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We first qualitatively examine the camera flash circuit, after which we will derive the equations.asu_toutdefinition1a_tinIntroductiondefinition1a2.1When the camera is switched on, a battery slowly charges a capacitor to its full potential via an RC circuit.definition1b2.2When the capacitor is fully charged, an indicator typically lets the photographer know that the flash is ready for use.definition1c2.3The photographer then presses the shutter button, quickly discharging the capacitor through the flash (a resistor). The current from the capacitor is responsible for the bright light that is emitted.intro1b_tinintro1b2.4The flash rapidly draws current in order to emit the bright light. The capacitor must be recharged before the flash can be used again.intro1b_toutintro1c_a_tinintro1c_aThe battery is modeled as a voltage source in series with the battery's internal resistance.2.5Now look inside the camera to see the circuit. Initially, a battery is connected in series with a capacitor.intro1c_a_toutintro1b_a_tinintro1b_a2.6If the capacitor is initially unenergized, then the capacitor is charged by the source voltage according tointro1b_b2.7NO TEXT: When the capacitor is fully charged, the voltage across its terminals is equal to the source voltage (Vc = Vs).intro1b_c2.8By pressing the shutter button, the photographer disconnects the capacitor from the voltage source. This action also directly connects the charged capacitor to the camera flash resistor.intro1b_d2.9This new mesh is an RC circuit. As the energy stored in the capacitor discharges across the resistor, the capacitor voltage drops according tointro2a3.01We will now take a more in-depth look at the charging of the capacitor and derivation of the equations.chargingintro1_tinCharging of the Capacitorchargingintro13.1The I/V relation for a capacitor ischarging1_tincharging13.2Because it is simpler to express the capacitor behavior in terms of current, we will use KCL (nodal analysis) to analyze this RC circuit.charging2_tincharging23.3We locate the ground node at the negative battery terminal.charging33.4NO TEXT: Applying KCL between the resistor and capacitor yields the following expression (note V1 = Vc)charging43.5Rearranging and grouping terms givescharging53.6This is a first-order differential equation with constant coefficients of the formcharging6_tincharging63.7In general, the differential equation has two solutions:charging73.8The complementary solution is found by considering the homogenous equationcharging83.9NO TEXTcharging93.10The particular solution is determined by considering the full differential equationcharging103.11NO TEXT: Substituting Xp into the differential equation yieldscharging113.12NO TEXT: the equation morphscharging11b3.13The total solution is the sum of the complementary and particular solutionscharging123.14charging12c3.15NO TEXT: Initially at t=0, the capacitor is uncharged, that is, Vc(0)=0. We can use this fact to find K.charging134.0We can now look at the discharging of the capacitor.charging13_toutdischargingintro1Discharging of the Capacitor4.1The I/V relation for the capacitor isadischarging1_tinadischarging14.2Since it is easier to express the capacitor behavior in terms of current, we will use KCL (nodal analysis) to analyze this RC circuit.adischarging2_tinadischarging24.3Locate the ground node at the negatively charged terminal of the capacitor.adischarging34.4NO TEXT: The voltage at node V1 is the voltage across the capacitor. Applying KCL at V1 yields the following expressionadischarging44.5adischarging54.6adischarging6_tinadischarging64.7adischarging74.8The complimentary solution is found by considering the homogenous equationadischarging84.9adischarging94.10adischarging135.0NO TEXT: Combining the graphs from the capacitor charging phase and capacitor discharging phase describes the complete transient behavior of the camera. Here we assume that the shutter button is pressed at five tau, when the capacitor is fully charged.adischarging13_touttime1_tinTime Constanttime15.1NO TEXT: Here we assume that the shutter button is pressed at five tau, when the capacitor is fully charged.time2_tintime25.2NO TEXT: Reality is that R1 is an internal resistance of the battery. Aging of the battery, in essence, increases R1 and hence lengthens the amount of time required to charge the capacitor. This leads to a conclusion on why cameras use a capacitor (because with a capacitor the discharge voltage is very reproduceable).time3_tintime35.3NO TEXT: time constant calculationstime4_tintime45.4NO TEXT: Another term related to the time constant is the settling time. The 5% settling time of a first-order system is three time constants, that is the system response is at +/-5% of its final value within 3 tau.time5_tintime55.5NO TEXT: Ditto for the discharge phase.time6_tintime65.6The time constant also appears in the frequency domain representation of a system. 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EzQJU p]P r]<@npr in3?W+pos1togglegotoAndPlaychargingcharge1 R R Fnu>oKFi@charge1Fvwx@ wy@ z@ -͎{@ dh|S} ~@ (Z@ps!yK@ X@_ įgMcrd`eHj Jj eإo6m@circuit1@@@@?@ in2?z:throwtogglegotoAndPlaychargedcharge1loop1circuit1 R R R@@@@?cLjnҵeH@ in4 ę ed`n kpeY L]P@ T"]P@ PVpe怡 iPeo2C@ 'ǯpe谥2C h( ǯeq8@ ĘsejХY jt:eXn@?[/dischargecharge1gotoAndPlayloop2circuit1 R R cƑ.eoj ƕex"􈟁 T\i@"@ oi@ _@S\i@t@ oi@ _@Ri@@ oi@ԓ _@Qi@X@ oi@ȓ _`Q\i@@ oi@ _`P\i@@@ oi@ _`O\i@@ oi@ _`Ni@$@ oi@_@Mi@*@ oi@ _N i@@ oi@x 􈟁N i@l@ oi@l i@X@ oi@` 􈟁O\ i@D@ oi@T i@,@ oi@D 􈟁O\ i@@ oi@8 i@@ oi@, 􆟁O\ i@@ oi@  i@@ oi@ 􆟁O i@@ oi@ i@@ oi@ i@@ oi@ 􆟁O$i@@ oi@ i@l@ oi@ܓ 􄟁O$i@X@ oi@Г 􄟁P\$i@@@ oi@ĉ i@,@ oi@ 􄟁P\$i@@ oi@ i@@ oi@ 􂟁P\$i@@ oi@ i@@ oi@ 􂟁P$i@@ oi@ i@@ oi@| i@@ oi@t 􆟁Oi@@ oi@h 􊟁N(i@|@ oi@` i@t@ oi@T i@p@ oi@L i@l@ oi@D i@h@ oi@8 i@`@ oi@0 i@\@ oi@( i@X@ oi@  i@T@ oi@ i@L@ oi@  i@H@ oi@ i@D@ oi@ 􊟁N$i@@@ oi@ i@8@ oi@ i@4@ oi@ i@0@ oi@܉ i@,@ oi@ԓ 􊟀N$i@$@ oi@Љ i@ @ oi@ȉ i@@ oi@ i@@ oi@ i@@ oi@ i@ @ oi@ i@@ oi@ i@@ oi@ i@@ oi@ i@@ oi@ i@@ oi@ i@@ oi@ i@@ oi@ i@@ oi@x i@@ oi@t i@@ oi@p i@@ oi@h i@@ oi@d 􊟀N\$i@@ oi@` i@@ oi@\ i@@ oi@T 􊟀N\ i@@ oi@P i@@ oi@L i@@ oi@H i@@ oi@D 􊟀N\ i@@ oi@@ i@@ oi@< i@@ oi@8 i@@ oi@4 i@@ oi@0 i@@ oi@, i@@ oi@( i@@ oi@$ i@@ i@x@ oi@  i@t@ oi@ i@p@ i@l@ oi@ i@d@ oi@ i@`@ i@\@ oi@ i@T@ i@P@ oi@  i@L@ i@H@ oi@ i@@@ 􊟀N\i@<@ i@8@ oi@ i@4@ i@,@ i@(@ 􊟀N\i@$@ oi@ i@ @ i@@ _N\i@@ i@@ i@ @? i@@?0dischargecharge1 gotoAndPlayR 􈟁 O\i@@ in1 oi@gMcrd`eHj Jj eؐ@?^2chargingcharge1gotoAndPlayloop1_tincircuit1 R R oi@ jKjeؕ$@ oi@ @ oi@ @ oi@$ @ oi@, Y>@ oi@0 n@ oi@8 @@ oi@@ {@ oi@H 4@ oi@P T@ oi@T x@ oi@\ @ oi@d Ø@ oi@l Ӑ@ oi@p 8@ oi@x ;@ oi@ ?@ oi@ 2C@ oi@ BF@ oi@ TJ@ oi@ dN@ oi@ vQ@ oi@ U@ oi@ Y@ oi@ \@ oi@ `@ oi@ȉ d@ oi@Љ h@ oi@ԉ k@ oi@ܗ j Jj eإo@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@$@ oi@,@ oi@0@ oi@8@ oi@@@ oi@H@ oi@P@ oi@T@ oi@\@ oi@d@ oi@l@ oi@p@ oi@x@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@$@ oi@,@ oi@0@ oi@8@ oi@@@ oi@H@ oi@P@ oi@T@ oi@\@ oi@d@ oi@l@ oi@p@ oi@x@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@ oi@@??.chargedcharge1 gotoAndPlayR oi@@ 2D &EzQF ГnGQG i@4@mnsbZfw&"Sb]͆ʉx>M9!O8rC'>-?T?xHUs$/oQfD ,s&G`friެL:#8mw7j\'M=qc۹ &-ېt=yANҶ*(kll4a? q}'l\.,?8;Ν ֺؙ17jbia<%VW]tM#i눻lzls5:ws/ x(O'8[Ono>VU6л KD &@@@@?@ D &@ xWD & pressŽlj>i@UFr>S&ʋ2?|wsz=L vxD2u]P|@ [AE]P@@@@rs?Frz=L5s@rx| fadein?,fadeincamera gotoAndPlayR6yE(camera@33L˹ @fgY˶@əff˳@s3˰|@ in "l=@??,insidecamera gotoAndPlayR@ flash_tin?/flash_tincamera gotoAndPlayR@?@ flash_tout?0flash_toutcamera gotoAndPlayR@@@?@ fadeout?-fadeoutcamera gotoAndPlayR@P @5UMUK)X@*J˲@ HK&@VEUH@ B #@?yE(@ releaseŽlj>i@UFr>Sʋ2Jwsz=L x@ ]P{@ \;]P@sy@syݩ@syi̒x@sy#H@x standard_x?xLtU{@ \<@rsx{ introflash_tinFr>S&ʋ2?|wsz=L vxD2u]P|@ [AE]P@sz=L@sz=L@sz=L@sz=L5@@~􈟁 bi@%@ ~_@Yi@@ ~_`T i@@ ~_`O`i@@ introflash ~_@Ni@@?~􈟁R@ introflash_tout ~_Yi@@ ~_\i@@ ~__i@@ ~􈟁 ^i@@~@@@@@@@@rsx|Fr>Sʋ2Jwsz=L 7x@ ]P7{@ \;]P7@sy@syݩ@syi̒x@sy#H@x?xLtU<{@ \<@ standard@@?@ ready}2#B|i@@@@@@?@rsx{} in1?*in1camera1 gotoAndPlayR6 "l=Ecamera1@@@@@?@ in2?*in2camera1 gotoAndPlayR@@@@@?@ in3?*in4camera1 gotoAndPlayR@@@@@?@6ƀ9>@camera1? cOveranda ddx5Vdro|2d ~ _ s (  - <P~ T@=^0BYs.Ji,0$6VSpt+CG 5 W !!!!\!!9"P"##X####6$$0%q%%^&y&K'''((((C)o))2*C*****+m+++`, -l---6...[//-0\0000171\111E22933`44555R667@77$88x9*::;>P???@(@O@@?AABBCCC/DDD9EEEMFF5,Lebcfka)\~Ivả05d1 /=}f{@5hR&ֻ6WbxWcjZ+6mvi{]ľda/Q+l&o5RnXֻjX5fn/>Isd߅ڴ7*FhH\ bPK٦[ZOCj|iDR`7 ,ѯWFTl,kdryCvчt%MzOv,KEdy@Oъn+~JVQY5j΋ m̈́V6*j;7Hl㲖80=` .Ix[3/>L8?5bH12Vtyp7D\{7mVcEfP$5eZY}M'bvo8٬dn6@5,,ePv#b*#D7fka5"'fZ5,Lebgfka5dvojЭ5gf@mO,,i` ;I@p7jVc]U ]XbUtAk??DZZ ǒx*8N֋[h5eyW7-Ö~Nseq8 G@5herw+mb- 1Z6U!RSИA7gyyUG6P\ո@&'dmS'SdLzw15g:ys'^dC `C Tj y1vzL JE*TMJʓj_{د"Xpetv)Wb P``%H}xL#Lu1r25+3FJih@5J]᭸jVj;5Ta'cS؝WSnx, 5g-,ZI 0!!̄02L+0N`MG{`Rb9S#lds+ӛWRZ.=6z~eX5g^ܳ(@`1-SMw*JC0- !L~0/丝?6a5u  a;?2-c3t &,G(yRNW ҘH` M}IlT5`ji'ݞH9W>[v( :c[. d5ge*irVd1bC@&^@Li@ (&$И=Yڗ-:ʘ%fXRh P+@pJ zM,yk*P D%HQH @ *WVmMk5bf1NUJ5f(_JZ AYN#JxsaWMT6NVE>nSPe? 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هs!"rƛy)/Bveranda -./0235689=CDSTVacdeghilmnoprstuvxyCxIÔ j7ԈX@ B*7i|z)o77̉"z9o77̊|fy87D( ފoMlSz 7 +> I8V+57i&"B8oF &AޤB2 HQ(72'ӍfEA 8ި7 D,3"H8ގo M3"$YoN7 HnE7 &c")odU7̊|fTި77A X7ԈPx 6 08V $77 no!@B>B BƝ@X $^ BB>B B7C*HcDpo^  j$oq oޤooM!oĜ޴̅oެooQ ̅ooDlEd|NWX<%/,FX]4Ā Ahhh<Ȉh G F5dpSG5c ep1p$dp@qw;z$ 32]|efP01| km)-•@K<φp7UtCs ZkһH5e:yQ\% Ȣ\\ލ J>%L PJαƙ70 4v;A5iOfB/\G}pp䈔4Rnځ";$JORsѷ($&@4NdVYWܘp` Mٷo4,5i:#qh۸N[ag]w@smi.yoFEѻK'loop1_nodal_analysis_1circuit1 gotoAndPlayR@@@@@@@@?StopAction=@ charging7?>'loop1_nodal_analysis_1circuit1 gotoAndPlayRNpp j.R77 z)HoLF |z)ooIc ")8ި7`|SzTނoT3Aަd ) dO7 5M|fy8ަdNOxž j*"o !@ fDzj@ޘ,7MA HdD(A<ޚ7MzLBSz$YoN7#$o !@ z Po,2*&" oR!@ "ވo !@ ̉fPo,7OrC@@@@@@@@?StopAction=@ charging8?>'loop1_nodal_analysis_1circuit1 gotoAndPlayR PJL}CP ,CME Q  e 5*ptؼeTR ~ajbMiܦqn5c.' 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FQ}4QggWus(1))@hUhݠ 2&z'y߾})ѷRO\Rf?(Kh{=﹬j ծ^tmB4S- ;5djwjP D "Bp-w΄6W58eSZ bj"2u[stV~tkH%hTtO78 !RV\¦۹ ]times1Kd^xD@¹ j!D7M3")o77zq4oO7Szq<ުoS2 "j0o7@ B 7E|Sxp0o7MxS!77̉"z9o77̊|fy8B4̀|x ȞoN7&z0o7 no q4VS7i&<ޜoS2* MAރ:oLix 8ވoM3")od no X4V : 7]oB>B7: x^*z[_eJ.WX<%g2``" / ͸]^&y$aX M!x Z:b`/ GG ^ 'zL4cXAvl<%c]dW xAhǀ veD &_`B Txa|ԉb`UPcK?"ЉL" 5؉ dw@em`j@@@@@@@@?StopAction=@ charging10?>'loop1_nodal_analysis_1circuit1 gotoAndPlayRfx$d` j f7̊|fTި7gx no 4Vj&7g ފoE|a)HoN7 E&dޢoU7"zqodIb3 fTgpp j/ވުކȒYގooޒYoޢުނިoYޜoޤެȒYފަooފoނޤoYȪޘYޤo)ȞޘYިoYޜg*zy#hP Ahh\]"iX MA  A @0 /jD &hԷ5 i+@jpXskeJ.WX<%g>lXo4Ā Ahh\]Ahh<Ȉh @m`#H*` dAdh#h h3nXAvl<%c] Boeedd%jD]D@k@dqU3cb$ped%kCxjo >qD &o@UU@@?p@rXDaـ G 9sD &qK~'6@@@?rF"(@ tD &klBT|ԉm`UPnK?"ЉL" 58( d@@@@@@@@@@@@@@@@@@@? s*c@t@PZUFs@@@@@@@@?StopAction=@ charging11?k?loop1_nodal_analysis_1circuit1gotoAndPlaystaticequation1 R Rup. j$hzH7|zޘ,Sz$YoN7 Ef@ ފoMhyo7M)&dO7 SzjޜoTԈ[&@ 8ވoMD-AH ȪoL`ԈP}3"y0YoT33 uRĮvpe@  R77 " ȂoS2"@ B7: > 8V  7A X7v)g3whѷ Ah̴\hAhxhٝuU$hOjpdW^}<˞弎eWt{e癩2j$WY\\U6@ lfb^-G6ds-jpe]Eph ,~}-| =9;9Ǭr[^E{F9⭾yxkMgaM]eӂF z\H)eJG ėM ^n[Y4 Ϸgsә\Sz:y^4ҺQfɫhM]E4oh%b,EVJdfeRKHI5i"$]v %Ok(~>5rsh5Y)sˋtqHvcNiٍ{dV6WkCNޭ;]@0:3p=->FjIdd8@FcFAl{Mzi9a |a,8<4REoP/dÖKdfeRLi*|~>5rka;%bv^uADPi Ʀ'Iԁ^Ӈyܴyi3V.BH+'!Ƣl32 gkL7ipV@.;9 P39\$,xM`Y\۞Α'3&r5vIFc$_zGeLB5 2*QwaSE<%o[$}XCaL Ah\~P+x Ajh"a97o%1(&H 68 D & static?yGz{@ morphy @@|l(@\5@<^C@P@Q^@ܰk@Cy@@|6@\@<(@@@ܮ@ @@?||}x~~@6ɀ`Y|equation1@@@@@@@@?StopAction=@ charging11b?j>loop1_nodal_analysis_1circuit1gotoAndPlaymorphequation1 R R@@@@@@@@?StopAction=@ charging12?.staticcircuit1 gotoAndPlayRaxTž j hzH7|Sz 5M7 . Hj(7i|z8ވoMfDSz!ooN7 Ef$YoL@ ̉z!$Y7gӍf@o)3hzH7fDzކdIj D(HL7gE|f 0Y,2 M3"AޤB7 x ނoT Ef@$Y72 dO7 5&sz)ooT "6)oPB7 :u7 Ef@ёޤB7 hܖ jhyRjhchs4ЈhAhhs4Јh0HvjhY@ A0ЊAjh h 8X Da G 9D &qK~'6@@@?:%@ (D &+W@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?32-YΠ'@=]lw=  j'B "6)odE7x ފo zqޜoT0MHL77E} `)bk\` :4 @ Ajh"p hȈ]h 0] jhȈ@h! hA瀊 8 o(D &P@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?@ EqԎ@@@@@@@@?StopAction=@ charging13?.staticcircuit1 gotoAndPlayRxt  jD7 3HL77 D,z 77  > $^j77&0TޜoC2* Ex<ތ7 &"9$YoG7 )7fMxRuilt557ol|p%qL8Vh8cL G 1Lp+GLp-h8cZ8VZ8i cZ8VZ8ibtLp-4Lp*4X 8(N|ahG Sjv4´p-4LpS:c|8(Nh_8iS8iShZ8iU8i c G 1p 0 8ZʏLp*4Y´p 0 [` @-e@8VS G1´p-4-e@8VSk´ThU8iZʂp 0 S8VhZ8Z@pP+GLp 0  8V chZ8VU8VhZc! p p @,pZ8cTZ8Z@p*;b GLpS+G p @+ZZ8cZ8iT+G ´p/+GLp-+G´p-Z8cZ8VhZ`! Bp ,C (+Zh @,CAbt Tg8GYVpPg1IS/1Lp4 1Lp4 1Lp4r.NhU8ST_d1´p-4 0 oKZ8h8c1´p-4 0 lySG (->8V `+GLp-<+GLp-4LpU4-L8)hZ8ciZ8ch8Nc{8(^`Ǧ G 1LDS8iYpg 0 ?8iYN1p 0 08VSU1Lp 1VL8Va{8(P[p-40 Z8*TZ8UL+GY´p*+G´pU+@,Z8cT-g p@Z8)hZ8Nc{Z8NZeG 1VpV{8(^SpS+GL  chZ8V chZ8VY!Lp-4-(8V _hZxV _hZxk@-8VZAm0@Lp G / k"Z8c8)[5p G fpcY!0 c- E0pP<%8G?^x8 D &@$X2TLـ BJBa X K`l PզBPPf $X)C BFhBarpYhlp P"!Z(T a!| VFBQ  `VE Ad+VЫ!OH5i!P̊@Y!P̊@7Y!P̊@'YP<YP gYwj lm\scd%8~ౖbx` D & : sޠ@  .D C Nd uFX]#)N#4@ř9<@ vD &?.chargedcharge1 gotoAndPlayRF.~pi@charge1 @ D &?FDϲlp@@ @ @@ @@ A@ A@ A@ B@ B@@ B@ B@ C@ C@@ C@ D@ D@@ D@ D@ E@ E@@ E@ F@ F@@ F@ F@ G@ G@@ G@ H@ H@@ H@ H@ I@ I@@ I@ I@ J@@ J@ J@ K@ K@@ K@ K@ L@ L@ L@ M@ M@@ M@ M@ N@ N@ N@ O@ O@@ O@ O@ P@ P@@ P@ Q@ Q@@ Q@ Q@ R@ R@@ R@ S@ S@@ S@ S@ T@ T@@ T@ U@ U@@ U@ U@ V@ V@@ V@ V@ W@@ W@ W@ X@ X@@ X@ X@ Y@ Y@ Y@ Z@ Z@@ Z@ Z@ [@ [@ [@ \@ \@@ \@ \@ ]@ ]@@ ]@ ^@ ^@@ ^@ ^@ _@ _@@ _@ `@ @ @  @ @ @ @  @ $@ (@ ,@ 0@ 4@ 8@ <@ D@ H@ L@ P@ T@ X@ \@ d@ h@ l@ p@ t@ x@ |@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @@ @ @ @@ @ @ @ @@ @ @ @@ @ @ @ @@ @ @ @ @ @ @ @@ @ @ @ @@ @ @ @FDϲlp@ ? <@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@pQp.  +joI!޼ތޤo̅ĜoI!Ĝotodol@tΩ6rSD@@@@@@@?StopAction=b$B,[E;b$B,[E;@ charging13_tout?.staticcircuit1 gotoAndPlayRɀ`9#Ph ´I8ɀ`b&ɀ` Sa@ɀ`FErpʀ`JAЏʀ`J}ɀ`LrNʀ`O:;ȏʀ`NP@ ^\8DFG8D@̍G'loop2_nodal_analysis_1circuit1 gotoAndPlayRao<%mwP AhP 0 AheO <%F>X|4Ā Ah\yRAhhxȈh$XEL Ah\ vD &-25*x|2sWF)}*  v` u@¢2p % FhhnH2"JŤ"`PddG2"H&EA8ȞdD2"Fǀa"AFh2I)J$")dZO2& H&Ds")=#dC-)̊e2PddE2 H&E" (T'  @ȠdL,E Ds ȬF,2 jdT "Ajh 2Y-$LC"hd2H2"H$"`0PdWA$@)`dR"JeBy8@ @@@@@@@@?StopAction=@ adischarging5?>'loop2_nodal_analysis_1circuit1 gotoAndPlayRdn<%_]RV<%}.Xo4 Ah\Ahz D &-25:&6hXU23W@` :0 Lމ V@J *w oX1htxtTexttext@ @@@@@@@@?StopAction=@ adischarging6_tin?>'loop2_nodal_analysis_1circuit1 gotoAndPlayR@ɺ-+O0@؊4׎P@'loop2_nodal_analysis_1circuit1 gotoAndPlayR@@@@@@@@?StopAction=@ adischarging7?>'loop2_nodal_analysis_1circuit1 gotoAndPlayRx j#R7 Ef@qކdE7̈&"ɐo77 MfD3"yTޜoT "PooE7 P @d7 %F#xl7 &҆7Q0dIg̈HoS2)EsxPooE7 ̉SzPooR!@ A<ޜo3"AHި77|z)o8 oIỉz ފoVxT9 nE7 M3"yooE7Ez Poo "3 ވP B7M) y# l@d!ț#x77A X &^7E3")H|1, Ef@!$Y7ԈXzo7!gT}AA72$MD,szH8ގo ElSx ȞoN7&z0o7c0oE7M3")o77D,Sz$YdTԈP|3"y8ޜoE7Cx$YoMD,f)L7|z)oJdA7MfDf<ޤB4̀|CzHo77MA 6 h*OJ72)x 6 h8VJB*</yX '<%3Y?-{ܦ'loop2_nodal_analysis_1circuit1 gotoAndPlayR)ù j1B7E$YoIj E&d ȞoN7E|fy8ަdzBooS2 <ޘ,2"|z oV"Hj7 Q.D7 D,SxPooE7 ̉SzPooR!@ A<ޜo4̀}z ަdS2" x Po73TئPB7:u4= @8177fDzކdIj D(HL7͓ ȐoA7CxPoo <ޘ,yo777FzPooR!l{d,=A7U@znud%q#yo#oI!B1y99qN$*ȭW"8 %u]YAЎ W(4uX]U<} Pt Z (rh(j AhA1 /<Zjc%kKS  H AjhZȈhjhs40 9D &q9V ۤ~@@@?%@ ^D &f2$5f/BPf09o̎zE321<@ɀ`9q`@@@@@@@@?StopAction=@ adischarging9?>'loop2_nodal_analysis_1circuit1 gotoAndPlayRx"  j1hފoަȠޞޜަȊoތoooފoȂޠނކȒYoޤoތooޤoޤަȦȒYގooފo) ުިooޜoYVZnՀd%X ΋^UI?-;{y8499N;onwCIb9W"8 %:f CD &?F] @ @ @@ @ @@ @ @ @ @ @@ @ @@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ |@ t@ l@ d@ X@ P@ H@ <@ 4@ ,@  @ @ @ @ _@ _@@ ^@ ^@ ]@ ]@ \@ [@ [@@ Z@ Z@ Y@ Y@ X@@ W@ W@@ V@ V@ U@ U@ T@@ S@ S@@ R@ R@ Q@ Q@ P@@ O@ O@@ N@ N@ M@ M@ L@@ K@ K@@ J@ J@ I@ H@ H@@ G@ G@@ F@ F@ E@ D@ D@@ C@ C@ B@ B@ A@ @@ @@@?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@mhڤj AhA1 /<ZyiJ S dZAr2dJ-+"%0d^x2/<^xiS CD &߇ {簉 ᠉h@ŀ99"`(( H jhvjhY@ xA8By(Y@ЊBh /D &5`3׸@  V@"@@@@@@@@?StopAction=@ adischarging10?>'loop2_nodal_analysis_1circuit1 gotoAndPlayRfTg*zyjpX+t@PZUF+@@@@@@@@?StopAction=@ adischarging11?k?loop2_nodal_analysis_1circuit1gotoAndPlaystaticequation1 R RxJ j3hzH7|zޘ,Sz$YoN7 Ef@ ފoMhyo7M|3"y5MoLd3TئzޤB2 )oN7z Po,2*&"LȞoLj"zqLRĮpO j R77 " ȂoS2"@ B7: > 8V j 7@ B7)gxp\|P46ɀ`Y4equation1@@@@@@@@?StopAction=@ adischarging11b?j>loop2_nodal_analysis_1circuit1gotoAndPlaymorphequation1 R R@@@@@@@@?StopAction=@ adischarging12?.staticcircuit1 gotoAndPlayRx1 j hzH7|Sz 5M7 . Hj%7i|z8ވoMfDSz!ooN7 Ef$YoL@ ̉z!$Y7gӍf@rBxν<% P p/+F jhzH7fDz`Tި7gӍ|fo77Ӎ70̉HL72 "CxooR!@ B>B u777 |#z)ooR!b|z)odH7|Sz ooU7 x$YdԈX3"ވox fB:7)ɀ`\5FhT jhyRjhhxȈhhBhYh h 8jh h h 8vjhY@ A0lhQ Bjh[H hO p jh x@h*B ;@YA jh $D &{wʉ@ɀ`9F$xvdK<%K @@@@@@@@?StopAction=@ adischarging13?.staticcircuit1 gotoAndPlayRxt4` jD7 3HL77 D,z 77  > $^j77&0TޜoC2* Ex<ތ7EfD3"AޤB7)7fMxRu_pmN@ P%!Z(T a!| VFBQ  `V5t*(W !XY zELP8 Y@ lm\sSd%>jb{ D & : sǷ}.D C Nd u  #G FX]#)N#4@ř9B̬ y#xhU@INUp@JV`@LVY2`@fR:W&@WNW@TC@G<@ap  :j#otodoI!̅޴̅oy!o̅oޔތ޸olxt`р hzH7|fj72'ӍfEA 8ި7 A X74̀|szHXȊoN7 &@ ފoԈYCz Ȩ7цxT,77D,Sz$YdTԈP|zq72 &3"HPooR!@ E ފo$(|3"HHdU75YĐT`@= A1 ܈ | ~ | D &1@ɀ` ?@@ time4@@@@?StopAction=@ time5_tinp- j+hzH7D,Sz$YdTԈP|z L77E}3 <ތ7AooIkESz!ooY2 )oMShMD,Sz8o#p( z񰍵[Dz+) 2zu,Q<%),XGL %PRƊlpXB  ND &_X(/Љ_ P@*_j@@@@@@@@@@@@ time5@@@@@?StopAction=@'()* time6_tinp耎 j.hzH7fDzކdIj D(AަdӍ"AooF Mmz)HoS2 "c"HފoD7 &@)dO7 5f@ޤBMfDzq7# p( z񰍵[Dz+) 2zu,T<%Sj@.`$@*P d&@G& ND &_o&@P @-z@@@@@@@@@@@@ time6@@@@@?StopAction=@,- time7_tinpﶀ *F7̈f`ި7gӍ}3"A<ޮ2 zo77|fj72'ӍfEA 8ި7X7iToX2(ԈX3"ވo3}3") ȞoN7́xp(zeaj܈VRe&xۯ`ZʈiT2@TG.Pj+7iv۹zc]zv(8bNZMJ04*`o@ɛWGM&<j L $f=epc9P"m.e.mvK,x,Y< ƫpZYVf$4dIp/]@ED.[B)&Ȝ[̤)>(n&WNMQ tWBwXi FhfȆ2]L\<%Js<%W܌0 !D &j@@, 0ɀ`A:5rE/w<%#敻.lnD9 .IDn1@@@@@@@@@@@@ time7@@@@@?StopAction=@ &,01 time8_tin(@Ӏ j+B2 M)`ȂoMSh7 "3" 0Y72 Tئ" oc xAެdE7 QdO7 z)8ި72 "AAodA7 5M3 ވ 6 o8V Qu 7A77 x $:A s *z7ɀ` ~cɀ` >@Xda8 h!XpC}V AX"Y5rhK<%#K܌3<%+s=$0h x!8 hק^נ BO`%!X2i4 h>&|t6z6<%w#<%+G敻/AP>#? lRȠ0$hUx!8 hק^נ BO`@$Gj頌A" @@@@@@@@@@@@ time9b@@@@@?StopAction=@ time9c_tinz%xT j-nR!d5"z9o77&z]!oR!@ EPooN7MD,Cx8ޞoT"zqooIkMf@%Eɀ`au/&hR4 1 )z-zzA zF&#'y_ P<%wy\e9cgb&G'@@@@@@@@@@@@ time9c@@@@@?StopAction=@ time9d_tin@@@@@@@@@@@@ time9d@@@@@@ time9e_tin@@@@@@@@@@@@ time9e@@@@@@!"$%&()*+,289:;<>?@AEFG time10_tin@G Y37j[,mᯅ| <%oeޓǻ/x- Cv^m; oHjݗ[zB7eސ{/-l/'<% .D & : *XǞF@  .D C Nd +mzspFX]#)N#4FX]#)N#4,FX]#)N#4-@.bcC/xDۀ )nH7Ӎ}AA72 &3"HPooR!@ &3 HoA7 Cx73Tئyo7X 77ԈY"z9o77|5dH7ԈXSx ȲdC2& 1MxHPo77̀|xXȞoLj MSxޢoU7}Ayo,o7 yo7j ̀xc77 3&@ ނoR!cMޘ,7Æ/|@b@rb@b@b@b@׊b@jb@b@;b@eb@rb@ time11NJb@@@@@?StopAction=@ time12_tin0x< (hzH74̀}")LȪoLj "3 HoA7 2EFDSz!ooY2 ̊#zPo,"z9oPB77: X 7g ފo|"dA7MfDf<ޤB &"9$YoG7 M&Sz Po,7FSz`<ޮ0|ҿ` 18:@Qc |P65j%SX8r\$2 )ħ +KY|P\l.ʠ%aJDXY&E %>5a i(z6dz`-x-%\D` S,H,"%,`Qtm| Fƕr&9uK嬺0 m[vWe`0IJUETZр e5)`Q2I*@S#Jk]ٮ.6gfٞe&'&`|eùNZcA\5`^L&33$bv  kGC}}uDiE)fWoKyvj\6fѬ5d_U;m֥6Vv5AU@R/P5( FA@|)J@ 0 d0 5d~𵫩cz5Dd^p0FXq,FvNpd3][2pdZ*L|98T6Y,4t0aluZ5au@9 :29xtR܀ݭ*Y߆CJ4̻_5e75HM Q[eRn,v~Hi"9V{. 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S b df'Fui)nL<fff-o![p.BK_$dP$ %x ݄8?p k  A[q@y[U% %u%̠%Ļ Ep)  jsפm[׽3BokGoRok|ON  w v@3 (

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Mac Radigan

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Fred Vieux

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