<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>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A capacitor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is being discharged through a resistor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. The capacitor is charged, at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= with charge LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.What is the charge on the capacitor after time LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ?LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>The characterizing equation for capacitors is 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 . Using this equation and Ohm's law 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, we can write the circuit's differential equation.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(); # input placeholderSubstituting LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= into the voltage function, we can find the value of the constant. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYFZfXzBgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2JVEpc2ltcGxpZnlGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSVzdWJzRidGTUZQLUZTNiQtRiM2KC1GLDYlUSJ0RidGTUZQRi8tSSNtbkdGJDYkUSIwRidGMy1GMDYtUSIsRidGM0Y2L0Y6Rk9GO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJUSwwLjMzMzMzMzNlbUYnLUYsNiVRJHJoc0YnRk1GUC1GUzYkLUYjNiMtRiw2JVEkb2RlRidGTUZQRjNGM0Yz = print(); # input placeholderNow we know the voltage on the capacitor as a function of time. In order to know the charge, all we need to do is to multiply it by the capacitance LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= .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print(); # input placeholder
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 2</Text-field>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JSFHThe capacitor of this LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUkNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn circuit: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is charged at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= with charge LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYFFfXzBgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn. At time LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= the switch is closed. What is the amount of energy consumed by the capacitor since the switch was closed?print(); # input placeholder
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>We will employ Kirchhoff's voltage law: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 to Ohm's law,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The characterizing equation for capacitors is 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 these expressions into Kirchhoff's law 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(); # input placeholderAdding the initial conditions 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print(); # input 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print(); # input 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Now we have the voltage over the capacitor at all times. In order to know the current, we have to multiply the voltage by the capacitance (to get the charge), and derive over time. 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print(); # input placeholderprint(); # input placeholderprint(); # input placeholderThe power consumed by the capacitor is 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print(); # input placeholderThe total energy is the integral of the power over time.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=print(); # input placeholder
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<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field>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What is the current throught the resistor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUjFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn 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Answer in milliampere.
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>Since all the current exiting the voltage source is flowing through LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUjFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn, we will find the total resistance of the circuit, and evaluate the current exiting the voltage source. The formulas for resistors in parallel and in series are: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(); # input placeholderIn our circuit, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUjJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUjNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn are in series. Their branch is connected in parallel to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUjRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn, and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUjFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn is connected in series to that group.print(); # input 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 = print(); # input placeholderThe current is the voltage divided by the resistance. 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print(); # input placeholderprint(); # input placeholder
JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field>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JSFHWhat is the current thruogh LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUjJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn 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<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>Using Kirchhoff's voltage law on the upper loop: 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print(); # input placeholderprint(); # input placeholder
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 5</Text-field>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What is the total resistance of this circuit? All the resistors are equal and have resistance of 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<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>The circuit can be rearranged and be presented as: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 circuit is symmetrical, and there is no current through the middle resistor.This circuit has the same resistance:MFNWtKUb<ob<R=MDLCdNFZD[N@[@ZoQgZoWTK\\aN\\@Nd\\QgqxhhQPQpd`qyuvkuVr]KFatQUUghLEUMfakwGgoFoG?gfO`nHoHat`fg;qlZGb?As=?f@HcUf\\^P]yA^GO[>A]NnwFAaF`[Ro]LFfrG]JHZfAxbOfUf]g>ebYb__n\\^s]qumosxvkhx_aYewvuxqwTyomwsuqyxGsQXhhIauwowOpQywuioYQigYc>Z::>rJFd;i_b^kLPkQQqbXoyHcwp_q`ylHqPA^DqZ`Xj=>v;^jlo^L^jCYiTXkahev`^kGnExfV_pPHb`gexyvV_qZQvrv\\QWqrydQvbK@_Mfs;xqmGx>Q`s>b@?^wv[rywgo_xi]v>]wNorhZsHkEObPogVocoGhyXkop_h_hKFqRX\\aGhg`]UqwmFarn`s@q<On_vt^ysiVl]QelQu;gtF_]AneToZA^_In`A>ij?gShv=fiZ`kU?drFbHWdCNvkv^iXeW_mb`jg`djFaraqOo_xf\\jgyYNhkYsly`tOZmxr;fwPgaInaS>v;p_yPZQGkhxx^n^BIwhnxT`ZKAaXirep_XP\\qxtc>lVfdCopE_eVhlZqyQWqrqZV`rFIhZ^r=xxu@qZFnvYbw_lI>rKok^FbXIv\\qu:OjvVfxqq:?kXG_jwiwi`RI_v_a_AqmgevHeLHo>v`kF`V>iLayGihrpnZvZBAqCigcvrWh^AadJXrJNsc?hKv`u@yAv\\GfxSV[SqfKVplojZHwkAod`hixeipqi?kuFxZwbsGmLNfBhv^?hZYphni`pa]QavAp\\AbPw\\v`f@xeRxaUNdHxviq`Cv[DAv;^J_d>CCs?cWqGheXk?v\\qImiuPQBhOtu?Cp=FQKeiqEJ_RNAIYOi]]VO[FCAusXw`ukvxqWaYqEllel_`ms@UKlufEKrltaTJVTt<]K:=OalO;mqfDS<Yv=eWCMLgQOQYqruU@@m_EqCmm?eqUir]pOXxPaqU[]u><PXlKfqTV<uU<XOxvaAXOPuGmT?IOhxPAau[DR@XVaPm[=MjEJ<EQkDKlXTL`j?`o`DXJirwlvrhOD]sDIOCLrQQYW=rGMX\\iyi`UauksqwFel^<XOXv]AJqlkoEv:IVcIVnYvddX=HWWavxuLyIv\\yJ;pJMYqD]sxURbtrL@NCUjpYQ^<Q;mLcXqjyxB`qYiWVev@DXOHNkTphLviekU`VaMpEEKkqQC]LGhW``WZ]xV<oCeyumKVIw\\iv<lol\\v`tP>ljr]QIlq\\mqUAOGlN@HVZ\\l]dqQlQ;mx`\\NBqXC=l?DSHXRdDTx]SWinuLMaqNBHmXMKlqNQtvRXxhEXkYTsps<`NCqSrPsChv:IVoqYqERQEoWavPUxWYvhlqaLNFIxGAR=HYP\\U_AxkLkWHQm@pHYsa<S^dUghRKtoP@lvAMslwptLy]nHYQ=]rfIOslp]MqVaYyIYPTYoPQaiVkmNvek``m=yrwLv\\IQQtqdpk_ijcyYdPshevneSFxUnEx\\PoYhlvpMIUQuXlm\\RLUXZEltUq^`YWLxrexA\\UvprrPsy]ToatPutGUXMXQNiPB=Q=YLAxMMurVXN_uyaPOyXlMXJytRkIXO]oCaS:ApQ\\mIQmBmt>ISVdlqIl[DPuLkM]UvhRWxymQNveWCdmV\\qN@wEln;QvgAXIUohqT^PlkiJQtY\\pkwUoEXJ\\QQLQL^`V>AvNEMuQvw]vIpN^DtDULDuUa\\OFuqhQvgiJr<tNmwJyuayXdXxs`osEX\\hWOuSxuXGtoC`qCirU\\tsTy^xVKUL[mk^aUXtovuoEXVOHu[YxYLP_uVo<KFIJXUJvYLdqQA=VTIQjApnAvpmSeXnV`vUxoWiuV@lIxXx<xXMuGQRhiML@KpDRvDwwao]QOsakCtyuIjhLxMPkBquGmUT@v`dyR<WWmQqYl<uuP`JLivmaKriuDiupPT@quDQxumWMtLvISDxWMXJt=qetNALUDAXrEt\\uTsyTcloLYmB`PqDqWEQQqj\\AUSMqqyLcXVsyXXeNyHpW<WndOA<mIxKBXWxHS<<sRTl;LvEeXdLt_hudlwHYkPxSJhRMQsq<oq<pYuLAxpIaliylmaTOXkRuSEur`tXEAYQeS?xLFuUxqXmmSXIS]lq`IuD]N;`XNDv:]nt`voEQ@qoyep]elcUVM`sYxwdlUOasotwa@y>INEDxsEOV<NDxwMui_vg;aZ@AwbvnCfgcgxYN\\Lh`OFdw@gSq_Np\\FA_?idxVnV?wOprGoaafegf_th[_q[vXww>l\\Q_UPsOOeK`q:_]Ghron_xV^QQcl_^eFfvOtuHr]gfBOvrqas>dQPiGOhOxtLwgfPaCicHY]K`kNyg_o[V^\\AYyaqbBxgNxuTQcJFs^HcdHeZArJwie^]_ww`vp?`^p_]dAkvp_RpwPpm:GgTFp^G`uqksprSQlBXo?@paoZLXbuPltP\\Xqjsagx>vdv`K_iSNkp__Qo^B`^iF`tpk\\Ye\\Fr;pyr>tlfhOpvdvvNAxESMwBNsdTKgXiX=Kie;vdsHLuWc?TSaHNGS\\CYw;Q<EmaDQtLs?MY[PK_<kiqVo@oqTWcusOqoLqNCyUu@y_DLEUmV\\w`tMkDs[yNC\\iCV\\dquyObogwdNc^vaIguoOmT^e@ivNie^vqLyxGx[<XZtHrf?o]AuOojPidhPlRam\\q^eQcNX^=Yj@@qDiy`augNdaidm^lN`pIgyEp_h?nrqhU__mVjJon`VcEahk`il__`_^Bpclf_`_aEvxfPq@VaCYk_hfYAm[q^]fvL_o]gxYye]_]?v_UNyJ@lXXv>G\\eyqkvttN^<IyRNwy?_V>slglvXZeaZKNsgF]hO`LgecAsnnrxOvj^tm@obFrvi]Dv_VxmQXx[Q^[^l?h]?WdCndGPv=nxpFbLPlFWlvoaJiyXq\\jWlIVmhhhMgei^vP?arGeAyt<feuhp\\Nlvhmhys<N^sGkrFlpPqHWklxlP@j=frr>l`Q_IYnjqmhIiMwrKP]m^ga^[kAuXhrYOkBvsCXlvx^ZNlUi^tnnxydTAynogZO`anctg_FOyYg_nOdB^\\DO`I_vA_rOoyTPhOxwpvvYA\\bqpUIZoQpC?fYihUi^CvpDg^[Vk_y]ANqn_qm?kYXlrYn:Aeb_f>Qp=n[Nnv:ffrPSeXvsSfgynsfU_WeCXhuBTSVpUctMVIWYesfCywrWTTcSGgENYUhafu=RKcrQ[g=]G[AGmcU?UiZUGUoHPEi]cvvku\\ox>GFfUtrWiH=rK=Y;WIR;XOwd?[RlIU_KdtEgEowLmhK_EEQv:Mee_i=AiDmYBKscCBQwtB[HXEWWYYy[rmaecSwdaDK_CgqGDCI`=B<EeS?G[?GLiXMQRsiGDwWMSh>icL]blWDBMRukTsUhSSgnWig?Ywku_GBK_x<EguOyjMD=Gv:=sOmwHEIqIhFsHceEemtJssuOH>Mh@ExaACNIW_mGGSbJmccCrfCd]CD]WU=srm?bxuePocGmFC_VUACkwIaAFgcYb]gAYT\\KdiOTvmFqAgLCsBCCl;XX[b>awh_d@SXa=f;[W?;IJKeWwc^wTlQXDyWTIgTcVw_wCyG\\ubU_bJmc_Wu`UiX]uwkYX=CEYSlkY\\kSJqFMmt^OcoUGxEyBSIDkYd_sQ?guWW=GxZcXqghgKEK_CoEiKiwX[IA[Xwcfo;efKXYYHvEW`_tE=guusoQYEMriMu__bRQc^meCMO[MPa=UhPtIhNtqTYxVUHYS=KieM^IK<xoEyVo`MhMlFDjguxxHN>yybdxxIvNtX]qw]puFioPDstLqUYNqelxqmmUjCYlgtuNxqqTS=HM?LMFaQMtjGeNf`wRuu]durmUdlX@dXYxUsXkPpoGdtuXk`ER^ttCYWGLRsdm\\EU]puFdXOELlHlLQoaElOuX;iy:`qYyRhyptluEUSqyNYdOZLs:QxdyQ^qyULtrlYFaPRxjcDYs<TaTVBxRI]wkEuQTSSiLSLuSyl\\aNaeR^dpJmqBDnVps^Dx\\eTKxwvUkQDTiIriPYE]UXHuoMPheVKeK[`PNipdaLY@qcHTrEwK<PVuTchjdmSo<m_`l@TPEXJp=kapnTTVYxtI@olykRHNQHULDSneqa]NCmL?@lK`NDxLtdqRHqbQjiuUxeUwmt\\puP]pHdrQdSUav:@SHpuOMw@TXoHWjdxmhOmakStj>PTQYY?mqi=o[tLWAU<]N[\\lMTl^dO=MWI=VL]jH@oraompOYYqLpplUlOTNNIL[EPkAqU\\SyaQCUuZmPclqaXqBasmhOuXn@XYvtJT\\Lymn_\\RLLRsDpHPrEDnXYTUInrQV`qXYhvqDOxDXZxyqtkhtMCIPSdK`Usn<mpMvitw^QUb=kaXnr<TKeXYDTvIWA=v;\\jlMvLdRMPpCExAHopxlcAxn@UPHOxyYR]xoiXsASHHxq<mGak@TpM=pfqlcQkQhl=aWa\\PBAv;\\jlo^Dp\\kN]J@iSiyCalJo^LVFqBm[xwuihgTiySQickCD@if[[dMmFRge[kdI_FRou@SXJec_ECGgF>OD:;tZMfk_EE;h?GL:>[_>Z:>Z>P<;B:?T<<Z[`:;BtyrCMxt[hAOV:=G;;BRgDFcwkSWJKS:>^N@:;B>OD:;J>Z><?<@D;BZ[d:;B:;DD=Z:>;B[B:?<[G;QIserXuW:<JSLRCxnAD:;toqJ:<:>Z[<ZbZ:>;B[B:?<@D:;<<LDC:arZaFser=EH:>s:g]<G;<RQY]:>Z>\\ZO_KghKIrgKjTJrPT<lkLBjkCAEUTKVsAXe?B:[cDsepEXO[E_;Z]?Z>P<<J[J:@D<RbB:;<dy]eovptZ\\l:bjktCYGXoE>;J:dUiC:[:\\:<J<K:D>>BBBc^:><B<J<[<;=?kF@sFCYGXKc;;JZTJr]sTJtpu::<JB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configuration has resistance of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= .
<Text-field style="Heading 3" italic="false" bold="false" layout="Heading 3"><Font bold="false" italic="false">If you don't believe...</Font></Text-field>QyY+SSpSX19zZXJpZXNHNiJmKjYkSSVSX19hR0YlSSVSX19iR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJjkkIiIiOSVGL0YlRiVGJSEiIj5JLFJfX3BhcmFsbGVsR0YlZipGJ0YlRipGJSooRi5GL0YwRi9GLUYxRiVGJUYlRjE=LUksUl9fcGFyYWxsZWxHNiI2JC1JKlJfX3Nlcmllc0dGJDYkSSJSR0YkRilGJg== = print(); # input placeholderprint(); # input placeholderprint(); # input placeholder