<Text-field style="Heading 1" layout="Heading 1">Question 1 & 2</Text-field>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Two identical circuits; voltage source LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and parallel plate capacitor of area LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and gap LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. The energy stored in the capacitor is print(); # input 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Then, the left circuit capacitor is disconnected from the the voltage source, and both of the capacitors' plates are brought to a distance of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRidGMkY1LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZFLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRj4= from each other:print(); # input placeholder
What are the energies stored in the capacitors?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>The energy stored in a capacitor is 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the electric charge stored on one of the capacitor plates, and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the capacitance. The capacitance of a parallel plate capacitor is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJm1mcmFjR0YkNigtRiM2JS1GLDYlUSJBRidGL0YyLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZW4tRiw2I1EyYCZ2YXJlcHNpbG9uO19fMGBGJy1GIzYjLUYsNiVRImRGJ0YvRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmRvLyUpYmV2ZWxsZWRHRj0tRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0= and the charge LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= depends on the capacitance and the voltage: 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 left capacitor has the same amount of charge as at the beginning, but its capacitance is doubled. 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The right capacitor has the same voltage as at the beginning, but its capacitance is doubled: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print(); # input placeholder
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field>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Two conducting balls of capacitances 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 are placed far apart from each other. Ball LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv is charged with charge 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, and ball LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv is not charged. The balls are later being connected to each other by a thin conducting wire. What is the potential of ball LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv?LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>After the connection, the charge LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is distributed on both of the balls. The capacitors are connected in parallel: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 the balls and the wire are conducting, the potential of all three of them is equal. print(); # input 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
JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field>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Two identical parallel plate capacitors are connected in series. A dielectric slab with dielectric constant LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NTQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIjpGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSUYy is placed inside the upper capacitor.What is the ratio between the capacitance of the system of capacitors before and after the insertion of the slab?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>The total capacitance of two capacitors in series: 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print(); # input placeholderRemembering 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 capacitance of a plate capacitor is proportional to the dielectric constant of the dielectric.Before: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYENfXzFgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EnYENfXzJgRidGLy1GLDYlUSJDRicvJSdpdGFsaWNHUSV0cnVlRicvRjRRJ2l0YWxpY0YnLUYwNi1RIjpGJ0YzRjZGOUY7Rj1GP0ZBRkNGRUZI After: 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Substituting it to equation (3.1.1), we can express the total capacitance of the system. 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(); # input 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print(); # input placeholderJSFH
JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Question 5</Text-field>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An infinite coaxial wire is made of two infinite thin concentric cylindrical shells. The inner shell's radius is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and the outer shell's radius is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Assume that in the space between the shells there's vacuum.What is the capacitance per unit length of the wire?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>In order to determine the capacitance of the wire, we will calculate the electric field and the potential difference between the two shells as a function of the charge density per unit length of the inner cylinder. (This charge density is equal to the charge density per unit length of the outer cylinder.)Using Gauss law, the field between the cylinders is: 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print(); # input placeholderThe potential difference is: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print(); # input placeholderThe capacitance per unit length is:
JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Question 6</Text-field>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JSFHWhat is the equivalent capacitance of this system between point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ?MFNWtKUb<ob<R=MDLCdNRernKb;rvIv^_aI>uC_b;_drOugimg_gNGeSvraOagwn=wul@d^@tpG_h^_@NcsGl@nh_GlRy[`NZEol>y_T@\\J>twA^>waKVn`PbT@waf^JvdGHtB>]oW\\yfgjFeB_\\[FbROp:G[C^l<H_Wp_nhv_WuLqlpouwxy[aml?]aiwXIqmwwVImyyasHmXYiaovpausiuaqaaIaaqaIXqeXoEibKocLG]IGZ??gcNkJQdNFn_@[gfbKNeDP^n`dkGoVxnZvhWnav?a`poqghoGqkh[i`au^jp@^;hc>X`KNfDpw;Gb=V_gf_Iq[[hhF>pNFno_oB^`[hnbNbEG\\TOKtNraocQRUEU@hqVIpR]oFTKxqLEYOuYTfuOcEYp`WSQrm@VJMusXQF<QkQmhLp:hxmyvIyyFEYY]MPqyxqyHYvAykYYtpiXOitOiYPAuRAY=iwpushywcIwSYtUYuuqujAxjQq`qv`yS>qqLxLAtLlAVkUL]tJCxwKAjnuR]HtlAS^LTctpcUwOLutejAYvCDkoQXGLuWqYyxyWPytQYyuRAuriHpIUJqLRbEOM=rOIxpAygqU:MwOXM=IvjeLZlOeTOE@JdeWWYowPY^\\vRyo;TMOArGPVMdYTMsLEKEUw;<mlU]E>l?xkeIZJAppPvwif:p\\UIxSoh>A_u^^u>fXfrw>xBqcSn\\rP[\\Xj`QlPHecApKNeDq`jguCqtkQ_ZictpcbG_Ddi[HxkIxQYyuYyytrMcYmrfEI_Eh:YfAsthgUUyY[Qr?wefiuuwxgov`qvEach[iLcIZOCGQt@KB;OY:SieuthosuwXiqW_IW`OCXKuAwCYkYsUypiwYiUn?WKiT:YCBGYdGg<obpqtgWUYaUv?YkIYiwtukisUx`qw;Gb;gsvctNEr<UIocHoibausXgHGYeqsgISwekTf?yuov\\[Y=wfTOGR=WY<xZURWeUWYJ>mKj@ND@xcynYpqIxTXpWd@N]xJQuoXeuyPWOQoy@soQkDPkc<qBTj=XjiUV\\yJphuyxYyUKPtNW@OgqwKaUMUTm\\UPmTPlsoYq>AkQevMynIuuFqvwIrZ=p`Qx_Ysy<OitOYpLMLW\\mVnxnmXpmyrOitOYN_dWcevI@tPqtpyp_TSP`yEmOjELhmuvHygtNYeuRpRBxMt@UfhLTYnWiLuLSXQtHdKGdoMeof`t<hJElWnixoiWYDMSDUGxqUUUUuyGhrCuNDUwFmYoesThPyMP[yyHxSE]joatHIsP]sQhsnIjDQsDIsGXMqlMoIyvuSoXQQapSTtMDtX\\YiEs=UKETmduMYpS_PKpXN@ET>pl\\JbE?:D\\NfbbG_<WcK_jPPnBfomf\\mWqWIpnVwNO[kvlQhi:qbUOeToymxiyqyH^sihodPoTvrpF[inyXoqvGyA?s^@ogY]=Qa[phb^p?QdmX[CpvjFoUUwWDBaEMETKExVSDFiBRGTvicSUX[?TbmcAYvCKcCyvksTCwFYWXV[h?MTmWGheR;CF:eB^?bPUBr;f;IEJSX_UVTQyFdkgAYi<JQ=n`xSeaTZen_hXTISA<YTVb<^sa?hG^n_hj?n\\JpZdV_ev^nhi]@idH]iirxNeTwjROu\\^oSiZeWwLvpvAc<wbFowMH[Nhu<^xBfofG\\o_rnSIqV[[XcaSI]f^mGnavJcFBmDg;XaOuQ?EW=GjqxJKuv]uOGxFSuSWHamYc_yJIUe]V^]fWUyfygjUgPYwD[ikqrUsVqcWTaxECEW;S>?FW;FcqiTCIguSX_IsySeWu=wfLwXhausiw^mwDgDWcvLEbpkyjCFLCc^TuGlYbUNYXRK<LSuS;anTHKk=VKhOVqkpANO<JXDjQQuL<Ti\\RePQDin:doUmnExRamncHocYLePt:YsrUovIl[EmL=UUeYqyVkUWAMyu]V^`RUaUyym^HQidw;Iv[EWkErBXkjLmcXnfmPrpk:pPMiO`TtgyRtqWBetnqwuxwhYK@Tjo@jbtmyLp>lLKEJVQj[EwO`XnIQwep:\\pFDOgyXfAukxJCly>es@tSxXu=@pVlJu\\Vu=XHtkVDQLdplXnfAMEUmD\\UoUmteRexwMxNV]jSPJrIpKYXIyp_ML=<KmLVj=rf@XO`kj<NfmL@yX]ljEtp=anEPNW<qKELImKDAYlmPKdKmHjp]lu=lhpVQMp<XX\\eQ`lj:UN\\Dt?LJqYtP\\LWAlKVpZQm[Q]^New^rsGZLPdsItDpx>>pBwt:Ht=VjQgg`XoSok`F[eWagQpbV^q`]wQ\\kotbHkYY]KVn_?pjXtsqplPgu_fU`wT^wbflbIbv>fyV`mVdq^av^q@QsDG`rIjeWgewjTN]TngU@[g_cN`]GPywqyi@cYvtdpxZQniGgcGq^WeIQem@d?wbbO\\Yy`XYp@OtoXdapcWhptyycwgiwa_hhRpxT@gggfA_ovXquXi@QwpA^TNhZAr;x`?AoW_`MwfRawrfgSG;qrO?UEotDEstwh`EU=aVOsEgcigEWAyDKyDI_XmOT?ohlIH>sUNmdpCHL?FxqeGGWxKYnAggqrGWEu_rCstOIDuoYwQyqmthgUuyR]kyfUV]UVIQsOWGy[RrYs>_yloWCcC<uXqqwWYyt=GNKg@iRcwF^iX_QsOwwicUt_x]IimuvXYtMIy=gXoIyvueiCUl_vVKP>uJMeWImn\\qtcPNvdNcYt`UTeXSuhoGlXn]Xv=V^lSE<WQuoXeY<uWBYS@IWmitkYWdMWtPLB\\JdaLEylO@JVVqjGv<Ywt^ybAiBY_WAtiOaJVt>?iDW\\Ta`Gxlkgc>@k<PuIh`?xq?Gp^gea^cm@`]PauVckYf\\^t``s?hsoxpWVi[?yXGgI_cNqtoAwr@n<A[QHrdOwcw[xvj]OoxaoCvqKVnAFshgglOto`ioN`mNotPqtIlK@xJNvcp^HYaJhwC@krfgN_pAwd>_Z:Yv\\^tMpqXGhKNrDatCojvPxOyhJVvxI`sa\\:HlUi`@x_G>e?IergcVx[uVg?irV`eWYxH^jeQ`?Vgexx<Hhw`]jH`VqmVOabgnnf`KombAofIZeq[o@gPirBhdNGZHgxp`bJY`fwlgI`vaZi@pRH\\KI`nNw`@eH^gKojvPprFtdhnBQiC?pRPixvlHykGxbpnsWXaq?]EiwUypqOs[AefNeaygInpYOqnGwAHg\\h]kVjEo_Yh`?>e]Xpy@yBFqGpop`_Gah[U[yfRAtXquxyv_UsPgy=;h]uUIuSIqWyw]Bnv]Nw[`c?^hfYfqNo?h`dggS`o=q_Mxy\\?jZ`aVn[QGsg?]:@\\M_[k>\\\\i\\KnkrYIwShwdt?CggSPmt_ke`?C?ORxCiKSFaMBH]iteVBSSFkcNEcjodU?tLmhSMUcqEb;tt]rMeDkICXQsjwOXEN[uNn`lg@v`<RbtmJhXeHXQaroMREeL<<qNDn_@KgN^n`<jbJ>pl\\\\pNdvRDX<lRPPr><XuPT_ySHmSh\\Qt]xbiYmtqMTp?qrAyrYuNnhRfXRApKwpV`TPRxf??bXxayouj_wRIpyqnuWhGgcGAtxhiuqulIyvwc?Oga`mYVusFh\\ars^cs_nu?bK_jP<NkJQdNVnAndb@eDwmLNuLNZp@[DwmLiabffZgn_hvSI^npk;nl\\^pHh\\;p^n`\\?K[JeaJYhPW=WeTmjxlFMTvpWWQqYYnXXReUWeIQQYsNlmKivEyly]jgYoPeotYoCIygeMglrcechOqLynC@ZEiwDgT[h[Ur@WVBUY>_FAQFGiYvSupUUUUuA?ex?g^sSpSFwiI[gFrGgEue`OBRUUAiEhmHeCYOeTO]IScefsuC_vGQEbowDQsDICSOyXcfDeVpSX<USSOBhoswExDWcloy=;f>mghcfPGRvSSq?Gtcw;afiEhi[SEUSbewNOUqCF\\oWMkw=]TvCfZcuCKUSMReeiL?yyGsdqF>atHOUlgwcQypMIyiF]Cg=UV>ohnEbGqB>_S:?iakF`kDwCYlavEMYmwGHuSIuip[Hn[hHuSOwRoQVd=Wb=wgggggYbQVCmf\\yBParsSCkyb]SytQypoexcYtyX@miZawSYhegcX[YUqhguu==IH=ipCWEacTgIIUbJQU:[WlwEmsVA?U^UCQCE<iGQ_gGCFVYeBMgEKHYStnCCggcKgbV]gf_g>mctqheytiwyG_SqueIaFGQWKuVVsDAaDkeVRUtbMgcMe`UbE=OUmwsYxayu<mU>\\K<=KjUxDdO:hRRpSgpUSPKRMyn`leDSNIN<HRA\\TNtj?Yp\\`VM\\YR]KB@vrHu@HvFqJT@ttdt>Qk;<kSHmSPyAykYtoJhTk]orlOZej?xjohtUEkV@tL\\ubuYyuYaIwMynyUWoIpqhWUqxxQuoXWyAVAUqsTsEIoxIjbAk[Ps]hSKYJ>mODiwbps]qtviKL<v:UNE<VKerk=Xj=xgYQqmwfAJ>MYVYj;Hj;hsTuJh=YXaqseYteoulvD=VTaVEUSEiRsDladUa]kkMUdmlY\\ORDmLAvUDK@TjOQY\\mpMTLMdSGhkGhQEulhdyRuVA]O^hXvqnntYp]Tg`khxXTpVh<LMLUaqRILnCMnAlMQmlmEKjDTaDPnelGIX?]xZmRR=ujPUOdQMaPGaTiINnhN>loVPubTrWMYVYJ>hovpUiYpdQwdIL=DTE@PZxjU@vD=mu=V?]qP@tttPl=LMplHNhCHdl`gyvgJQtDImaOtLYulA[JFnoopE@^ah`@_f>GrBhrnRuSyy;uKAX<UU>;x`?BdSWEGwnoBmpllELTMkDAnVUQe]jPPn_hnbLREk\\\\`D\\[D<PnBNKFn_@o<P\\aGisVehW\\xvgnYa\\_jPPt?V]`qspaxnawXV]UVgoNZXNh_>^aOrbAwby\\oQrDHk]Y]qBIOscic>odDaSGYcAyre;BgwuiyYasdiQwgiw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<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>We will use the formulas for capacitors in parallel (QyQvSSxDX19wYXJhbGxlbEc2IiwmSSVDX18xR0YlIiIiSSVDX18yR0YlRighIiI=) and in series (QyQvSSpDX19zZXJpZXNHNiIqKEklQ19fMUdGJSIiIkklQ19fMkdGJUYoLCZGJ0YoRilGKCEiIkYr):The capacitors on the top and right edge of the top square are in series: QyQ+SS1DX190b3AscmlnaHRHNiIqKEklQ19fMUdGJSIiIkklQ19fMkdGJUYoLCZGJ0YoRilGKCEiIkYrThe capacitors on the bottom and left edge of the top square are in series: QyQ+SS9DX19ib3R0b20sbGVmdEc2IiomLUkiKkclKnByb3RlY3RlZEc2JEklQ19fMkdGJUYrIiIiLUkiK0dGKUYqISIiRi8=print(); # input placeholderThe two capacitors not part of the square are in series: QyQ+SShDX190YWlsRzYiKihJJUNfXzFHRiUiIiJJJUNfXzJHRiVGKCwmRidGKEYpRighIiJGKw==The two branches of the square are in parallel: QyQ+SSpDX19zcXVhcmVHNiIsJkktQ19fdG9wLHJpZ2h0R0YlIiIiSS9DX19ib3R0b20sbGVmdEdGJUYoISIiprint(); # input placeholderThe square and the "tail" are in series: QyQ+SSdDX190b3RHNiIqKEkoQ19fdGFpbEdGJSIiIkkqQ19fc3F1YXJlR0YlRigsJkYnRihGKUYoISIiRis=print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=print(); # input placeholder