = 0;2 @% 0 " " $ ; . !!!/ = − − − + − = − 0%! 4 = 2 "," 4 0;. 0;2 ! %/ !"3 ! @ 3 $! !! %%! !2 !&! !$3 ; 73 $&!%%2 !&! !$3 ! $$! $#$ A $ ; < ;= ⇔ % % %#$! < $ !%#. ⎧ = ⎪ = ⎪ ⇒ ⎨ = 4 ⎪ ⎪ 4 = ⎩ %/ B < B = !"!!!#$ %&& ! ! ","'%$=() +> "* ) > - @) .!2 73 &$ %%! !$&! B + (!% !%$ & =$! + , 0$$ %! B &! B + 0%5>6!&+ & 9!$ (!% $$ !&!! 7:!$. , !& ( %&$ %%! !$&! )%? ; " % ; " / B ) $ ⇒ %%! !$#" $ @$& %%! !$&!% $. ! $#" $! ! 7:!$ / B . ?$ ! 7:!$. #" $ @% @ " Ω Ω $ %%! !$#" $ Ω / B ) − + − + − = Ω ϕ ϕ / B . + − + − = / B 2 − + ϕ + − = ϕ = − .%? @ % A B % )2 !&! !$3 Ω Ω $#" $ Ω B % . , C/$! !& ! !! Ω / B . + − − + + − = ⇒ = A )2 !&! !$3 = + ⋅ = − = = − = ⇒ !! % %!!2%!!.&! 2 %/ !"3! @% 0 A B % Ω Ω $#" $ Ω Ω B -1$ ! 2 !&! %%! ! !!% !! D ⇒ #" $ !$ = / B . + + − = / B 2 − + − − + = @ 3 $! !! !$3 2 !&! %%! ! 3 C#" %& $$ ! 3" $&!%%2 !&! %%! ! % ,!% !!$%!(!%56> B − + + = < !% %&$ !% ! $ = − % = − 0$$ = ! = − % B C ;2% % . ,&! !%% D!% &!! 7:!$!!$$E%$ '& ,!,1 F#" $ 0E$!< & >!$:!$&!# 0E$!&!? %%! !$&! J(! Ω Ω %" 5 %1 3" 5 5 . (@5 &! !%% $( %!$&! 5 ! 5 &! 2 % !($ & $ !%$!, $& $% $,1 $3 ! (! !$ 5 ⇔ 5 5 5 - 3 $! $ $ !%$!, 2 !&! %%! !&! ( % $& $% $.$ !$:!$ ! $& $% $&!(!$!% ! (! !$ ⇔ 5 5 5 5 %& $! 7:!$ ! &! $&!& '% ! 5 = 6 5 = 7 5"79( ", .0" "! *"! !! # )!Q 5 5 5 ! = − 5 + 5 5 5 = − 6 5 = 7 : &! !%% % ! (! !&!>J(! Ω Ω %" 5 B$ % %% !& !$2 !$&!!&! !$ %" 5 • !%.0" 5 ( "! 6 !% !0" )! " !% BC B5C' • !%.0" 5 ( "! 6 !% !? + )! )! " !% BC B5C "% !" *"! ! % " "' <"! !0" % " " ⇔ = B !"D !"C <"! "! % " " ⇔ = B !" 5!"C' :E &! !%% ! (! !&!>J(! !! %" # Ω Ω # Ω 5 .% D 0 1 5H+" 5!.0" !" + )! % B*"! "! % " "% % !"C ! + + ' # # # ⇔ # 5 5 I&! C %%! ! !(&!%, %(C$&! % /% + C%!$$ )! (! !($ & $ !%$!, ) J% 1 3" F&!%!% & >J(! = = 5 % 1 3" . ! B! !⇒ = ! = 7 6 5 5 ! 1 .+)*! ))*+ )+ . + . + B! !%73 &! &! 5 B! !%73 &! &!$ ! %%". % /% %!,!&! !%% %%! !&! % /% !(& !% !%, : Ω Ω # Ω 5 2 % 1 3" 0% %& % ! (! !&!>J(!.2'!% %$2 %73 &!2 !$ 5 # ⇒ = 5 5 5 5 # 5 % : (@5 , !%E1 ) $$(!&! %!&! !% 5 # 5 # # ⇒B! !%% # &! !% ! )&$$&!$!LE1 ⎛ 5 ⎞ ⎟⎟ # = = # ⎜⎜ + ⎝ 5 # ⎠ # = ⇔ # = 5 ?1'% # ⇔ # # # - 3 # .84 ⎛ 5 = 5 ⎜⎜ ⎝ 5 + 5 ⎞ ⎟⎟ = 5 5 ⎠ # 5 5 # 5 2+ η = # 5 ⎛ 5 ⎞ ⎟⎟ # ⎜⎜ + # ⎝ 5 # ⎠ = = 5 5 + # 5 ⋅ # + 5 . 5 # ?E1 %$2!%)&! )3 C!!$$%! !( L $-1$$ !$&! ) %( E 3" $! % C! & %$&! 2 !&!!!%". C" Σ&$%!$ $ $& &$2 !$&!!&! !$!%! $ (@ 39 <"! !0" % " " ⇔ = B !"D !"C <"! "! % " " ⇔ = B !" 5!"C' <"! "!" 9 "2 "" % " "' I)3)( "5! 6 " ".0"' Ω Ω 6 &!'(K*01!(+ (+ 1 *+ 01 )+3+) *+ \%! " *+ # % "!)" !% "%"!" % *" " !"Q "" % ' "%"!%!" " !" 5 % *a%" "" %" %6#!"' .0" % "! )&) " !" " A % %" %6#!" )&) " "' 4% %" %6#!" )&) A % !0" " !% " !" !0" # """ b !K ).0" "! + " !)' !%!%!( "!M0N < K" %6#!" "!" Φ = # ⎫ ⎪ ⎬⇒ Φ O <L = ⎪⎭ 0" % -"! %" TU *+#) % JK TJU # = # = # # = − # 5"7?( P " )+ , )++Q +9 ! " !% % !" # *! 1 %Q " !" "%"! "%" % !"D !" "! "!2 ' "! + !) % !" 0" " ) !!%!Q " [Q I+ ,) )+ *+' )+ " 5*)2+ # "+ >- +9 + B%"! " % !" K!"C ! " !% " !"' "!" % " # !A" %" %!%!%! ! *a%"' ! " !%" % 2.*! +9 " !% " !"' ' "! % % !" % * .0" !0" ! " !% " !"( = # ⇒ ∫ ⇔ = # = = ∫ ∫ # # ⇒ − = ∫ ⇒ = + ∫ # # ' "!? 6 " !"( ⎧ ⎪⎪ = ⋅ = # ⎨ ⎪ = ⇒ = ⎪⎩ ⇒ ⇒ = # ⇒ ∫ = # ∫ ∫ = # ∫ ⇒ − = ⎡ ⎤ # ⎣ ⎦ ⎡ # ⎣ − ⎤⎦ = Q = Q !0" = # ' ⇒ − = 1 .)+ !" # % "!)" !% "%"!" " " !" " % "!' "%"!%!" " !" 5 % *a%" "" " %" #!"' %" #!" 0" " A" " % "! TU .0" 6 #!Q " [Q " !0"' !0" 6 # """ b *. "! "%" ) + + $ )' 5%" + $ +G!' % .0" !0"D "! " !" " ! 6 ! *"%( 0" T-U Δ = .)+#)Q % TU 5"7?( P " +9 # )++Q )+ % % !" , *!Q " [Q " !" "%"! "%" % !" 5!" "! "!2 ' !0" " !% % !" 0" " ) !!%!( I+ ,) +9 ).)+' +9 " 5*)2+Q # "+ ,& )+ + B%"! " % !" K!"C " " !"' "!" % " # !A" %" %!%!%! ! *a%"' ! " !%" % 2.*! )+ " " !"' %1 !7? +G . ).)+ ⇒ = ⇒ ∫ ∫ = ∫ = ∫ ⇒ = + ∫ D1 +=) G ).)+ ⎧ ⎪⎪ = ⋅ = ⎨ ⎪ = ⇒ = ⎪⎩ ⇒ ∫ = ∫ ⇒ ⇒ = + ∫ = ∫ ⎡ − ⎤ ⎦ ⎣ = = Q = 1 )7? *+ ).)+ 2 , 2 .!! 01 )7? *+ 1 *+ 2 , # # # # = + + + + # + + # = # = # ∴ # = # + # + + # !" % # "% "%" !" % #' L1 *+ 2 .!! # # # ⇔ # = + + + = + + + + + + ∫ ∫ # # # ∫ ⎛ ⎞ ⇒ = ⎜ + + + ⋅ + ⎟ ∫ + + + # # # ⎠ ⎝ # = + + + # # # # !" % " "% "%" !" % "' !"Q # = # # ' # + # %1 )7? ).)+ 1 .)+ 2 .!! = + + + = + + + = = + + + = = = + + + !" % " "% "%" " !J % "' L1 .)+ 2 , ⇔ = + + + = = + = + + + + + ∫ ∫ ∫ ⎛ ⎞ ⎟ + + + + = ⎜⎜ + + + ⎟⎠ ∫ ⎝ = + + + ' !" % # "% "%" " !J % #' 1 *! 79( " !" 0" * + .0" %, + !A % !% %% *"% %!%&! + + .0" " + !A " " !"' .)+ = *+ = # ↔ ⎫ ↔ #⎭ 0" 6 !? !J !"D !" %J R B0"D*?C R *? %" &)" # : A ⎬ *! "! < K" " !J !J !" 5!" %!J , , K! B."C %" 6.0" " : I2.!( !%.0" % !" !A" !5 % E' "" % R % %, c % R *? # ' 6 # 1 .+ +*! *2 ))*+ !" !) "" % 6% %! + " % = ".0" ".0" L' !% . ≥ M' # = ,) = = Ω = Ω = Ω # = 5 A2 !$& (!! %!"!!%! ! # ⇔ # # = = . + ⋅ # − = . B 2C " &! $& (!! # # # # ⇔ # + = # + # = # = − ⇒ ∫ # = − ∫ # # # # # − ⇒ # = − + 9 ⇒ = # 9 $ ⇒ # = $ − # ⋅ 9 # ".Z ( # + = $ = $ "%" ,& # "! " !"Q # − = # + = . = $ ⇒ # = − . # : " . " # % = + = − ( C !A" KZ "! % ! $ MD % ! $ Mc ⎡ . − . ⎤⎦ = ⎡⎣ − . ⋅ .− . ⎤⎦ = − " ⎣ = = # + = # − = 5C 4!A" " !" "6" " " ,)%!" # + # + − ⋅ . # = # ⇒ = # + = = − " + = + ( = # ⇒ + # + = = ⋅ − . ⋅ .− . = − " = &!'(L*0,'1 +!(0(1 01 + 1 <"! !0" B"!C " " A% % !0" B"!C + ) "% " !%"' = $! = $ v (t) i( t) 1 c ic lo Ip x 1 V p x 1 0 .8 0 .8 0 .6 0 .6 0 .4 0 .4 0 .2 0 .2 0 0 -0 .2 - 0 .2 -0 .4 - 0 .4 -0 .6 - 0 .6 -0 .8 - 0 .8 -1 -1 0 1 .5 7 0 8 3 .1 4 5 9 4 .7 1 2 4 w t 6 .2 8 3 2 7 .8 5 4 9 .4 2 4 8 ra d 0 1 .5 7 0 8 3 .1 4 1 6 4 .7 1 2 4 6 .2 8 3 2 w t 7 .8 5 4 9 .4 2 4 8 ra d "5'( • • * .0" " # % * .0" R !" # ! % !)" 6 ' 4% " * .0" # % !," + "%. % % ! %! !% %% %! ' !%" &" " % " # ,%" 2""' • *+=? # " ;%" " " 6 " • <+=? 6 • = π → = = M 5< N " "G' π M ! "N • < .0" "" *" = $ + ϕ ϕ # " J6 " * * .0" "" # 6%! !" % 6 ' G K'( = $ + *"%.0" " = $ + • π !% *6% ! * .Z "' [ = $ + α = $ + β !0"Q !& !" α − β % .0" b K'( = " − = $ + = $ − − = $ − = $ + + = $! + !& ! − − = − % .0" b ' " !& ! + % .0" b ' %1 .+ $ = + # $ # # R!( !" !& % 6% %! $ = + # 5! % "! % 6% %! " "" "5! " .0" ! + .0" * BEC' " .0" ! + .0" * !% %% *"% + *"! K!.0"Q !0" )%" " + = $ + ϕ ' 5[!)"( !% ϕ ' $! ± = $! $ ± $! $ $ ± = $ $ ± $! $! $ = $ + ϕ + # − $! + ϕ $ = M $ $ ϕ − $! $! ϕ N − # M$! $ ϕ + $! ϕ $ N = M $ϕ − # $! ϕ N $ + M− $! ϕ − # $ϕ N$! " !*.0" )&) $ ϕ − # $! ϕ = BC − $! ϕ − # $ ϕ = BC *A" +' BC c BCQ !%"( + # = ⇒ = + # +' !%"Q $! ϕ = − # $ ϕ ⇒ ϕ = − ! % "!!"Q = # + # $ − ! % # "%" "!! + "! !& ! ϕ % .0" b !0"' D1 1 *.0"( <" # % ;%" "%K" + ! % !0" " % "! !Q [ ! ! % 6A "D" % !$M' "!" *" # 5" ! ( ± =θ = $θ ± = $! θ !*"% *" % !0" " # *! 6 ! *"%( = $ + ϕ { = ℜ { = ℜ { = ℜ = + ϕ = =ϕ } } } = = <"% K" <" !0" = =ϕ = ∠ ϕ = $ϕ + = $! ϕ <"% " ⇒*"% *" !* * .0" " " "%2" " !%" " "%2" *+=?' K'( = $ + MPN = ∠ − MPN = ∠ MPN = $ − MPN E1 I)+79 2.!I )B!C B!C = $ + θ ⇒ = $ + θ = = $! + θ ⇒ = = $! + θ @ '& ! &!$ !% $73 = + = [ $ + θ + = $! + θ ] = = + θ ⇒ = + = [ $ + θ + = $! + θ ] = = + θ = + θ = + θ <!" = % !"" " !%"Q " %%" " !0" %" *" 5!"' % " !" " "%2" *+=? #( =θ =θ F1 !2+ ." 23 MN=) X'EC " !"' 4!A" % K!.0" "%K " !" = = + θ !%" % "! " !" = = + θ " ,% = + θ = ⇒ =θ = = + θ = =θ ⇒ " "%2" *+=?( = !" " "%2" *+=? # 0" "! % * X'C " !" = # # = + θ = # = = + θ =# = + θ =θ = =# =θ =# = =# = #∠ " !"Q "! ! ! NM° % .0" b !0"' X'C " !" = + θ = = M = + θ N = = = + θ =θ = = =θ = = = = = ∠ − = " !"Q "! !& ! NM° % .0" b !0"' K%"( !% B!C % 6% %!' # $ " "%2" *+=?( = =# ∠ + =# = ∠ + # ∠ ! % ∠ = ∠ ∠ − ! % 2. #) ; > < 2+#) ; 7 < %JB >C A0" ! " *" !0" " *" "!' > BΩC > # % ;%" "%K" % 0" # % *" # + # = >= # + # $ − ! % # ℜ { > } = = ""0%! > = > ∠ θ = + = Ι { > } = = !?%! %J "% %% *"% + !?' # > = > + > + + > " = + + + > > > > , %!J B 7 C A0" ! " *" "! " *" !0" % % %!"' 7 = 7 Ω B " C = 7 7= > 7 = 7 ∠ θ @ = + = " !J !J %!J "% %% *"% + !J' # = + + + 7 7 7 7 " 7 = 7 + 7 + + 7 5).0"( > = ! + = 7 = !− = = = + = = ! + > !+ = ≠ ! = ≠ ! ! + = ! + P1 -! ))*+ !2+ . + 1 !% " !" + )! " "%2" *+=? " !" ! "' d'EC & " %" "%!" + " 2! " ' d'C & %, % ! " ' d'C *"%.0" *"! - 2! " ' d'C "% ,8) " "!" "5'( *"! !! $ *"! %! * M' = ∠ d'XC ".0" Ω $ + Ω 5 $! + = ! " Ω Ω ∠ = Ω = ∠ + = = .∠ − . = ! " ′ ′ = − Ω Ω = ! " ″ ″ = Ω − = ∠ + = = Ω ″ = − .∠ − . ∠ ′ ″ ≠ + + " 0" !0" %% *+=?' = . $ − . − − . $! − . Q1 G2 0" !.Z " " "%K" !"" " *" !0" "! + % % !"' %!% ) A *6% ! " *" !Z "!' 6 "! .0" " 6%( • • • • • " !" "! !& % * "% !0"' " !" "! !& ! NM° % .0" -' " !" "! !& ! NM° % .0" -' K%" E( # μ A .5 4 % " % 6% *" !% + "! " !" *+ ! X° % .0" b "! *"! ' = ! " = # + + ∠ = = = ∠ − # − > # = × . × + # = = ∠ > X = # = ⇒ = ⇒ = = Ω ∠ K%" ( " !" 5K"Q " %2%!" X ' "!" " *" "%" *?Q , " 6% *" !% ' Ω 6 Ω = Ω XM = = × = × = = = = = = 6 θ 6 = . + = . − = ! % = − 6 = = × . = . = 6 + "%"! ,"A"! = + 6 $θ = + . $− . = "%"! )! = 6 $! θ = . $!− . = − = θ + − = . − = ! % = − . 9! θ θ e + θ = ! % OX θ = + = OX = .∠ − . M N &!'(M* (N0 /+!(0(1 01 +=) ++# = %1 +=) 2, = ∫ + " D1 ! ) )+ +9 #!"" "% "!? %# % !" %! " *"% " *!' = $ω + ϕ = AQA $! = $ω + ϕ = P!%273 +=) + !2+ . = A ) %!$$ %! & %0 = = $ ω + ϕ ! $ = + $ = [ + $ω + ϕ ] = ⇔ = = → = " 0"( 4% " "% %! " 6 %% "!? + % "! "!! )" "5 % !"' #!"" 6#" !% " )" *A % 6A ⎛ ⎞ + = ⎜ ⎟ = " = ∫ ⎝ ⎠ " = + ∫ 5'( " " = Q " = 01 +=) 2 !2+ ." 'E' " 6 B%J + + C ϕ = θ − θ ο = ο >= > φ $ω ° = = = − φ = − φ > > > ϕ ° = $ω − ϕ = = $ω $ω − ϕ ⎡ ⎤ = ⎢ $ω − ω + ϕ + $ω − ϕ ⎥ Q" ⎣ ⎦ $ $ = [ $ − + $ + ] = $ϕ + $ω − ϕ = " " $ϕ + " " $ω − ϕ Q" $ − = $ $ + $ $ = " " $ϕ + " " [ $ω $ϕ + $ω $ϕ ] = " " $ϕ [ + $ω ] + " " $ϕ $ω • "!? !!J "!? !!J ! !) > ! !) > "!? %#( = • ∫ = " " $ϕ Q T I U "!? !)( -" " "!? !!J ! !)' B = " " $ϕ '' !" !)" 0" "! % *' θ = θ ⇒ ϕ = ' = " " [ + $ω ] = ∫ " " [ + $ω ] " = " " = " = B = '' !" K )%! !)" θ = θ = − ° ⇒ ϕ = ° = " " $ω # = " B# = " " = 6 # " = 6# !" K )%! !)" θ = θ = ° ⇒ ϕ = − ° = − " " $ω = = − " B = − " " = − 6 " 6 %1 +=) .+ + .+=) C "!? !( = " " Q T-U "!? )") *"!' 5C <!" "!?( <!" "!?( "" " J6 " 6Q " "" *6% ! !0" "!' A = $ϕ = $θ − θ T%"U "%" * .0" "" # % * .0" Q $θ − θ = $θ − θ ' !D ^!"_ " ^ !)"_ "! 6 # ! % .0" b !0" " !%Q ^!"_ " ^!)"_ "! 6 # ! % .0" b !0"' • < K" "!? % !"( < " ! 6 • .Z "( = $ϕ B = $ϕ = + B B ϕ = D1 +=) )2.!I ° = " θ φ ° =θ−θ >= > φ = " θ = " " $φ = " " $θ − θ = ℜ { " " $θ − θ + = " " $θ − θ } = ℜ { " " = θ −θ } = ℜ { " =θ " − =θ { } ° ° R = ℜ = ℜ { } } *" "!? "%K = ℜ { } B = F { } = A = $φ ° ° R = = φ "!!" • = + =B ").0" "!? "%K( ° ° ° ° ° R = ° ( ° R ° = + ° ° ° R ° ° = + = + R R ) ⇒0" %"! "%" " %!" !0" "!" ! Q !% "!? "%K )") *"!Q 5! "% !" "!? "%K %!"' • J6 " "!? B!!.0" 6"%#! "!? "%KC( ϕ > → 6 P ϕ • .Z "( !) ° ° = > ° R ° ° ° R " = = > ⇒ = > " = ° = ° > R R ⇒ = " > R 7 R = 7 " E1 79 + .+=) 5[!)"( %A !" 6 !) ! *"! 6Q % ! 6 ;! 5") 6' ϕ P f ϕ S Pf K%"( 4% 6 XMM 7- "% *!" "!? 6 MQO !"Q # %!" "5 % !0" EQe 7-%' * $ OM A C !% "! 6 5C [D "6 " *!" "!? MQN !"Q !)# 6.0" !" % " "% 6' !% " )" !J + ' C ") "! 6' " .0"( × = = . " C = . × ° 5C = × . ° = 9 + = 9 = 9 B = 9 $ϕ = . ⇒ ϕ = . ° B S = ! % $. = .° = .9 S = $ϕ S B S = S$ϕ S = .9 P f ϕ "!? !) " !"( Pf ϕ S B = B S− B = − . 9 "!? "%K " !"( ° ° ° R = = ° + =B ° ° R = =B ° ° > > = R R = =B ⇒ > R = =B R ⇒ > = =%ω − =%ω . × = − = .μ A π × × − . × S . × = = . C S = . × = − B π F1 =) 2-I2 .+=) 5[!)"( "5! > # %"" + "!? !) 6 [ %&K%' > = + =6 ° > # = # + =6 # \ e'E 6 %! !) → > # > ° # ° # ° ° # = = > + # + =6 + # # = + # + 6 ° "!? 6( = # # # = # # = + # + 6 # 1 " # = # = # + 6 = > e' 6 "% *K" g )&) > ° # # ° =6 # \ ° # = + # + = 6 + 6 # ° ° ° # = + # + 6 + 6 # "!? 6( # = # # # = + # + 6 + 6 # # 1 " 6 = − 6 # # 1 # = + # > e' 6 "% )&) g *K" # =6 # \ # = ( # = + # ) + ( 6 + 6 # ) # ( + # ) + ( 6 + 6 # ) + ( 6 + 6 # ) !0" # = Y # 1 " # = # e' 6 "% )&) g )&) > # ° =6 # # = ( # + # ) + ( 6 # + 6 ) <A" 6 # )( # 1 6 # !0"( # S = # = − 6 ' ( + # ) ' % 6 Q *A" # )( # 1 " !0"( > # R = − =6 = > ' # S = ⇔ # = ' # &!'(O*+!( +?,( 01 ? +-) M*!5 • 4% !% !Z !*& + 5 # % "[ !" !Z " "% %% %% %! Q %% *+=? % * ! EMh' • !Z 0" ,% !Z * Q Q ' • +=? * B*6% ! !Z *C( ° % ° ° ° ! ! ° ° % +=? Q 6!) " ! +=? Q "!) " ! ° ° ! = ° ! = ° ° ° = − ° = ° ° ° % = + ° ° ° % = − ° ° ! + + % = • " 6.Z "2) % 6" φ ( ° ! ° % ° ! ° ° % 5 !" i ° %! 5 !" Δ %1 -! ))*+ RCR ;M*!5 < ° ! ° ! > ° ° ° % 5 ° \ > > ° % • Z *( Z ! " !" % ,Q " !Z " !% %!"' ° ° ° *"!( ! Q Q % ° ° ° 6( Q Q • Z ,( Z ! , ° ° ° *"! $ 6 ( ! Q % Q %! ' • "! " !"( ° ° ° ! ° ° = ! + + % ° = > ° + > ° + % > = ° ° ⎞ ⎛ ° ⎜ ! + + % ⎟ = >⎝ ⎠ "!!"Q 0" K! "! " " !" % !% + 5"' !0"( ⇒ P " K! %J , " !"Q " %%" " "" "%" % !" !"' ⇒ P " " !" 0" !& "2)Q " %%" " """ " !" *!" & "' • .0" ! !Z * ,( "" +=? ⊕ !0"( ° ! = ° ° = − ° ° % = ° ° ° ° 5" + ! = ! + ° ° = ! − = ° − − ° "6" ° ! = ° % = ° %! = ⎡ ⎤ = − $− ° + = $− ° = ⎢ + = ⎥ ⎢⎣ ⎥⎦ ° ° *"% % 6 !" = ϕ − ° ° .&! = ° φ + ° ° % ° ! ° ° ! ° • !" %""*&" + )! B)&" "%! !% + 5"C( Q5Q Q\Q ° ! ° > ° % D1 -! ))*+ RCΔ ;M*!5 < ° ! ° ! 5 ° ° ° % ° % "! *( ° ⎛ ° ° ⎞ 6( ⎜ . . ⎟ ⎝ ⎛ ⎠ ° ° ° ⎞ *"!( ⎜ ! . . % ⎟ ⎝ "! ,( ⎠ ⎛ ° ° ° ⎞ 6 $ *"!( ⎜ ! . . % ⎟ ⎝ ° \ • >Δ >Δ ° ⎠ !%.0" "! ,( >Δ ° ° ! Q5Q ° K'( Q\Q ° % ° ! = > >7 = ° ! >7 ° % = ° % >7 ° ° = >7 !" %""*&" + )! • !%.0" "! * 6 .0" ! "! , "! *( ° ° ° ! = − ° ° "" +=? ⊕( = ° ° = − ° ° = ° ° ! = ° − ° ° ! = − $ ° + = $ ° ° ⎛ ⎞ ! = ⎜ − = ⎟ ⎜ ⎟⎠ ⎝ ° ! = ° = ° % = − ° − ° ° *"% % 6Q ° !" = ° ° .&! = φ − ° 5).0"( " 6" !) 6" % ΔQ 5!! D " %%" " % 6" + )! 6" % i ! + !0" , , %%' ° ° − ° ° 5 − ° − ° 5 +=? ⊕ .&! = !" ° ⇒ !" = .&! )*+ D M*!5 φ 'E' 6 + 5 % i "% !" ° > ° > ° > \ ° !" !' ° ° ° ° = + + ≠ ° ° ! " = > ° = ° = ° > ° > − ° '' 6 + 5 % i % !" ° ! ° > ° ° > > ° ° % 4!AD " %#!"" %,' ° ° = ° ° ° ° = − ° = − '' 6 + 5 % Δ • " 0" ", !Z , 6Q 5!! D " !" Δ " + )! % iQ !AD " %#!"" %,' > > > • > > > ",D !Z , 6( ⇔ ° ! ° ! ° > ° > \ > ° % ° = ° > ° = ° ° ° ° $V ! = − > +=) 2 +2 D φ > = > φ > = > φ > > = > φ > > \ φ . . = θ . . − θ . . Z * !!J( "! * !!J( = $ω + θ = $ω + θ = $ω + θ = $ω + θ = $ω + θ = $ω + θ 5" + $ $ = [ $ + + $ − ] "!? !!J % *( = = " " $ φ ⎡ ⎛ ⎢ + " " $ ⎢ ⎜ ω + θ ⎜ ⎢⎣ ⎜⎝ "!? !!J !"!( = + + "!? !) !"!( = + + = " " $ φ + " " $ φ + " " $ φ X'E' % !% + 5" " = " = " = " > = > = > = > ⇒ φ = φ = φ = φ " = " = " = " • "!? !!J( = " " $ ϕ • "!? %#( = " " $ ϕ → 6 6 % i !" = .&! !" = .&! 7 = .&! .&! $ ϕ ⇒ 7 = .&! .&! $ ϕ → 6 6 % Δ !" = .&! !" = .&! = = 7 .&! .&! $ ϕ ⇒ = .&! .&! $ ϕ ⎤ ⎞ ⎟−φ ⎥ ⎥ ⎟⎟ ⎠ ⎥⎦ 9!$ P!F!( %!$!2'!$ "! "!? !) = $ ϕ = $ ϕ = # # $ ϕ "!? !) B = $ ϕ B = $ ϕ = # # $ ϕ "!? ! = = = "!? "%K ° <!" "!? ° °R ° ° ° R = = A = $ ϕ A = $ ϕ X'' % !% + 5" "!? !) !"!( = + + "!? !) !"!( B = B + B + B "!? ! !"!( = + B <!" "!?( $ ϕ = ° ° ° ° "!? "%K !"!( = + + A .+=) 2, 2 *2 ))*+ Dφ O'E' I!!2%!" 5"5 "! B!? 5KC - 5"5 !0" B!? !C 5"79 L5 )+ 2 , )2 )G \"5 !0" % " "% 6' = $θ − θ O'' %#!"" " " I!!2%!" # # " 5 7 = !% ! $θ !% − θ ! = % $θ % − θ = + K%"( 6 !) 6 % iQ " 6" 6" % i( +=? ⊕ ! = ° = − ° % = ° >= >ϕ .&! = ° %= !" ° ° ° %= − ° ° ° %= − ° ° ° !% = − %! ° %! = % ° ° %! = ° ° ° %! = ° ° ⇒ = − ° = ° ! = ° ! > = ° = −ϕ >ϕ ° = − ° ° = = = ° > = − ° = − ϕ − ° >ϕ $− ° − − ϕ $− ° − ϕ − ° = # # $ϕ − ° = # # $ϕ + ° 5'( " !% + 5" # "2) !% " *!" "!? 6' = # # [ $ϕ $° + $ϕ $° ] = # # [ $ϕ $° − $ϕ $° ] + = # # $ϕ $° + $° $ϕ = − − $ϕ $° − = − # # $ϕ $° $ϕ + − = − = − ϕ $ϕ − ϕ = + ⇒ = ϕ = ⇒ ϕ = ⇒ $ϕ = ⇒ 6 !) = "% "!" → 6 !) > ⇒ ϕ > ⇒ 6 !) < ⇒ ϕ < ⇒ 6 !) J@ $ PQ R%0 P %+%% S P:B P)TTT%J0UG.U)G82LK2G)% 8 P1 %Q B P Q B '%S@ PQ B V+%Q B %% S J P W 3" P)TT8%J0OKGMUK8GU8MGM% % DP/%1 %% R @B $ VP)TTO%J0UGK28GTKUTKGM% + E G ! P+ @'%J V %% S J PO 3" P)TTO%J0OKGMUK8GUMOGM% ! @PQ%1 X %% P8 3" P.UUU%J0OKG28LGULT2GK% ! @PR S%S VQ%PQ Y% ZV%%/[ XGSP)TM2% PQ B% %%/[ XGSP)TOU%