<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>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A coil of resistance LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and self inductance LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is connected to a voltage source LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.How much time after the circuit is closed will the current reach LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEjOTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSJ+RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEiJUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0Yv of its value at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y4USdub3JtYWxGJ0YrRjo= ? and how much enegy will be stored in the magnetic field at that time?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>We will write the diferential equation of this LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUkxGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn circuit. The current-voltage relations are LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbWlHRiQ2JVEpcmVzaXN0b3JGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYjUSdgVl9fcmBGJy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GLDYlUSJSRidGL0YyLUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZmbi1GLDYjUS1gSV9fY2lyY3VpdGBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRInRGJ0YvRjJGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0Zmbi8lJmRlcHRoR0ZbcC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GLDYlUSlpbmR1Y3RvckYnRi9GMkY1LUYsNiNRJ2BWX19sYEYnRlItRiw2JVEiTEYnRi9GMkZYLUkmbW92ZXJHRiQ2JUZobi1GNjYuUSIuRicvJSxwbGFjZWhvbGRlckdGMUY5L0Y8USZ1bnNldEYnL0Y/RmVxL0ZBRmVxL0ZDRmVxL0ZFRmVxL0ZHRmVxL0ZJRmVxRmVuRmduL0ZJRjFGY28tRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZlbkZnbg==JSFHprint(); # input placeholderBy Kirchhoff's voltage law, 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(); # input placeholderThe diffrerntial equation for this circuit is: print(); # input 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(); # input placeholderAnd the solution is: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(); # input placeholderWe want to find the current, so we have to solve this equation: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print(); # input placeholderJSFH%;
JSFHThe energy stored in an inductor 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(); # input placeholder
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 2 & 3 & 4</Text-field>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The next questions refer to this circuit:MFNWtKUb<ob<R=MDLCdNbcr`Kb;BtSErCZKV^C_b;_drOugims?dNvdXvrYArZ>^B@nb>];F`?pbCP^@wp>WdKOneQgLvs^P_@gkrww\\Htg`g\\qrGqrdNfcoyjAcDV\\ewdWQ_iWnUOwP@[XHcNQxx>k:Pm>gob>\\kFZI@[D`m=VpiYylq]cwbHHZa_mhovqioTPf`xfXahMiySxwiyxuguwqmcF_cFkK@ctWlAfw<N\\;Hc\\F\\R`^<Vl>O^jFc>n^C`bZOlBwqEacu@bYQer@h[hduQacF_CafIYi@wlCA_W^wqwwXiwtwyxiyjfxthiuqxQ`yvayhGqM>noHjQwtlO[_ycCwdipeWFmYxmYY]Iy]x^iRqisQx_iZSIuSYjCYdcvrnGq<Wb=W`tvhhaibxbIp]UQ\\LN\\@`gVAqkY]t^j>nnh`\\J>\\JxvHwZDFvTq`a`ghHfVAh?y[<?iKGdK_j?QfkIar?xZQxkYvAyk\\vg[PoVivDisGi]nAv;YjHP[DqoWWq`Pt[^nJowlgbAwbiwwYyqyynmqvGY[SQqoWwh?qaXq@Xx`a]@i[UXf\\XmbikqnuRvigQuoHf^i_>nnhdAwbY_SGeSWUTXmUXQeHSVmYda]Yv]i[kHnsGisW:wiywYx=TJ=TpkUuAyraDkQVb[hOUgPuHWIg<uvAYW[UXISvJGchegZCTbsFK_wNcU>Iv\\Ac_GYhefWIRZMw<KsfawfydmMXl]RLwEQsDQ_weYwuuc:cFjcUDcVoeXoGe=GI^AukWVyar<?eR?eg;GbaS`SToCrCEI`WgZ_xn?UfkuOeTOeGNQrDQsDqdvihQgtdeHSabrMBM_xn]r[YxZAXtEW;arsyYfSru]hA?CFudtoFXKW;;FO?TT?WqADRoGoeSgWIDyt>cfUsDyKifQf[;GGWwRoFX=FrieusXhieUuhhexr?YkQv>oR>oIKqH]SF]MyOYoxplPplpPs:DVManVetWTRvHTVTTnuoj=OauYoitQUSk@rMYtmPN\\LN\\aJHYlq<t?QNTqmwTYpimixqxQYC`yVHo\\Pn<yWFAmkTTsUudDuXuW[mun@WKQnD]qHHkCHunLYnAwcmMXlMO]sGMqL`QFPJ_EUSEUZIsMxNaIWEhJnIJp<Tn<k\\Tnn`pn<wNIoMuweuuZqkuDXQqoWUwoqTCTJBEuW`v]HU`IosyQc\\leAw:EmMYtMYLkUW?llsUYuuL[yW`mV`av<Qr<qSr<lohvbMoUmvUyWyhyEPWUdMWdqmhREpL?QLHIKcDOcTWo]JaHS@@XI]xeMWy]jvIvgTorUL;HoM`Qe`qv`qOImmtV`QkGlxjAofIumfolAjsWrCFZhg_ZGopHZdhoIxkIiaHnvHHr=xZi>te^mdyjbhw]alihqVI_Iato>mdA^;IxDOcDOu[GeN_dNIjBAsBYr;Hj;Pvt`sf`OMDhEhjgCaQtgCvngHgEB_sXUYy;Ir;ydAoCWKy;eEjMiVidNqhUqXgCiMevhwVjsEm]IN[IrwfV;RkQbZUhGWWtEWH[UGUUX]xFIr<sUYuuYueymysiwvywW]Iiuuxgy?IV=qbwwTE[e`ee:;Vd=voCbcagVMGasFaiVoaiXshvYhl]IViDSQioUwV]U?WxfYhIqYM[DN[XGEi`kbIGttgElIHgUUXkyy_WSQh_iE:Ecy_IfwDD=Iyqf?WH]SF]MenUGdyTneVqEtlgVEqWmYbQ[ynwTV;DJ;X=WrNkIl]vBIekGhkWwgMi<]b]iTN]TZshvYglUSxIiG;C?AYHOvZwXiqueqCWKIn?EhGsekxqybI\\yW]XwAJdeoMQJ@]u[Es;\\YZtoZIolTmGiVRuN@AR<UqwYyqyNuIysiLfIumxvY=YbIwZdUsPX_]LXLYSqM^HTwPYoQuRtMYtykXt:ajU]sVHQmyKveVstScXwAYxtixeyYVQp_Usx\\OBeSGeyI\\mHXRppToIOdMOkQmvAxsxvXXuGpQEWk=HeHInl`hdatcA_ZX_gf_gWrWW`[?r:HZYPrKGZop`ifwVIqmy`j?civ_iP\\xAiB>^syxQXsYNjo^^^^v<AukXfMNuphgug\\?N\\PIZjGpwnsRyZb^gDQsDQeYFal_v]oyynsd?o;nyqI\\]nb^NfUAypglmv\\qif`of`oc;iaxisd^l=NrHh]unm]irAyuOQ`VHksvixayn_qav]IHq_vy?pGcd>DOyIRw\\r;Pv[LYEPsoDtIIky@wmat`injMUvmMgEyeQSNmx:XMyLS^hJBYQK=L;lRvxSQaRtHUHHKa\\TOtNIyLMqJH\\Mr@Swxr=yvyHJaPwdDRyhngXU<lOHtSc<n<\\fPv_@pyEvtNGq`Nyofpsh^iWm<`p;ObSGZbAx:Xg<iin@h<idkiyLIqC^cQovRxcoPvsiwZWeKnj;nZAXhINocYvAykyYb;I[AawPioUq_gXvCwpfFlJodBaiNHrsFtSq[QavOyxV?q_IkMv^x>d=F^BwpVwocWecHawA_pXb<OeCyuqArpIcjWoBI`WA[FGfKa]@f\\@GhOv`VX\\HOs;PmIxxqqwWYqLXjoynt^uLFq_gl>Hs<>uNXg\\a\\]NhGywxXyh_mdYZNpgsW\\gglUOUIU_yXSeWx]I^sHeqG<WSOEBL[vE?CW?Xvxw?yLY]Udho<ePhEqKEQXPXrdJN\\MJMq`iYnuJCqW\\Tp`hw`Dup`SMqxkhWLEvWUJhDrcqjwAmPEwpeVV<oALLHYybYn^iToQPoIMSyWSpjKpP^\\U\\PLQuw;IuNEL=xxuxXiqyy\\YIPUCulhdUpQxpxQe`uLAjQmvRUMreS[`uCDq`@K?Aj@ewj]L?W\\Dv]:njVWxSxfXHcQgtn>^nHhvFvn?ZPvw=IikN\\VN[SPn\\PnjoesymOgdvg_gghgfdVh^`n^pQbXakyYbtNqO@rvO[uvef?ZqocpYyOg`X^qjIc;owC@`GPcSFa^PsgfgWWbtpnBi`KyxBXp;?qZYZWwabQc<X^Ufsgff;nd_VxjyjV^c^ha\\@hmw^Qa`eArS^ZRO_qXZ>@hG__AX[<i_nfjEggsInbqx;yf;n`xQvmdPgecqD=Ci_eSigbnMYV?CjaBN?BOietyTGQIj=cdEuGWF<UHVIRXEG^edWkuOKuVQhpsbKow<wiOOwHYRnWdISRsccl]SowUJYV[OF=GdLID=YbcgGB?INOFa]TASr`OThWhgkIeGGH_SD;Y]OIFObMwwAOWUoGfKC_qg:Wt`qyUSWM=vhmRAqrdqswMgt]iScsgsC@cXfYwY[SqEBkOIf[GfaCtWbjaUPcW>sF;GwlaetOG\\KF\\AUB=SBmDXWv>UBWet>=Vt_ugCtcychcGomwYAcaKBB[s`=wP?w?=damgjMb;eXieTdWGj?CFMde?vn?segxecfEoTK[d>kfh;vNaxoOH<Kd:atO[enWCduDGwcCMFjCS^KC_qSPgw^oxdmVVqvxcdXCbcWXbcW;[h?cd>EfVivJMGAafwWvrwEcCI`WBZ_FskId=d]MIJmwHcGxyYAew=KBM_RskFC_RZMdB[SqMs[OwE=xcWsB?rNiEV_TkWIP]tW]vZ;ICKS<STq;XLqUZ?THMHB_T^`nsqPslviMPWqqwUquEXkEXblo\\tkF`kvLNQXksuNkdvYER;ERi\\K>AjkPw=Pj<PpSdUEEwNAS<=VDIKE<PdHx?XKQlN[Er<hJEVgAgxrivQxetagTapcA^Xx[V>ajG``WgjwvuN]kvtL_dN_txO[_qc>P\\]a^[?\\ifwF_fR@fNosS^rfwnIYlmQadqi<Id>PdoAh>?gw_rGas`Q`ywiyaidniV@_rhnV@bNYc=nninw^_rgap:@duV\\hPZMWatHpXFnNqjNW^pyothp]OgaGtjHhFQmSpgOalFQ]jfqn_`gxe=@dTfpAFjdPhSXfdWbmPmtycGo_dpjp^liIiRFhtof]HrC?fD?aggmNquIQwK>bgogc_dKgdXa[_`uKGrCGnV`nu>bUNqjaj:a^s`avX\\R`^Qpd_is[yyZ>`WAZHW^XOlAgrIX]>pg]n\\y^Z`W`g@sGpiSo]?PhLpaWV\\Q`hgausXheP]SqtW`^uNtkovAaiqqwWqopap;as:iZ?fZkfs[Obb^cUh]Qv\\Q`oE?`kn[rwqxgyP?auQgKfmDajmAvOf\\OnyapcWPii`n^`^rHn@>mrg`pn`pg]`Iifxg@q`]>[QqldqtkF`hyhR?eRIgwvg^X\\WV\\Q`qswlOhl?nf_gf_>uMqZMgcAxjAxm>and@]qfmKiZ=al]OlB^cLFk:a>KBM_RZMlB^n`g^tf^COhR`]soiX@r^FaFNcUYamvm>ncDfv^vnbIcinc`>`Co[=FlDx]Lfd_a^LX^locdniTp^e?fZ?fp?gb?g@nbuWlmqjQAsUYuuqiAp[Wns]Q`s@j:@jvVuqiuGwhhaucqdR?eRFeQArTokrhl=@rvigLWydpqwWyhpkCHkSakehojFowVtFy^XN\\LNh[_tbHdm>`<vZA`x;XaI`x@fv_iv?iv`qvHNoG^cAguY_vPAf<IYEcEytjeUd;b>iHPoUXmU_OCJexTmcQ]v;yeQ?VjgG]wU^[gAAxGEI`YfjmT=[S>WWYuUYyUw]YvMCGqVmEg<wCiIB@myXiIvwCAarlsXqeSu=fvMdhQFquC_qT?sEVIdyiGQGI`eh`IV?iWaLo<DUXqT;=TPQJaXnxXkl]sYIvfpT=HWC=wfPmV\\t\\TxHmn;Ll:atBItwAm>ln@Lpt]UJQSHDyneRwAm^LJM^ne@dXWeL_cM>aK`eHnnp?^KOZL`b[`m>?fL@c>n^C@Rj>S>kV=KWhSBTYdTGDR_tqGSdgSIeyFyCsWFCuHZtR^DTkYR\\<PCOqFfvkHpkXdrYflfw@gid@qr@aywrHh]]iuH^s:Ar:Ach@i<?bYP_f^_FInJoc\\F\\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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= the volatge on the capacitor is 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 and the points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR0Y7L0YwUSdpdGFsaWNGJ0Yv are connected.What is going to happen?
<Text-field style="Heading 2" layout="Heading 2">Solution for 2</Text-field>The relevant part of the circuit is: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LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlZztGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiU/NkYqLSUpQ0hJTERSRU5HNiI=The differential equation of this circuit is 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print(); # input 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print(); # input placeholderJSFH
The capacitor will be charged until it reaches a voltage LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.
After a long time, the points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR0Y7L0YwUSdpdGFsaWNGJ0Yv are connected instead of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR0Y7L0YwUSdpdGFsaWNGJ0Yv .What will happen now?
<Text-field style="Heading 2" layout="Heading 2">Solution for 3</Text-field>The relevant part of the circuit is: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The equations for the components of the circuit are: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(); # input placeholderand 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print(); # input placeholderThe voltage law for this circuit is: 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(); # input placeholderWe will derive this equation by time, and substitute the components: 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print(); # input 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print(); # input placeholderAt this time, the voltage of the capacitor is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, and thus, the voltage on the inductor is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtaUdGJDYlUSJWRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8=. 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print(); # input placeholderAs we can see,JSFH
The current will oscillate at a frequency of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Iy1JJm1zcXJ0R0YkNiMtRiM2JS1JI21pR0YkNiVRIkNGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRictSSNtb0dGJDYtUScmc2RvdDtGJ0YyLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlotRj02JVEiTEYnRkBGQy8lLmxpbmV0aGlja25lc3NHRjEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXm8vJSliZXZlbGxlZEdGSy1GRjYtUSI6RidGMkZJRkxGTkZQRlJGVEZWL0ZZUSwwLjI3Nzc3NzhlbUYnL0ZmbkZnbw==print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
What is the first moment after the switch from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv that if the switch will be set back to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv, no current will flow out of the voltage source?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print(); # input placeholderJSFH
<Text-field style="Heading 2" layout="Heading 2">Solution for 4</Text-field>As we can see from the solution for the previous question, the current oscillate at a frequency of 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A simple substitution shows:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoYWxnc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJXNvbDNGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRKWluZHVjdG9yRidGL0YyRkE=print(); # input placeholderthat the voltage oscillate at te same frequency. Since the sine and cosine are periodical with period of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JI21pR0YkNiVRJyYjOTYwO0YnLyUnaXRhbGljR0Y4Ri9GLw==, the first time in which the system will reach its original state is when 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(); # input placeholderThis time is:
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 5</Text-field>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A coaxial cable is made of two concentric cylinders of QyQ+SSZyYWRpaUc2IjwkL0kiYUdGJSQiIiIhIiIvSSJiR0YlJCIjWCEiI0Yrcentimeters. A current LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYElfX2VsZWN0cmljYEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== is flowing throught both of the cylinders, in opposite directions.Find the specific self inductance of the cable. (Its units are henry per meter.)print(); # input placeholder
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>The definition for inductance isPkkkZGVmRzYiL0kiTEdGJComSSkmUGhpO19fQkdGJCIiIkksSV9fZWxlY3RyaWNHRiQhIiI=print(); # input placeholderThe magnetic field produced by the inner cable (between LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRi9GMkY5 only) isPkkiQkc2IiooSSgmbXU7X18wR0YkIiIiLUkiL0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJkkjUGlHRitGJ0kickdGJEYnIiIjRidJLElfX2VsZWN0cmljR0YkRic=print(); # input placeholderThe magnetic flux per meter between the cables is,PkklZmx1eEc2Ii1JKWFzc3VtaW5nR0YkNiQ3Iy9JKSZQaGk7X19CR0YkLUkkaW50R0YkNiRJIkJHRiQvSSJyR0YkO0kiYUdGJEkiYkdGJDckLUkiPkclKnByb3RlY3RlZEc2JEYyIiIhLUY2NiRGM0Yyprint(); # input placeholdersubstituting this into the definition of the inductance: Pkklc29sNUc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiRJJWZsdXhHRiRJJGRlZkdGJA==print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=