capacitors in series and parallel problems with solutions pdf
mPrf_qp3gm>X*O`HXn\iGF+.XI%i?$2tg59jfIV=Q@-_gZ=7):L? Current will flow until)]TJ T* 0 Tc 0 Tw (that voltage difference disappears. )Tj /TT6 1 Tf 12 0 0 12 90 429 Tm (14.14\))Tj /TT5 1 Tf 3 0 TD ( Assuming there is)Tj -3 -1.25 TD (no charge initially on any)Tj T* [(capaci)-27.5(tor, answer all the)]TJ T* (following questions for the)Tj T* [(capaci)-27.5(tor circuit in )]TJ /TT7 1 Tf 8.9704 0 TD (sketch a. ._YYSnn>G\"/UqPdnf"iatdmL,-anc%&Zba.hW/XfkAeH )Tj /TT7 1 Tf 0.8335 0 TD (Without disconnecting the battery)Tj /TT5 1 Tf 15.4209 0 TD (, you)Tj -33.6252 -1.5 TD (carefully insert a piece of plastic between the plates. )Tj ET 130 360 m 168.706 360 l S BT 10 0 0 10 130 361 Tm 0.0081 Tc 0.0911 Tw [(Solution)-21.3(: This is really a review question designed to remind you of the nuts)]TJ 0 -1.3 TD 0.0042 Tc 0.0422 Tw [(and bolts of an AC circuit. That)]TJ -21.9449 -1.2 TD -0.0007 Tc 0 Tw (means, according to )Tj /TT7 1 Tf 9.4303 0 TD 0 Tc (C = )Tj /F4 1 Tf 12 0 2.64 12 231.75 409 Tm ()Tj /TT7 1 Tf 9 0 0 9 239 404 Tm (o)Tj 10 0 0 10 244 409 Tm (A)Tj /TT5 1 Tf 0.7041 0 TD (/)Tj /TT7 1 Tf 0.2959 0 TD (d)Tj /TT5 1 Tf 0.6108 0 TD -0.0006 Tc (, that the capacitance should diminish by a factor of)Tj -14.3108 -1.6 TD 0 Tc (4, giving us )Tj /TT7 1 Tf 5.6 0 TD (\(1)Tj /TT5 1 Tf 0.9 0 TD (/)Tj /TT7 1 Tf 0.3 0 TD (4\)C)Tj 9 0 0 9 201.1133 388 Tm (original)Tj /TT5 1 Tf 10 0 0 10 234 393 Tm (. !mSf%-(q5N^C#fFd1O(J+W,I(B$deQbB%qid/AUl-g7D&gD_2^quQb_NPOn[17^:I 62']dpI:9XSR_[2o24WrbQ`-=GpW&,bZgK:feWHZ*97s33Z2%mIYC`kP4a#h*i:[, )3XGM63;>Og_V4[5D&+WFhc/N3CX?oj>`":mG]Q)I70!phB_AR-#T^34bM4+K22\1aL?Y )I`\`HAmX(\#n0FO):Rk[GB/BA'o7Jmj;7<1jkYU fp,_%#X:dM`5.U/"l")L-f:IJj@Ad]nqrXt:)9! )Tj -38.4 -1.3 TD 0.0045 Tc 0.0449 Tw (These move through the resistor and back to the ground side of the power supply. M(-)7&1Z\C,XMSE^:&jj9@]V=dM1"0BITQo. ]SA?dNIO>647#*9ie)#=?D>FpWa(!XkfkFrS@4]n,&Wiqk!8% Eo2]qG!`+XcPF&oQ&.89VOn`8a-[1q;s$%*1c*D5B,SLrfsPXdrKt:=gh/$qiRfOl )eac\o_P76*-\<78UEMH((!Le%d>kLWAC!&?MJ"tjkLqL5kga;,N5i&67.#!$o,>$EN+\>S+qLTubf>Zp81f'NQRc.X61X\V]s3W1)Qk^dgaXdLc )Tj ET 135 549 m 173.706 549 l S BT 10 0 0 10 135 550 Tm [(Solution)-29.4(: This, by Ohm's Law, is true. ipe=&?nV:=&L(NH$.UN6Q$mS`?`n\L0m.hQn8>j/K6PpD@V . VUd5V@[!. 8^1B2lFN[?p9k**Rau;7:NS\PG^a#CcHbK5O53r@\c%/Q4`%s,-E_[je67[k7T?N2KI\[l PYG@q0-(afMG;NsoMC:Ac^I?`-Q2Ye#f\P+ZT,-,$b&Q>8'HPH7%20cmr91_i_ReN#Im)LN.L&""DBD>VN%s8r]or!H[Jbd(b"rC8@6GMEiE:j )Tj ET endstream endobj 59 0 obj << /Type /Font /Subtype /Type1 /FirstChar 1 /LastChar 15 /Widths [ 768 549 439 384 384 384 384 384 384 549 576 439 987 521 549 ] /Encoding 75 0 R /BaseFont /JAFCJG+Symbol /FontDescriptor 65 0 R /ToUnicode 76 0 R >> endobj 60 0 obj << /Type /Font /Subtype /Type1 /FirstChar 32 /LastChar 181 /Widths [ 278 296 389 556 556 833 815 204 333 333 500 606 278 333 278 278 556 556 556 556 556 556 556 556 556 556 278 278 606 606 606 444 737 722 722 722 778 722 667 778 833 407 556 778 667 944 815 778 667 778 722 630 667 815 722 981 704 704 611 333 606 333 606 500 333 556 556 444 574 500 333 537 611 315 296 593 315 889 611 500 574 556 444 463 389 611 537 778 537 537 481 333 606 333 606 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 556 556 0 0 0 0 0 737 0 0 0 0 0 0 0 606 0 0 0 611 ] /Encoding /WinAnsiEncoding /BaseFont /NewCenturySchlbk-Roman /FontDescriptor 73 0 R >> endobj 61 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 117 /Widths [ 287 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 759 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 611 537 0 0 0 0 0 389 0 0 0 0 0 0 0 0 519 0 407 685 ] /Encoding /WinAnsiEncoding /BaseFont /JAGBBL+CenturySchoolbook-BoldItalic /FontDescriptor 71 0 R >> endobj 62 0 obj << /Type /Font /Subtype /Type0 /BaseFont /JACCJC+CenturySchoolbook /Encoding /Identity-H /DescendantFonts [ 77 0 R ] /ToUnicode 78 0 R >> endobj 63 0 obj << /Type /Font /Subtype /Type0 /BaseFont /JAEEPE+CenturySchoolbook-Italic /Encoding /Identity-H /DescendantFonts [ 79 0 R ] /ToUnicode 80 0 R >> endobj 64 0 obj << /Type /Font /Subtype /Type1 /FirstChar 32 /LastChar 181 /Widths [ 278 333 400 556 556 833 852 278 333 333 500 606 278 333 278 606 556 556 556 556 556 556 556 556 556 556 278 278 606 606 606 444 747 704 722 722 778 722 667 778 833 407 611 741 667 944 815 778 667 778 741 667 685 815 704 926 704 685 667 333 606 333 606 500 333 574 556 444 611 444 333 537 611 333 315 556 333 889 611 500 574 556 444 444 352 611 519 778 500 500 463 333 606 333 606 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 556 556 0 0 0 0 0 747 0 0 0 0 0 0 0 606 0 0 0 611 ] /Encoding /WinAnsiEncoding /BaseFont /NewCenturySchlbk-Italic /FontDescriptor 74 0 R >> endobj 65 0 obj << /Type /FontDescriptor /Ascent 0 /CapHeight 0 /Descent 0 /Flags 4 /FontBBox [ -180 -293 1090 1010 ] /FontName /JAFCJG+Symbol /ItalicAngle 0 /StemV 85 /CharSet (/parenrightbt/plus/tau/equal/epsilon/mu/nu/pi/parenlefttp/arrowdblright/\ parenleftex/Omega/parenrighttp/parenleftbt/parenrightex) /FontFile3 66 0 R >> endobj 66 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 1839 /Subtype /Type1C >> stream [ig'D!&]+q'r.uO[HEj)UNEO/A_^?M"\NtLi#n$L]jGit(mD[rqs8pE2&X'tpZg*6e!Hdp )Tj /TT6 1 Tf 12 0 0 12 94 96 Tm (b.\) )Tj /TT5 1 Tf 1.6021 0 TD ( What is common to all the capacitors in the series combination? V(huT$jO=jTWm03Zgh=_UfMcdaq`Q_:[[+&,p\)[,cQZ3!S"f8&2UWpLi )Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 1 i 135 678 m 173.706 678 l S BT 10 0 0 10 135 679 Tm [(Solution)-29.4(: The energy wrapped up in a charged capacitor equals:)]TJ 9.9 -2.8 TD ( Energy = \(1/2\)CV)Tj 9 0 0 9 328.0234 656 Tm (2)Tj 10 0 0 10 333.0288 651 Tm (,)Tj -19.8029 -2.4 TD (where )Tj /TT7 1 Tf 3.1104 0 TD (C)Tj /TT5 1 Tf 0.7222 0 TD ( is the cap's capacitance and )Tj /TT7 1 Tf 13.3164 0 TD (V)Tj /TT5 1 Tf 0.7511 0 TD ( is the voltage across the cap. As a consequence of this change in)Tj -20.1667 -1.25 TD (geometry:)Tj /TT6 1 Tf 1.8333 -2.5 TD (a.\))Tj /TT5 1 Tf 1.2778 0 TD ( How will the capacitor's )Tj /TT7 1 Tf 11.8888 0 TD (capacitance)Tj /TT5 1 Tf 5.3682 0 TD ( )Tj /TT7 1 Tf 0.2985 0 TD (change)Tj /TT5 1 Tf 3.2207 0 TD (? [FjZ@97)L )Tj -10.8526 -1.6 TD 0.0074 Tc 0.0738 Tw (--The full 120 volt drop will be across the 30 )Tj /TT1 1 Tf 21.6444 0 TD 0 Tc 0 Tw <009f>Tj /TT5 1 Tf 0.7755 0 TD 0.0074 Tc 0.0738 Tw [( and 20 )]TJ /TT1 1 Tf 3.9676 0 TD 0 Tc 0 Tw <009f>Tj /TT5 1 Tf 0.7755 0 TD 0.0074 Tc 0.0738 Tw [( resistors in series. cZeD^7@r7Om&Z#-o@Yt9mO,hh_,G:a>Vj;WZD]etR`2=1eBLurI=+/A(Fl+X60R0'1o/g$'RsFQ)q'G]'KhS!D)l`IUmDG.HYat7 )Tj -16.2108 -1.6 TD 0.0262 Tc 0.2623 Tw (Mathematically comparing the given capacitance of the dielectric-filled)Tj -1.8 -1.2 TD 0.007 Tc 0.0703 Tw (capacitor \()Tj /TT7 1 Tf 4.9803 0 TD 0.0272 Tc 0 Tw (2[)Tj /F4 1 Tf 12 0 2.64 12 181.75 131 Tm 0 Tc ()Tj /TT7 1 Tf 9 0 0 9 189 126 Tm (o)Tj 10 0 0 10 194 131 Tm (A)Tj /TT5 1 Tf 0.7041 0 TD (/)Tj /TT7 1 Tf 0.2959 0 TD 0.0233 Tc (d][2k/\(1+k\)])Tj /TT5 1 Tf 5.992 0 TD 0.0086 Tc 0.0861 Tw (\) and the calcuated capacitance of the metal filled)Tj -14.292 -1.6 TD 0.0047 Tc 0.047 Tw (capacitor \()Tj /TT7 1 Tf 4.9317 0 TD 0.0182 Tc 0 Tw (2[)Tj /F4 1 Tf 12 0 2.64 12 180.75 115 Tm 0 Tc ()Tj /TT7 1 Tf 9 0 0 9 188 110 Tm (o)Tj 10 0 0 10 193 115 Tm (A)Tj /TT5 1 Tf 0.7041 0 TD (/)Tj /TT7 1 Tf 0.2959 0 TD 0.0253 Tc (d])Tj /TT5 1 Tf 0.9944 0 TD 0.0077 Tc 0.0768 Tw (\), we can see that the two capacitances will be equal if )Tj /TT7 1 Tf 26.6056 0 TD 0.0097 Tc 0.0974 Tw (k = 1)Tj /TT5 1 Tf -35.8 -1.6 TD 0.021 Tc 0.2105 Tw (\(i.e., if the dielectric is )Tj /TT7 1 Tf 12.2 0 TD 0.0497 Tc 0 Tw (air)Tj /TT5 1 Tf 1.5002 0 TD 0.0188 Tc 0.188 Tw (\) and the dielectric-filled cap will have a greater)Tj -13.7002 -1.2 TD 0 Tc 0 Tw (capacitance for all other values of )Tj /TT7 1 Tf 15.8 0 TD (k)Tj /TT5 1 Tf 0.5562 0 TD (. )Tj ET 139 403 m 177.706 403 l S BT 10 0 0 10 139 404 Tm -0.0005 Tc -0.0001 Tw [(Solution)-29.9(: Energy in a capacitor is calculated using )]TJ /TT7 1 Tf 23.725 0 TD 0 Tc 0 Tw (.5CV)Tj 9 0 0 9 399 409 Tm (2)Tj /TT5 1 Tf 10 0 0 10 404.0053 404 Tm -0.0007 Tc (. `6;3+FU60%(N?p@:adK@=\/sQ.a^a``H0sO=lfI.5"Q\l$pkrb)FBZV+_KAE@`sCL What happens to the current in the system when you do this? KLe? )Tj ET 135 175 m 173.706 175 l S BT 10 0 0 10 135 176 Tm 0.0058 Tc 0.0698 Tw [(Solution)-23.6(: What is common in series combinations of)]TJ 0 -1.3 TD 0.0036 Tc 0.0361 Tw (capacitors is the )Tj /TT7 1 Tf 8 0 TD 0.0104 Tc 0 Tw (charge)Tj /TT5 1 Tf 3.1161 0 TD 0.0031 Tc 0.0314 Tw [( on each capacitor. Give an example. (A`2gr@*rQ%.g5`Y]uB9$tlJE5m5M>7+prjpt?5/RmckBIQq; +>5BcOCT&kkjkDr"&Ju?:@ka7N(=2L'@Mj3T(G:r:J!g7'TAB@dQfh0Tr? %[F(0GqgjFKtWajPJ5W05R[0"U+?I6(/jN!9/t(o4!Z7_>r2KLF%#DBo5":&@!W`^LkE_Xr=:C(QAR80eOfq8;r-<7lM_c 6#13IokEVf"#-XIKNRoD*[t4W=*+r?dojnm`2dAb_.!7gR*b#0^! 2k/(7.CHCL]e`Pj%. "%Vq$V5?C7sWCsG1=#@ )Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 117 694 m 155.706 694 l S BT 10 0 0 10 117 695 Tm 0.0021 Tc 0.0234 Tw [(Solution)-27.3(: There is always some resistance in a circuit. RcQRWBY*MoJo5]OHjodO? @].&G*UUMleM,M"LQoZrbA7g%[a\,ce%--^le%Pp/8S$#Q(\[1e8eD0W\hfiW)_hB 7H,T[_WUmcqnB]250rgap[5Wu+H@bp[iXt^!kZT?A\^gl7(ZmO+43#UBCQaHiV? Which of the)Tj -3 -1.25 TD (following statements are true \(there can be more than one\)? LbtjkO&NM9jhC>J35KUi(5efp*?oH]c6[M&3eUc\;%02/7/s.FA#\\aX!<5D(nd99 If)]TJ 0 -1.3 TD 0.0055 Tc 0.0554 Tw (that is the case, there will be no voltage difference between the high voltage sides of)Tj 0 -1.2 TD 0 Tc 0 Tw (the caps, and no new current will flow. )Tj /TT6 1 Tf 12 0 0 12 112 578 Tm (b.\))Tj /TT5 1 Tf 1.3333 0 TD ( The RMS voltage across the resistor is equal to )Tj /TT7 1 Tf 22.5566 0 TD (R)Tj /TT5 1 Tf 0.6934 0 TD ( times the RMS current)Tj -26.4167 -1.25 TD (through the resistor. Bs^@Rg%_;=At+FkiiiUn0)uP3!E`2JWJhJb!2l`L< BT /TT5 1 Tf 12 0 0 12 72 39 Tm 0 g /GS1 gs 0 Tc 0 Tw (910)Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 1 i 117 709 m 155.706 709 l S BT 10 0 0 10 117 710 Tm 0.2735 Tw [(Solution)-29.4(:)-24.9( )]TJ 5.3054 0 TD 0.0249 Tc 0 Tw (The )Tj /TT7 1 Tf 2.3946 0 TD 0.0103 Tc 0.1029 Tw (capacitive reactance)Tj /TT5 1 Tf 9.5 0 TD 0.0186 Tc 0.1864 Tw [( is inversely related to capacitance, so an)]TJ -17.2 -1.3 TD 0.0076 Tc 0.0756 Tw (increase in capacitance will create a decrease of )Tj /TT7 1 Tf 23.2807 0 TD 0.014 Tc 0.1399 Tw (capacitive reactance)Tj /TT5 1 Tf 9.6193 0 TD 0.0121 Tc 0.121 Tw [(. 3%CLn,M>!O_Gl>eFOHGm>5cc98JXqP/tA8X+_d*W9*\>p04K>4=KK1;e0C*?TTF`W' /q:DqVpOIE-J7_BN-(U1AQl&CD2'+$(/BE*I#Mr_kgo5XC:-&3eu?LX_h"+K)bPNm d:/m,jOUn@)`-bQU,be! )Tj ET 135 491 m 173.706 491 l S BT 10 0 0 10 135 492 Tm 0.1396 Tw [(Solution)-29.4(:)-12.7( )]TJ 5.0254 0 TD 0.0127 Tc 0.1269 Tw (The capacitive reactance is a measure of the resistive nature of the)Tj -5.0254 -1.3 TD 0.0196 Tc 0.1962 Tw [(capacitor. What)Tj T* (is the )Tj /TT7 1 Tf 2.8335 0 TD (maximum current)Tj /TT5 1 Tf 8.3332 0 TD ( drawn from the source? )Tj /TT6 1 Tf -7.25 -2.5 TD (i.\))Tj /TT5 1 Tf 1.0371 0 TD ( How much charge is on the )Tj /TT7 1 Tf 13.3796 0 TD (plate B)Tj /TT5 1 Tf 3.2773 0 TD (? @kmV?jj5,%GcdG$ZPfOo\9P\F]=9j]:jpm.^XITr8D2Q )Tj ET 135 325 m 173.706 325 l S BT 10 0 0 10 135 326 Tm 0.009 Tc 0.1011 Tw [(Solution)-20.4(: Energy in a capacitor is stored in the electric field found between the)]TJ 0 -1.3 TD 0 Tc 0 Tw (capacitor's charged plates. Electrons in)]TJ 0 -1.2 TD 0.0028 Tc 0.0283 Tw (the insulator will stay in their orbitals \(remember, valence electrons in insulators)Tj T* 0.0099 Tc 0.0987 Tw (can't wander about the way valence electrons in metallically bonded structures)Tj T* 0.0045 Tc 0.0451 Tw (can\), but the plate charge will motivate them to spend most of their time close to)Tj T* 0.0128 Tc 0.1277 Tw [(the positive plate. To find the total capacitance, we first identify which capacitors are in series and which are in parallel. Doing so)Tj -4.9217 -1.2 TD (would have yielded the equation:)Tj 18 -2.4 TD (V)Tj 9 0 0 9 277.2217 518 Tm (o)Tj 10 0 0 10 282 523 Tm ( - i)Tj 9 0 0 9 294.0361 518 Tm (3)Tj 10 0 0 10 299.0415 523 Tm (R)Tj 9 0 0 9 306.2632 518 Tm (30)Tj 10 0 0 10 316.2739 523 Tm ( - i)Tj 9 0 0 9 328.3101 518 Tm (1)Tj 10 0 0 10 333.3154 523 Tm (R)Tj 9 0 0 9 340.5371 518 Tm (20)Tj 10 0 0 10 350.5479 523 Tm ( = 0. BUV_WJ=dMP3>D#9[&l=gjL`d=^UWZJ.f<1%Hi8j]fISgnUCHoKb= ;+%/'L?^1.aA@B#.QQ 1F`+KKnA'^$InATM#tTe> _0lbjS(&ep9-_k^kmu4PoIjo^UARoCPX7SO,g#,2Bo+PI.FZBAmQ9YYg[K*.1Hpa> Y%md,jTCGdJM#Eo4On9)Nq+@m>)p;sf=hB4JIqU(Aso]GmLlV_E_QmuO]RVO$iskR )Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 1 i 135 619 m 173.706 619 l S BT 10 0 0 10 135 620 Tm 0.1349 Tw [(Solution)-29.4(:)-12.3( )]TJ 5.0156 0 TD 0.0123 Tc 0.1226 Tw (The average voltage across a resistor in an AC circuit is )Tj /TT7 1 Tf 28.0844 0 TD 0.035 Tc 0 Tw (zero)Tj /TT5 1 Tf 1.9906 0 TD 0.0084 Tc 0.084 Tw [(. RQZGX\-/cb8iIp#N'3,oJe endstream endobj 79 0 obj << /Type /Font /Subtype /CIDFontType2 /BaseFont /JAEEPE+CenturySchoolbook-Italic /FontDescriptor 69 0 R /CIDSystemInfo << /Registry (Adobe)/Ordering (Identity)/Supplement 0 >> /DW 1000 /W [ 146 [ 712 ] 155 [ 548 ] ] >> endobj 80 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 309 >> stream b"s/R%s_TiW1g9)Nq3l\A8-o$_&\$EdMZ't, %qBn@W)*-aGqYd)ZC@if(tE+6j3dNuF]S-?#C;R^[gTnkntXi(uq$& B-][VaF##'n. ;qG_t26H-:#WmeF>1U,uD;!A^\$aSAFN-3e-9s]%^LXj"\FGF"K@A?hP+lg]47e/1.JB,ij1f_+?_)28c?QY?ph$)%^tce];@P2nbGD3qM0,D'"BF[p@\`"ZWgfDcp+Qr0I6ePa$MDJG\aRXUMi-i?UdJTS>ifSP=qWmP.s2AH<8*"?>l9hi#N In other words, in this problem, the resistance)]TJ T* 0.0016 Tc 0.0159 Tw [(information won't be used. ?hfnL)5QKfk":7T;U4ld"D+5c=r"?5.Y&9V*QT#uBtf!4d&hiM")@*:0$\mF;W[R65e]+Z^*6gn[A3og )Tj 2.7 -1.2 TD 0.0063 Tc 0.0632 Tw (--When the switch is closed, the 30 )Tj /TT1 1 Tf 16.9461 0 TD 0 Tc 0 Tw <009f>Tj /TT5 1 Tf 0.7744 0 TD 0.0063 Tc 0.0632 Tw [( resistor is in parallel with the two series)-33.4(-)]TJ -20.4204 -1.2 TD 0.0028 Tc 0.0284 Tw [(connected capacitors. )Tj /TT6 1 Tf -25.0833 -2.5 TD (a.\))Tj /TT5 1 Tf 1.2778 0 TD ( Current initially flows between the high voltage terminal and )Tj /TT7 1 Tf 29.3359 0 TD (Plate A)Tj /TT5 1 Tf 3.3862 0 TD (. hn@Uif#)9+? -k@7?YUh&n>:!pW1gAZ*;I2HUFW@4H.SYH;7fJH0:b! "(&f/V)!2'Lo^e8>KeE\jXqt#o.-l#INZajEIjS(Zl In short, )]TJ /TT7 1 Tf 5.128 0 TD 0 Tc 0 Tw (C)Tj 9 0 0 9 310.2217 206 Tm (2)Tj /TT5 1 Tf 10 0 0 10 315.2271 211 Tm 0.0009 Tc 0.0085 Tw [( gets two-thirds of the original charge on)]TJ /TT7 1 Tf -19.8227 -1.6 TD 0 Tc 0 Tw (C)Tj 9 0 0 9 124.2217 190 Tm (1)Tj /TT5 1 Tf 10 0 0 10 129.2271 195 Tm (. HR+8;/;>gIPIGe-k+c=Nq04Kpa6k^Yd[HB;TRY4mRC%8t. k5Iei@&\?>>>K8::HoKUA\.RArB]nF]H#Ps0b*HKEL,ppmqXo/7WjfP;TZPpHW_e6 *).F=3S&3"En#'0iE4@0MIQf[/4U,(M*p2D*2(h+,H*?HA(46&%Fbr(&9Sc=M`QLu )k4&D[>r-N_sHdMiRnudY%'SaC*>Am )Tj /TT6 1 Tf 12 0 0 12 94 237 Tm (c.\))Tj /TT5 1 Tf 1.25 0 TD ( How will the )Tj /TT7 1 Tf 6.7227 0 TD (energy stored)Tj /TT5 1 Tf 6.0273 0 TD ( in the capacitor )Tj /TT7 1 Tf 7.7593 0 TD (change)Tj /TT5 1 Tf 3.2407 0 TD (? 8;Z\6!KP&O#kS'\R.&h0%G2q3@G4GR9e`QkRc"/HLG;t95#VH#C_,1^GAn%3V7Rlg ()?,Q \S2WXO;?DJelNti::0*q)\,2##3AHjC\#GPil(6t$FetdL5S9Go7T,1kV`l4XF#hZE@O.#;>.,6RR;A(aQUIkM . )Tj /TT6 1 Tf 12 0 0 12 72 480 Tm (14.2\))Tj /TT5 1 Tf 2.4167 0 TD ( What do capacitors \(often referred to as )Tj /TT7 1 Tf 19.1099 0 TD (caps)Tj /TT5 1 Tf 2.0361 0 TD (\))Tj -23.5627 -1.25 TD (generally do in DC circuits? VT = V1 = V 2 = V3 - Charge in Parallel connection is the sum of each charge of capacitor: - Charges: QT = Q1 + Q2 + Q3 - Equivalent Ce for capacitors in parallel:-n Ce Ci i 1 The teacher during discussion will show a series of sample problems involving both series and parallel capacitors. Ceq = 6F + 2F = 8F. d8)#Kk.4DLSLdWbK;tKn]65Cno6_hNb[$/u. )Tj /TT6 1 Tf 12 0 0 12 112 402 Tm (d.\))Tj /TT5 1 Tf 1.334 0 TD ( The RMS current in the circuit will be very large if the capacitive)Tj -3.1673 -1.25 TD (reactance is very small. )Tj ET 135 150 m 173.706 150 l S BT 10 0 0 10 135 151 Tm [(Solution)-29.4(: The energy content of a capacitor combination is such that:)]TJ 13.5 -2.8 TD ( \(1/2\)C)Tj 9 0 0 9 317.2314 118 Tm (eq)Tj 10 0 0 10 327 123 Tm (V)Tj 9 0 0 9 334.2217 128 Tm (2)Tj 10 0 0 10 339.2271 123 Tm (,)Tj ET endstream endobj 38 0 obj << /Type /Page /Parent 129 0 R /Resources 39 0 R /Contents 40 0 R /Thumb 107 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 39 0 obj << /ProcSet [ /PDF /Text ] /Font << /F3 60 0 R /F4 59 0 R /TT1 62 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R >> >> endobj 40 0 obj << /Length 5718 >> stream Parallel elements have )Tj /TT7 1 Tf 26.2441 0 TD (voltages)Tj /TT5 1 Tf 3.7031 0 TD ( in common. (F%=>q,^!/?dSubJV)(1b5Ka[aAd`G+@,\ebGDA!$P8)d:NFB_I0"c&mBG#\m888S S7[,G^9^?PG#3,`Ea0ZYDmgC#'T7-eFR3b `;08>e=`lg"m1&mrIK(tahC#uQ`4ur<=B#cRd(CX!rbriWDlf5=s-pD&? $EMXaN7o3Z_IOgT>/47BFi#>gUDcgm7*.0F's@F]JT[O;LpZ:q:j:p87mPFZd1H-m kT! Because the fact that)]TJ -4.9648 -1.3 TD 0.0085 Tc 0.0846 Tw (there are three unknown currents might lead you to believe that you need only)Tj 0 -1.2 TD 0.0129 Tc 0.1292 Tw [(three equations. )Tj ET endstream endobj 10 0 obj << /Type /Page /Parent 127 0 R /Resources 11 0 R /Contents 12 0 R /Thumb 89 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 11 0 obj << /ProcSet [ /PDF /Text ] /Font << /F2 134 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R >> /ColorSpace << /Cs6 138 0 R >> >> endobj 12 0 obj << /Length 7999 >> stream /@H0B76R7%8kmsVPAK8_LUl,YSA9K]5`laN))R?n;3kZ]:^ +N=2V9Y%cm?R)Z-UJe%cn[(4YXi>/A8lNVp?Oqc(>sn((lp;F:K^YM";Pacu)5CG0 i5kE+b&F@*r'XL(G`rN2:7IPrBPZTkSJOS\Wg. M! )Tj /TT6 1 Tf 12 0 0 12 112 282 Tm (g.\))Tj /TT5 1 Tf 1.2778 0 TD ( You are told that the time constant for the system is 10)Tj 10 0 0 10 441 287 Tm (-2)Tj 12 0 0 12 450 282 Tm ( seconds. )Tj /TT6 1 Tf -4.8333 -1.25 TD (14.19\))Tj /TT5 1 Tf 3 0 TD ( An AC voltage source is found to produce a 12 volt peak to peak signal at)Tj -3 -1.25 TD (2500 hertz. W/\R@P3!08]=1j&S6Hj4Zpp$fIYPlS=3U',t")]2u3'O\`>B0hdE^^.AN9i\dee;\E]WR9W5F?jTG%Q:5R 9QETgi/7\fgW,rFa7u/%'`T'N2kK8`^Y6M2(AGcVL\&e5"nE42/kRmh`Z-4A:7W4u6@]n1,&oV*EV>U:CG3gTF7eAG-%D%C(]$,F*CJ2Zp[( You disconnect)Tj -2.4167 -1.25 TD (the battery. "`8>M[_/<27LfWt4U5/G>I1H]<9nWVDS=#uII9hNrUPbhU9\+#SD`@E"ILn_AQ=GeSoKSmL%gJC\^g^ucUPZ!Kng? VUd5V@[!. '7/p:Sd3N+T?\&,+p 3M6h@LnogQOa\nuo1L+OW'@BO?j?RN&Z=^&js6]sjSUu"QZKCE!nAiD#q:FAL'7s* )Tj /TT6 1 Tf 1.8333 -2.5 TD (a.\))Tj /TT5 1 Tf 1.2778 0 TD ( The RMS voltage across the resistor is the same as the average voltage)Tj -3.1112 -1.25 TD (across the resistor. As such, we can write:)Tj 6.3 -2.7 TD ( .37\(7.2 x10)Tj 9 0 0 9 268 547 Tm (-4)Tj 10 0 0 10 276.0024 542 Tm ( C\) = 2.7 x10)Tj 9 0 0 9 334.1226 547 Tm (-4)Tj 10 0 0 10 342.125 542 Tm ( coulombs)Tj -20.7125 -2.4 TD (will be left. D/J3429_%MK0q%'Cq^AndX+hFUZR[?I6PQjjRq'! )]TJ 0 -1.3 TD 0.016 Tc 0.1601 Tw (Just as a )Tj /TT7 1 Tf 5.1 0 TD 0.0227 Tc 0 Tw (series)Tj /TT5 1 Tf 2.6884 0 TD 0.0095 Tc 0.0951 Tw [( resistor combination \(i.e., )]TJ /TT7 1 Tf 12.9523 0 TD 0 Tc 0 Tw (R)Tj 9 0 0 9 350 529 Tm 0.1008 Tc (eq)Tj 10 0 0 10 360.814 534 Tm 0.016 Tc 0.1598 Tw [( = R)]TJ 9 0 0 9 383.6783 529 Tm 0 Tc 0 Tw (1)Tj 10 0 0 10 389.6927 534 Tm 0.016 Tc 0.1598 Tw [( + R)]TJ 9 0 0 9 412.557 529 Tm 0 Tc 0 Tw (2)Tj 10 0 0 10 418.5714 534 Tm 0.0109 Tc 0.1094 Tw [( + . k5Iei@&\?>>>K8::HoKUA\.RArB]nF]H#Ps0b*HKEL,ppmqXo/7WjfP;TZPpHW_e6 The voltage )]TJ /TT7 1 Tf 17.3936 0 TD 0 Tc 0 Tw (V)Tj 9 0 0 9 316.0856 665 Tm (R)Tj /TT5 1 Tf 10 0 0 10 323 670 Tm 0.0026 Tc 0.0259 Tw [( across a resistor is proportional to the)]TJ -18.8 -1.6 TD 0.0155 Tc 0 Tw (current )Tj /TT7 1 Tf 3.9991 0 TD 0 Tc (i)Tj /TT5 1 Tf 0.4009 0 TD 0.0178 Tc 0.1775 Tw [( through the resistor with the proportionality constant being the)]TJ -4.4 -1.2 TD 0.0014 Tc 0 Tw (resistance )Tj /TT7 1 Tf 5 0 TD 0 Tc (R)Tj /TT5 1 Tf 0.7531 0 TD 0.0019 Tc 0.0188 Tw [( of the resistor. =0;AOCK;CNJQN/).&H*GOk-,SAnT"]]&23Jc..btr?8j$1,m-\AOHrk2S/Tp']l`l (V@r4]?THnAokF!Z1p4^;,.$Q?f! Its form is)]TJ /TT7 1 Tf 0 -1.6 TD 0 Tc 0 Tw (i)Tj 9 0 0 9 115.3911 477 Tm 0.0014 Tc (1 )Tj 10 0 0 10 123 482 Tm 0.0011 Tc 0.0112 Tw (= i)Tj 9 0 0 9 135.313 477 Tm 0 Tc 0 Tw (o)Tj 10 0 0 10 140 482 Tm (e)Tj 9 0 0 9 144.4385 487 Tm (-t)Tj /TT5 1 Tf 0.6851 0 TD (/)Tj /TT7 1 Tf 0.2662 0 TD 0.0068 Tc (RC)Tj /TT5 1 Tf 10 0 0 10 166.2924 482 Tm 0.0013 Tc 0.0129 Tw [(. gF/(+GaKo$qneLWDrQ#;5\S(\$q'4Q,85`-8;S(=Z"WSBOV*FM)4,?B],R endstream endobj 123 0 obj [ /Indexed /DeviceRGB 255 122 0 R ] endobj 124 0 obj << /S /D >> endobj 125 0 obj << /Nums [ 0 124 0 R ] >> endobj 126 0 obj << /CreationDate (D:20070623123553) /Producer (Acrobat Distiller 4.0 for Macintosh) /Creator (Microsoft Word 5.1: LaserWriter 8 8.7.1) /Author (Craig Fletcher) /Title (Solu H.Phys Ch 14--Caps) /ModDate (D:20070623123621-07'00') >> endobj 127 0 obj << /Type /Pages /Kids [ 132 0 R 1 0 R 4 0 R 7 0 R 10 0 R 13 0 R 16 0 R 19 0 R 23 0 R 26 0 R ] /Count 10 /Parent 128 0 R >> endobj 128 0 obj << /Type /Pages /Kids [ 127 0 R 129 0 R ] /Count 20 >> endobj 129 0 obj << /Type /Pages /Kids [ 29 0 R 32 0 R 35 0 R 38 0 R 41 0 R 44 0 R 47 0 R 50 0 R 53 0 R 56 0 R ] /Count 10 /Parent 128 0 R >> endobj xref 0 130 0000000000 65535 f 0000080537 00000 n 0000080704 00000 n 0000080879 00000 n 0000089076 00000 n 0000089243 00000 n 0000089429 00000 n 0000097808 00000 n 0000097975 00000 n 0000098106 00000 n 0000107306 00000 n 0000107476 00000 n 0000107652 00000 n 0000115705 00000 n 0000115875 00000 n 0000116051 00000 n 0000123880 00000 n 0000124050 00000 n 0000124182 00000 n 0000130483 00000 n 0000130653 00000 n 0000130863 00000 n 0000143540 00000 n 0000143618 00000 n 0000143788 00000 n 0000143987 00000 n 0000154395 00000 n 0000154565 00000 n 0000154720 00000 n 0000159528 00000 n 0000159699 00000 n 0000159866 00000 n 0000164922 00000 n 0000165093 00000 n 0000165248 00000 n 0000169827 00000 n 0000169998 00000 n 0000170196 00000 n 0000176278 00000 n 0000176449 00000 n 0000176615 00000 n 0000182387 00000 n 0000182558 00000 n 0000182757 00000 n 0000193251 00000 n 0000193422 00000 n 0000193589 00000 n 0000199556 00000 n 0000199727 00000 n 0000199894 00000 n 0000205145 00000 n 0000205316 00000 n 0000205483 00000 n 0000211126 00000 n 0000211297 00000 n 0000211429 00000 n 0000216264 00000 n 0000216435 00000 n 0000216601 00000 n 0000221221 00000 n 0000221463 00000 n 0000222154 00000 n 0000222546 00000 n 0000222708 00000 n 0000222877 00000 n 0000223569 00000 n 0000223911 00000 n 0000225861 00000 n 0000226076 00000 n 0000231788 00000 n 0000232013 00000 n 0000238746 00000 n 0000238977 00000 n 0000248433 00000 n 0000248645 00000 n 0000248859 00000 n 0000249064 00000 n 0000249557 00000 n 0000249794 00000 n 0000250188 00000 n 0000250432 00000 n 0000250834 00000 n 0000251550 00000 n 0000251571 00000 n 0000252470 00000 n 0000252491 00000 n 0000253413 00000 n 0000253434 00000 n 0000254322 00000 n 0000254343 00000 n 0000255244 00000 n 0000255265 00000 n 0000256098 00000 n 0000256119 00000 n 0000257091 00000 n 0000257112 00000 n 0000258170 00000 n 0000258191 00000 n 0000259118 00000 n 0000259139 00000 n 0000259803 00000 n 0000259825 00000 n 0000260611 00000 n 0000260633 00000 n 0000261321 00000 n 0000261343 00000 n 0000261973 00000 n 0000261995 00000 n 0000262736 00000 n 0000262758 00000 n 0000263534 00000 n 0000263556 00000 n 0000264382 00000 n 0000264404 00000 n 0000265171 00000 n 0000265193 00000 n 0000265913 00000 n 0000265935 00000 n 0000266776 00000 n 0000266798 00000 n 0000267526 00000 n 0000267548 00000 n 0000267570 00000 n 0000268148 00000 n 0000268203 00000 n 0000268235 00000 n 0000268281 00000 n 0000268531 00000 n 0000268678 00000 n 0000268755 00000 n trailer << /Size 130 /ID[<92b641842cb1a1baf2a10215ebdb8c8c><92b641842cb1a1baf2a10215ebdb8c8c>] >> startxref 173 %%EOF, D@'rqtpN$L/<5N`>g+CU6a!\aq?_8m60`47m3G9/p^IJhHLnmbtQB309tBg8hV 8;Z\7$W[?Q%%R3%0\9094p/6JpPA0NRAZ>;i\1]7JB5RCrrCbK)-8!N-1)?L[$=*] This statement is)]TJ T* 0 Tc 0 Tw (true. KAeV#ZI^$JjJg*\r#4;oT31ag.c$>C(H^O`l:*h ;WBLe^X[(2^i:sMCgbJg'u^pt2/"hraJ`-9W^MihqTdZS PbLSZTLEE(8E@'*1mg_*eTnN*;*'V3+gm-EEetX%;Bo$ur2ss*N`.-!.kG_q6GDD' Whenever a dielectric is placed)]TJ T* 0 Tc 0 Tw (between the plates of a capacitor, the capacitance always go up. qpJh($E&:e%od[K\f5kS-LjLHd!T/3E*60OlXskuT&7H^35r/1mAqDu2RJ\8GRfJWo7W(@ )Tj -15.766 -2.4 TD (For the 6 )Tj /F4 1 Tf 12 0 0 12 163.625 540 Tm ()Tj /TT5 1 Tf 10 0 0 10 172 540 Tm (f cap:)Tj 8 -2.6 TD (Q)Tj 9 0 0 9 260 509 Tm (6)Tj 10 0 0 10 265.0053 514 Tm ( = C)Tj 9 0 0 9 284 509 Tm (6)Tj 10 0 0 10 289.0053 514 Tm (V)Tj 9 0 0 9 296.227 509 Tm (o)Tj 10 0 0 10 252 495 Tm ( = \(6 x10)Tj 9 0 0 9 306 500 Tm (-6)Tj 10 0 0 10 314.0024 495 Tm ( f\)\(120 volts\))Tj -6.2002 -1.5 TD ( = 7.2 x10)Tj 9 0 0 9 311 485 Tm (-4)Tj 10 0 0 10 319.0024 480 Tm ( coulombs. 13IYjg]TRT9lkNg"\tbD/0e+N@B4(i:'in3@sA2b`&B@Pe7O9eKZ7>FE_$i".HVgq h"u-D? The frequency is )]TJ /F4 1 Tf 10 0 2.2 10 287.0625 332.0001 Tm 0 Tc 0 Tw ()Tj /TT7 1 Tf 10 0 0 10 294 332 Tm 0.0064 Tc 0.0645 Tw [( = 2500 hertz)]TJ /TT5 1 Tf 6.2542 0 TD 0.007 Tc 0.0702 Tw (, so the sine's argument, )Tj /TT7 1 Tf 12.0335 0 TD 0 Tc 0 Tw (2)Tj /TT3 1 Tf 0.6075 0 TD <009b>Tj /F4 1 Tf 10 0 2.2 10 490.0625 332.0001 Tm ()Tj /TT7 1 Tf 10 0 0 10 497 332 Tm (=)Tj -36.7 -1.2 TD (2)Tj /TT3 1 Tf 0.5562 0 TD <009b>Tj /TT7 1 Tf 0.5488 0 TD (\()Tj /TT5 1 Tf 0.333 0 TD ( )Tj /TT7 1 Tf 0.262 0 TD (2500 hertz\) = 15700)Tj /TT5 1 Tf 9.1 0 TD (,)Tj /TT7 1 Tf 0.3 0 TD ( )Tj /TT5 1 Tf 0.3 0 TD ( yields a time dependent voltage function of)Tj /TT7 1 Tf -11.4 -1.2 TD (V\(t\) = V)Tj 9 0 0 9 166 303 Tm (o)Tj 10 0 0 10 171 308 Tm ( sin \(2)Tj /TT3 1 Tf 2.8325 0 TD <009b>Tj /F4 1 Tf 10 0 2.2 10 207.0625 308.0001 Tm ()Tj /TT7 1 Tf 10 0 0 10 214 308 Tm (\)t = 6 sin 15700 t)Tj /TT5 1 Tf 7.8 0 TD (. This, in)]TJ -32.9 -1.2 TD 0.0235 Tc 0.2347 Tw [(turn, will mean less net resistance in the circuit and more current. "d.CTlo>OFRKT)e@^-C6)UR(92Ur=P/B00(616#3XKT\`rGSbK+8mlN,?B`]mmdS- [/latex], [latex]{C_{\text{p}} V = C_1 V + C_2 V + C_3 V} .[/latex]. *).F=3S&3"En#'0iE4@0MIQf[/4U,(M*p2D*2(h+,H*?HA(46&%Fbr(&9Sc=M`QLu )Tj /TT6 1 Tf 12 0 0 12 117 398 Tm (b.\))Tj /TT5 1 Tf 1.3333 0 TD ( Assuming each capacitor's capacitance is 25 mf, how much energy can)Tj -3.5833 -1.25 TD (this system store if it is hooked across a 120 volt battery? )Tj /TT6 1 Tf 12 0 0 12 90 605 Tm (14.6\))Tj /TT5 1 Tf 2.4167 0 TD ( You have a parallel combination of capacitors. That is, how much charge ends)Tj -3.4354 -1.25 TD (up on the second capacitor? That means the voltage drop across the 20 )]TJ /TT1 1 Tf 31.0664 0 TD 0 Tc 0 Tw <009f>Tj /TT5 1 Tf -37.3847 -1.6 TD (resistor will be:)Tj 13.5 -2.4 TD (V)Tj 9 0 0 9 277.2217 349 Tm (20)Tj 10 0 0 10 287.2324 354 Tm ( = i)Tj 9 0 0 9 302 349 Tm (1)Tj 10 0 0 10 307.0053 354 Tm (R)Tj 9 0 0 9 314.227 349 Tm (20)Tj 10 0 0 10 270 338 Tm ( = \(2.4 amps\)\(20 )Tj /TT1 1 Tf 9.646 0 TD <009f>Tj /TT5 1 Tf 0.7681 0 TD (\))Tj -10.4141 -1.2 TD ( = 48 volts. )Tj ET 139 506 m 177.706 506 l S BT 10 0 0 10 139 507 Tm 0.0014 Tc 0.0205 Tw [(Solution)-28(: The time constant )]TJ /TT7 1 Tf 13.5425 0 TD 0.0218 Tc 0 Tw (RC)Tj /TT5 1 Tf 1.4575 0 TD 0.0021 Tc 0.0215 Tw [( tells you how fast the cap in a cap/resistor circuit)]TJ -15 -1.3 TD 0.0112 Tc 0.1119 Tw [(will charge. )Tj T* 0.0126 Tc 0.1259 Tw (In that case, the conductor's electrons will attract to the capacitor's positive)Tj T* 0.0169 Tc 0.1693 Tw (plate \(the left plate in this case\) )Tj /TT7 1 Tf 16.8 0 TD 0.0171 Tc 0.1707 Tw (in the amount equal to the charge on the)Tj -16.8 -1.2 TD 0.0016 Tc 0.0157 Tw (capacitor's positive plate)Tj /TT5 1 Tf 11.366 0 TD 0.0009 Tc 0.0093 Tw [(. If capacitors are connected one after the other in the form of a chain then it is in series. *G)"jqYC4teTQ&/RD,q"gHZeFm)$+]abd B3)_KMT? The short-lived current)]TJ T* 0.0054 Tc 0.0537 Tw (puts more charge on the plates thereby bringing the plate voltage back up to )Tj /TT7 1 Tf 36.7823 0 TD 0 Tc 0 Tw (V)Tj 9 0 0 9 514.0945 106 Tm (o)Tj /TT5 1 Tf 10 0 0 10 519 111 Tm (. 8;V^n$ZK),(&lL.n(l6@OQ@Jq8FLRj!dP>"]FlEaliTT(Oq>\e:tX$N"GoM[1LO/+ @].&G*UUMleM,M"LQoZrbA7g%[a\,ce%--^le%Pp/8S$#Q(\[1e8eD0W\hfiW)_hB . ,e/81k'nbPG]-FYTQ1V-Echq;;)E0pNNs8/Do'eLqD7l3p#MBB_^!oCmX,]*?5CAmoY'KbM%[6g^e#L#N3RWB^PK! R esistors and capacit ors connected in. (="RnVm"q\pnT;4RA,[>Y_ML+92[$!1sRSX8~> endstream endobj 69 0 obj << /Type /FontDescriptor /Ascent 985 /CapHeight 0 /Descent -216 /Flags 70 /FontBBox [ -156 -215 1048 969 ] /FontName /JAEEPE+CenturySchoolbook-Italic /ItalicAngle -15 /StemV 0 /FontFile2 70 0 R >> endobj 70 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 6625 /Length1 7772 >> stream )Tj /TT6 1 Tf 12 0 0 12 112 339 Tm (f.\))Tj /TT5 1 Tf 1.0833 0 TD ( Where is the energy stored in the capacitor? [AL:1OKUhA@?28n51,a 't"4-HCJ>VL"2\0KkT4n("V#Ri'f #bi:=9la7P3'^0)CC0-,+jl[;gc=>t 5: Find the total capacitance of the combination of capacitors shown in Figure 6. For a)Tj -4.7325 -1.6 TD (given voltage, that means the most energy-storing capacity will go to the combination)Tj 0 -1.2 TD (with the largest equivalent capacitance. ^'! )Tj /TT6 1 Tf -18.4032 -2.5 TD (a.\) )Tj /TT5 1 Tf 1.5833 0 TD ( The capacitance value tells you something that)Tj -3.4167 -1.25 TD (is always true no matter what the voltage across the capacitor happens to be. ;qG_t26H-:#WmeF>1U,uD;!A^\$aSAFN-3e-9s]%^LXj"\FGF"K@A?hP+lg]47e/1.JB,ij1f_+?_)28c?QY?ph$)%^tce];@P2nbGD3qM0,D'"BF[p@\`"ZWgfDcp+Qr0I6ePa$MDJG\aRXUMi-i?UdJTS>ifSP=qWmP.s2AH<8*"?>l9hi#N That means the capacitance ratio )]TJ /TT7 1 Tf 22.0275 0 TD 0 Tc 0 Tw (q)Tj /TT5 1 Tf 0.5725 0 TD (/)Tj /TT7 1 Tf 0.3 0 TD (V)Tj /TT5 1 Tf 0.7187 0 TD 0.005 Tc 0.0502 Tw [( increases. )Tj ET endstream endobj 44 0 obj << /Type /Page /Parent 129 0 R /Resources 45 0 R /Contents 46 0 R /Thumb 111 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 45 0 obj << /ProcSet [ /PDF /Text ] /Font << /F4 59 0 R /TT1 62 0 R /TT3 63 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R >> >> endobj 46 0 obj << /Length 5913 >> stream A capacitor is what is called a )]TJ /TT7 1 Tf 30.9001 0 TD 0.0023 Tc 0.0229 Tw (high pass filter)Tj /TT5 1 Tf 6.9999 0 TD 0 Tc 0 Tw (. BT /TT5 1 Tf 12 0 0 12 72 39 Tm 0 g /GS1 gs 0 Tc 0 Tw (908)Tj /TT6 1 Tf 1.8333 55.75 TD (e.\))Tj /TT5 1 Tf 1.25 0 TD ( Once totally charged, how much energy do the capacitors hold? [BEqgVrd_&! )Tj ET 117 265 m 155.706 265 l S BT 10 0 0 10 117 266 Tm 0.1106 Tw [(Solution)-29.4(:)-10.1( )]TJ 4.9648 0 TD 0.0101 Tc 0.1005 Tw [(Note first that this is also a bit tricky. )Tj ET 135 110 m 177.733 110 l S BT 10 0 0 10 135 111 Tm 0.006 Tc 0.0484 Tw [(Solution: As before, the caps will act like shorts when uncharged. 'r;nJ?cg6riIM8BD,:EZ!`6`Fj--^CHJst/4:FU"1KY8)^S/5^2`:5Dflt$fm#As< 8;Z\7$aRYm#i,;aOR)PP";]3OD.QW"AnR9?U1?PT'Y/5DPC_fsQ8\`39E22Tp! )Tj T* 0.0111 Tc 0.1109 Tw [(That is why capacitors don't pass low frequency. P$nqiS1(9Vim8+_ckA'"[Ih+OEqU)_V)epG>M_gc,^M*Y,Y-Q&g!=j1]!C; In series, the capacitance is less. The more the current drops \(i.e.,)]TJ T* -0.0002 Tc 0 Tw (the more the frequency is lowered\), the higher the voltage across the capacitor and)Tj T* 0 Tc (this statement is true. 8;Z\6$[.1W#itt$j>q]I^^T`HXBFG(='hqFN0Af$"P(O6qf\08qYRa,QJ4:0j_FhL The total voltage across )Tj /TT6 1 Tf -30.8005 -2.8 TD (Note:)Tj /TT5 1 Tf 2.7217 0 TD ( You could have used the outside loop instead of either of the two loops used. )Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 1 i 139 694 m 177.706 694 l S BT 10 0 0 10 139 695 Tm [(Solution)-29.4(: In such cases, the insulator is called )]TJ /TT7 1 Tf 21.714 0 TD (a dielectric)Tj /TT5 1 Tf 5.0332 0 TD (. g^'A1-G)O,qu\[sFbD`/$?FWbIW_"2AobNY%. Substituting this in equation (1.107), we get. That will be the pure, parallel capacitor)Tj T* (combination in the sketch. (, of C2 due to electrostatic induction. The consequence of this polarization \(it is a Van der Waal)]TJ T* 0.0025 Tc 0.0249 Tw (phenomenon\) is that the polarized charge will set up a weak, reverse electric field)Tj T* 0.0076 Tc 0.0756 Tw [(through the insulator and between the plates. XQaXPPD1JGQpC=,"0XD>709FK2r$%+Lp+'`%]3jKQhHu!p[rZ@ BT /TT5 1 Tf 12 0 0 12 72 39 Tm 0 g /GS1 gs 0 Tc 0 Tw (906)Tj 10 0 0 10 144 710 Tm 0.026 Tc 0.2601 Tw [(--Initially, the capacitors have no charge on them. )Tj ET 117 349 m 155.706 349 l S BT 10 0 0 10 117 350 Tm 0.0041 Tc 0.0456 Tw [(Solution)-25.3(: Before charge redistributes itself, the voltage across the 2C capacior will be)]TJ 0 -1.3 TD 0.0136 Tc 0.1362 Tw (zero \(remember, )Tj /TT7 1 Tf 8.3035 0 TD 0 Tc 0 Tw (V)Tj 9 0 0 9 208 332 Tm 0.045 Tc (cap)Tj 10 0 0 10 223.5456 337 Tm 0.0094 Tc 0.094 Tw (= q)Tj /TT5 1 Tf 1.5621 0 TD 0 Tc 0 Tw (/)Tj /TT7 1 Tf 0.2833 0 TD (C)Tj /TT5 1 Tf 0.7801 0 TD 0.011 Tc (--no )Tj /TT7 1 Tf 2.2196 0 TD 0 Tc (q)Tj /TT5 1 Tf 0.6003 0 TD 0.0223 Tc 0.2228 Tw (, no )Tj /TT7 1 Tf 2.5 0 TD 0 Tc 0 Tw (V)Tj 9 0 0 9 310.041 332 Tm (c)Tj /TT5 1 Tf 10 0 0 10 314 337 Tm 0.017 Tc 0.1701 Tw [(\). )Tj /TT6 1 Tf 12 0 0 12 94 240 Tm (c.\))Tj /TT5 1 Tf 1.25 0 TD ( What is the voltage across the 6 )Tj /F4 1 Tf 15.7187 0 TD ()Tj /TT5 1 Tf 0.6979 0 TD (f capacitor when fully charged? )Tj -35.75 -1.5 TD 0.0065 Tc (At )Tj /TT7 1 Tf 1.5 0 TD 0.0056 Tc 0.0559 Tw (t = 4 seconds)Tj /TT5 1 Tf 6.0833 0 TD 0.0053 Tc 0.0524 Tw [(, the current is )]TJ /TT7 1 Tf 7.4086 0 TD 0 Tc 0 Tw (i)Tj 10 0 0 10 256 527 Tm (4)Tj /TT5 1 Tf 12 0 0 12 262 532 Tm 0.0048 Tc 0.0474 Tw (, and at )Tj /TT7 1 Tf 3.9829 0 TD 0.0068 Tc 0.0678 Tw (t = 8 seconds)Tj /TT5 1 Tf 6.1005 0 TD 0.0052 Tc 0.0526 Tw (, the current is )Tj /TT7 1 Tf 7.4086 0 TD 0 Tc 0 Tw (i)Tj 10 0 0 10 476 527 Tm (8)Tj /TT5 1 Tf 12 0 0 12 482 532 Tm 0.0065 Tc 0.0652 Tw [(. .sjPEJU[co".oUd!r%8\"4r&Xi6T1B?i]sJcj01E0*4:%2m=CV$UfM!cic0PT6"(` )Tj /TT6 1 Tf 12 0 0 12 112 89 Tm 0.0209 Tc (b.\) )Tj /TT5 1 Tf 1.8953 0 TD 0.0298 Tc 0.2983 Tw [( Out of curiosity, why was the resistor)]TJ ET endstream endobj 13 0 obj << /Type /Page /Parent 127 0 R /Resources 14 0 R /Contents 15 0 R /Thumb 91 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 14 0 obj << /ProcSet [ /PDF /Text ] /Font << /F2 134 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R >> /ColorSpace << /Cs6 138 0 R >> >> endobj 15 0 obj << /Length 7775 >> stream )Tj ET endstream endobj 7 0 obj << /Type /Page /Parent 127 0 R /Resources 8 0 R /Contents 9 0 R /Thumb 87 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 8 0 obj << /ProcSet [ /PDF /Text ] /Font << /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R >> >> endobj 9 0 obj << /Length 9147 >> stream .2J.W-[ht"H`T0P1h]TVEt%EB39^[I9nF(UbW:ZQg:HTC^IZ*"Ek579"49JF=I5! @+W9_p#Td6%&0#-(g8-QrV\3VO'#a^>Q]Ne*\VK/\$jrg!lm1$9Q)ad`;1KZRVM/n EmtWKAN&RO38'pFlD&YHkqE*%G"+CD)!O`)+!C$d;0A"[b^eY(0 -BE@"UIjc>=qkG@(g*;,0dW:XEI:YKL/bLr! 8;Z\7$aRVl%,C_eOR#"4o:nTj8?M!Y3`;YfPcrYU_O(:EOfNVBCAQ*1$eL9*-gQR&Vc)\dNY4`J190Gl^6aO%; *7](L0dQP[k?HKJpt5>L7@+Fu[o&pZphujSSO+ZVn4K3rU`aB\:L[+! )Vgb\J?6-I0i )Tj /TT6 1 Tf 12 0 0 12 90 637 Tm (14.17\))Tj /TT5 1 Tf 3 0 TD ( Determine:)Tj /TT6 1 Tf -1.1667 -2.5 TD (a.\))Tj /TT5 1 Tf 1.2778 0 TD ( The equivalent capacitance of the circuit)Tj -3.1112 -1.25 TD (shown in Figure III. g]F[VCP"Gpr/#G54#dm/*N>IMdNoI-#kkbOFqjU?i="W=_B]`U_QIiZ\2QMeSdjQe Mfr)*3h_M8$h5:'K:NJba#`P'01G7%aLt7^Z+r4VH,"G2Toi]W$$(q63pRbrR]hGi @CnrM2l0hWHcqQ*jX]>igEXEPD:J^S^"YLIF3W stored in each capacitor is not the same. )Tj ET 117 340 m 155.706 340 l S BT 10 0 0 10 117 341 Tm 0.002 Tc 0.0238 Tw [(Solution)-27.4(: A capacitor's net resistive nature is called the )]TJ /TT7 1 Tf 26.4406 0 TD 0.0051 Tc 0.051 Tw (capacitive reactance)Tj /TT5 1 Tf 9.3594 0 TD 0.0035 Tc 0.0353 Tw [(. K=t? .cBkX\R$sNb+UgFU,(./N/D4+RQ]K/eHX,YNP^]p]5iK)&M`(+5$N*>oR+nt[\-8b $ejAUS=Gc;p8S3"6_SWeLd'Hi?@&Q*R2LHf:cN[t(W)6Y^!`No9E=7o8! )Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 1 i 135 678 m 173.706 678 l S BT 10 0 0 10 135 679 Tm [(Solution)-29.4(: The energy wrapped up in a charged capacitor equals:)]TJ 9.9 -2.8 TD ( Energy = \(1/2\)CV)Tj 9 0 0 9 328.0234 656 Tm (2)Tj 10 0 0 10 333.0288 651 Tm (,)Tj -19.8029 -2.4 TD (where )Tj /TT7 1 Tf 3.1104 0 TD (C)Tj /TT5 1 Tf 0.7222 0 TD ( is the cap's capacitance and )Tj /TT7 1 Tf 13.3164 0 TD (V)Tj /TT5 1 Tf 0.7511 0 TD ( is the voltage across the cap. ;+%/'L?^1.aA@B#.QQ Using this yields:)Tj -8 -2.7 TD ( Energy = .5\(6 x10)Tj 9 0 0 9 330 605 Tm (-6)Tj 10 0 0 10 338.0024 600 Tm ( f\)\(80 volts\))Tj 9 0 0 9 390.0435 605 Tm (2)Tj 10 0 0 10 270 588 Tm ( = .0192 joules. J,?.5,?e#LCKk.Z4jPY`30Tp/c3)?mk8^PA91SI_P*f7!cHd'IAhHQGOECqM!iKNd qfN9h*Sb6MmaQ+:qLnh&6%M"m4'jTLLNT?q3n4Pi,bV51b#m/kihuZIa )Tj ET 117 263 m 155.706 263 l S BT 10 0 0 10 117 264 Tm [(Solution)-29.4(: The energy wrapped up in the 6 )]TJ /F4 1 Tf 12 0 0 12 315.625 264 Tm ()Tj /TT5 1 Tf 10 0 0 10 324 264 Tm (f cap when fully charged equals:)Tj -10.8 -2.9 TD (Energy = .5\(6 x10)Tj 9 0 0 9 298 240 Tm (-6)Tj 10 0 0 10 306.0024 235 Tm ( f\)\(120 volts\))Tj 9 0 0 9 364 240 Tm (2)Tj 10 0 0 10 252 223 Tm ( = .0432 joules. Attached to )Tj /TT7 1 Tf 19.9448 0 TD (Plate A)Tj /TT5 1 Tf 3.3885 0 TD ( is a)Tj -23.3333 -1.25 TD (switch. m)8Y>K+o:m*]Coo657ll[(sI.jJ)_BaM9'3RX\lIJ&b\\Lf2=,! -=`"\;!7W/kue77,k+[M=tm)Lj#iHKR90.nT'!5<4fI$(Aba&nL%#2fr'L1]A\JLD iE!D;[)ob;go!,(*`X0pcS=I[9?`e&P2VR-'9N:]D!rhrd+%Y)iB,Oc^_Og/+^*8pX'Lir=sJ# Will it hold its charge forever? Once)]TJ T* 0.0011 Tc 0.0109 Tw (discharged, the switch flips back to charging mode and the capacitor recharges \(this is)Tj T* 0.0064 Tc 0.0641 Tw (why it usually takes a few seconds before you can take)Tj T* 0 Tc 0 Tw (the next flash picture\). )Tj /TT7 1 Tf 29.2213 0 TD 0.0017 Tc 0.0166 Tw (Two time constants)Tj /TT5 1 Tf -29.2213 -1.2 TD 0.0072 Tc 0.0716 Tw (is the time it takes to charge up to 87%, and )Tj /TT7 1 Tf 21.7707 0 TD 0.0128 Tc 0.1276 Tw (three time constants)Tj /TT5 1 Tf 9.7293 0 TD 0.0092 Tc 0.092 Tw [( is the time it)]TJ -31.5 -1.2 TD 0.009 Tc 0.0896 Tw [(takes to charge to 95% of its maximum charge. That will drop the effective voltage across the plates which,)]TJ T* 0.0143 Tc 0.1428 Tw (in turn, will create a voltage difference between the high voltage plate of the)Tj T* 0.0145 Tc 0.1454 Tw [(capacitor and the high voltage plate of the power supply. . $skm@71>Jn=gS'h5]._*cRL`['@n9ejFg7p^f&=_'B(%>6)1fr'7()&CSHlBl >#?8[iN=B^S3&Z'7[BW\5CPE]i4XPg)E7bsr@bY10.n]2$DrcPb-`Hu@,^P4=2)!c :7 8;Z\7$$(YP%,Cl4:u>t"FS^e&ndptY:2+D.7E9_:Li3)6"('U"cgrB%=L'#/SDQ3n Their plates are charged too)]TJ T* 0 Tc 0 Tw (much of the time at low frequency. They can be connected in series and in parallel. =0.W+dga&fB*A^^#,HWEdc)B[1c8n$GrClK>ru'3P1c+:E$G1L(;S4PbZ9aIFW:fTBI'f=HMPp"GR(HBnQSDT7UHn`!-],5fu'3!,;* ])*=Gc\BCr1g9npP/`%sf2MI1,#%2\q\4SagpsV1$[Dlu'35rTdkhdBQlE6WHL] )Tj /TT6 1 Tf 12 0 0 12 90 270 Tm (14.8\))Tj /TT5 1 Tf 2.4167 0 TD ( You charge up two unequal capacitors that are in)Tj -2.4167 -1.25 TD (series. @YMBteFR5E^_Y[@)N.&:,X+RTCO#"2TgK"p)ON7pm7L1?hlgs58ftaU;u8ka7sZL0 ``F-Q$#MH#8ZMmRF8Xs+=iWb1o_?FeI!Tjn[N@\_munI-*Cp*2%XsFUb.qo=`36Bb Electrons in)]TJ 0 -1.2 TD 0.0028 Tc 0.0283 Tw (the insulator will stay in their orbitals \(remember, valence electrons in insulators)Tj T* 0.0099 Tc 0.0987 Tw (can't wander about the way valence electrons in metallically bonded structures)Tj T* 0.0045 Tc 0.0451 Tw (can\), but the plate charge will motivate them to spend most of their time close to)Tj T* 0.0128 Tc 0.1277 Tw [(the positive plate. 2j!R!>nk>JAZ5D#H%1=",l(8o"`:>fZ^ZNdYshCMCo3GZOa%tIY;Drd2r$D#b6\cmV;!dZ%4LBAoC@# eh5UUXdF#0PuC@D6P=drcr06[*,$sp/mM!bHA#62!h'qm&T0(NY<=R(Sb@;up8KOS (U$piH+I7Dr4d?bD&`=&.#gs=DG)f)EJ3lGmfKo=TK]!230=`2&)"XKWRoC 8;Z\7!Kr'X&Bk)4CmnL&1%gk[@XtnqGhQ@0Dd+2oqbXiDU9O0nHRh\d032 $-2?r]/iP"cIOSu/d+a`\-to`>)>Sp,a,1?I,9=Yo$l_I)$>*5>$>*5r_C$8q.TRA!9]FcK`~> endstream endobj 120 0 obj 567 endobj 121 0 obj 481 endobj 122 0 obj << /Filter [ /ASCII85Decode /LZWDecode ] /Length 121 0 R >> stream )Tj ET 157 238 m 195.706 238 l S BT 10 0 0 10 157 239 Tm 0.0038 Tc 0.0931 Tw [(Solution)-25.6(: The )]TJ /TT7 1 Tf 7.1151 0 TD 0.0317 Tc 0.3172 Tw (time constant)Tj /TT5 1 Tf 6.8849 0 TD 0.0183 Tc 0.1828 Tw [( gives you a feel for how fast the cap in the)]TJ -14 -1.3 TD 0.0033 Tc 0.033 Tw [(capacitor/resistor combination will charge or discharge. Z7_bGTVO*!.IG9M/K:h,[@R_.6F!6Tn75,6NXC0WJH.c\pK )Tj -19.6127 -2.7 TD (Each capacitor will hold 4.8x10)Tj 9 0 0 9 261.2871 274 Tm (-4)Tj 10 0 0 10 269.2896 269 Tm ( coulombs per plate when fully charged. )Tj /TT6 1 Tf 12 0 0 12 112 559 Tm (e.\))Tj /TT5 1 Tf 1.25 0 TD ( Determine the RC circuit's )Tj /TT7 1 Tf 13.1667 0 TD (time constant)Tj /TT5 1 Tf 6.1836 0 TD (. If)]TJ 0 -1.3 TD 0.0055 Tc 0.0554 Tw (that is the case, there will be no voltage difference between the high voltage sides of)Tj 0 -1.2 TD 0 Tc 0 Tw (the caps, and no new current will flow. ]`.P>GHf! )Tj ET 135 447 m 173.706 447 l S BT 10 0 0 10 135 448 Tm 0.13 Tw [(Solution)-29.4(:)-11.8( )]TJ 5.0053 0 TD 0.0118 Tc 0.1182 Tw (What is common to )Tj /TT7 1 Tf 9.8336 0 TD 0.0396 Tc 0 Tw (all)Tj /TT5 1 Tf 1.359 0 TD 0.0159 Tc 0.1586 Tw [( parallel-type circuits is voltage. W^jj;UEK. )Tj /TT6 1 Tf 12 0 0 12 94 309 Tm (c.\))Tj /TT5 1 Tf 1.25 0 TD ( Without solving them, write out the equations you would need to solve if)Tj -3.0833 -1.25 TD (you wanted to determine the currents in the circuit at any arbitrary point in)Tj T* (time. M3o'3%e^Q]1Y8iu#F%gta Explain. \:r_H3XW_#<8J4G^lgQ0BkfZE,ISs8b Hu7J'26uAKAk4_XahY1YjMms/4Y?6_, )Tj -36.1 -1.2 TD 0.007 Tc 0.0701 Tw (The charge on each individual capacitor will be the same as the charge on the)Tj -1.3 -1.2 TD 0.0036 Tc 0 Tw (circuit's )Tj /TT7 1 Tf 4 0 TD 0.0056 Tc 0.0564 Tw (equivalent capacitor)Tj /TT5 1 Tf 9.4623 0 TD 0.0034 Tc 0.0339 Tw [(. )Tj ET 135 175 m 173.706 175 l S BT 10 0 0 10 135 176 Tm 0.0058 Tc 0.0698 Tw [(Solution)-23.6(: What is common in series combinations of)]TJ 0 -1.3 TD 0.0036 Tc 0.0361 Tw (capacitors is the )Tj /TT7 1 Tf 8 0 TD 0.0104 Tc 0 Tw (charge)Tj /TT5 1 Tf 3.1161 0 TD 0.0031 Tc 0.0314 Tw [( on each capacitor. m'8r\Q#*AbJW/iY%Eh3H_W/-=EFCL0B;t:5%5Z;opUcqGbstJIY@=7 mu*%@BT*D,Oj3W4.W^aX#9tphR@2B5Eau-GEAW@9(OURU<3Vg./HUmL#0,Y6^@ti7 EmtWKAN&RO38'pFlD&YHkqE*%G"+CD)!O`)+!C$d;0A"[b^eY(0 R+YW1RC5Qi>bRP4R Why? 6\nLlMdD+VT'Q\'EDdS>_(A7:O.0msGgA0jQ*+N&B58n-MnHi^I5"!QM7D2#/p the circuit diagrams illustrate four different methods of wiring.solution (a) the capacitance of the capacitor is = 221.2 1013 f c = 22 . iQ? . )Tj /TT6 1 Tf 12 0 0 12 95 550 Tm 0.0186 Tc (i.\))Tj /TT5 1 Tf 1.0929 0 TD 0.003 Tc 0.0298 Tw [( At )]TJ /TT7 1 Tf 2.0493 0 TD 0.0071 Tc 0.0708 Tw (t = 1 second)Tj /TT5 1 Tf 5.6911 0 TD 0.0053 Tc 0.0537 Tw (, the current is )Tj /TT7 1 Tf 7.4167 0 TD 0 Tc 0 Tw (i)Tj 10 0 0 10 294 545 Tm (1)Tj /TT5 1 Tf 12 0 0 12 300 550 Tm 0.0034 Tc 0.0345 Tw [(. !<4[bM/3~> endstream endobj 67 0 obj << /Type /FontDescriptor /Ascent 985 /CapHeight 0 /Descent -216 /Flags 6 /FontBBox [ -165 -216 1006 986 ] /FontName /JACCJC+CenturySchoolbook /ItalicAngle 0 /StemV 0 /FontFile2 68 0 R >> endobj 68 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 5604 /Length1 6572 >> stream '&beU2#E0Opn*2$&TcHR45A^@j+e` BLbA\WSD!7cprQDg62M(U';3r?^l\Bm?PO:"@%,@ercI`1B28X^E/p% E@mh?@WZEXJNp.($fkm\o1EplrJP/rfSpLVOFkL[-HKBYfBW=gMI%^_PJtS,on$9. If, at low frequency, the current in the circuit is small \(this is what we)]TJ T* 0.0009 Tc 0.0086 Tw (concluded above about lowering the frequency\), little voltage drop will exist across)Tj T* -0.0001 Tc 0 Tw (the resistor. Why? That suggests that the RMS current will be large,)]TJ T* 0.011 Tc 0.1102 Tw [(relatively speaking, when the capacitive reactance is small. >,6T+SIC1bHlu,'"23PkZor7JBn:-N(&6;UQdS/nMp]e#l/$.HPMY93(&0pl"aXkf `\ld+#--_?`+[P=`tmj#&CdM>8=8!=(6e"6k#OHkI[*u_P$0!pN ;oNJn'W`nAIci')prL\RJ*6?mF8kd'PIp!b];58>Q99Y->=HAW/A6c]W.fMld3r8* )Tj -15.2155 -2.8 TD (These are the four equations we need to determine )Tj /TT7 1 Tf 23.7041 0 TD (i)Tj 9 0 0 9 366.3711 582 Tm (1)Tj 10 0 0 10 371.3765 587 Tm (, i)Tj 9 0 0 9 380 582 Tm (2)Tj 10 0 0 10 385.0054 587 Tm (, and i)Tj 9 0 0 9 415 582 Tm (3)Tj /TT5 1 Tf 10 0 0 10 420.0054 587 Tm (. *SiA;]l(iE["7;mXS]Rfdd329)5c,h,1dI\H bqgK'+(:!k$K'f#&7GY]@_='Z$Fbf[He=NU+X+RVlcO>_2",lF5o1*I_;n"c.c@M1$kt@MB?b6IF-r#P ,/#/9),o;*9A[]^jZkSY@JJ*lCmP/ke?^1 If it goes up,)]TJ -3.621 -1.25 TD 0.0014 Tc 0.014 Tw [(from whence did the new energy come? h&0if)fXRJ7).OsfR_Iuh``erc>YIZkR(l!l??D$$W]C26n>.O]+M-@#`\0J.2?!$F.\L%c*)rAt1!Xb:&'.JX@,#(#h['^Ne(F%gB>G89S-Aq*;SKdhZ? >n;47nUT7,D$iAL6:q/J\X5j/J)TMA,t8\?7Q/rB? g:hh!NO*5Ph].e/>9`CZ^3X>aE7o!#fS=B4ITld3X]p+,i0%$8Q-N::e\<63D<09c )Tj /TT6 1 Tf 12 0 0 12 94 653 Tm (h.\))Tj /TT5 1 Tf 1.3521 0 TD ( After a very long time, the switch is opened. 14 \(Capacitors\))Tj 12 0 0 12 502 39 Tm (909)Tj /TT6 1 Tf -34.3333 55.75 TD (14.20\))Tj /TT5 1 Tf 3 0 TD ( An RC circuit is hooked across an AC power supply. This)]TJ 0 -1.2 TD 0.0054 Tc 0.0541 Tw [(makes sense if you think about how charge passes from plate to plate. TrORG!ROXf=-6I=a497`>pN=(gP6!-f2*pPT=OPb ;O-\d+5"mo7*_8e?/@AQ%AG)^d:\-_8V"&E6f4: 14 \(Capacitors\))Tj 12 0 0 12 502 39 Tm (909)Tj /TT6 1 Tf -34.3333 55.75 TD (14.20\))Tj /TT5 1 Tf 3 0 TD ( An RC circuit is hooked across an AC power supply. >X$l6j@<=[9-3F'EnWh^cqZjjFWJM=ZX_7)4ss!VpF+ScflU+'ZJI!`CR*=?MUX5n 1]:hN,AjJ&WVs!QS7i\Mh;S;Q#A+)#IE?+456(! It also means that for different size capacitors,)Tj T* (the )Tj /TT7 1 Tf 1.8 0 TD (voltage)Tj /TT5 1 Tf 3.2593 0 TD ( across each capacitor will be different \(remember, )Tj /TT7 1 Tf 23.5407 0 TD (V)Tj 9 0 0 9 383.041 155 Tm (1)Tj 10 0 0 10 388.0464 160 Tm ( = Q)Tj /TT5 1 Tf 1.9395 0 TD (/)Tj /TT7 1 Tf 0.2559 0 TD (C)Tj 9 0 0 9 417.2217 155 Tm (1)Tj /TT5 1 Tf 10 0 0 10 422.2271 160 Tm (\). )Tj ET 117 196 m 163.396 196 l S BT /TT8 1 Tf 10 0 0 10 117 197 Tm (Circuit a)Tj /TT5 1 Tf 4.6396 0 TD ( finds two capacitors in series. )Tj ET 135 150 m 173.706 150 l S BT 10 0 0 10 135 151 Tm [(Solution)-29.4(: The energy content of a capacitor combination is such that:)]TJ 13.5 -2.8 TD ( \(1/2\)C)Tj 9 0 0 9 317.2314 118 Tm (eq)Tj 10 0 0 10 327 123 Tm (V)Tj 9 0 0 9 334.2217 128 Tm (2)Tj 10 0 0 10 339.2271 123 Tm (,)Tj ET endstream endobj 38 0 obj << /Type /Page /Parent 129 0 R /Resources 39 0 R /Contents 40 0 R /Thumb 107 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 39 0 obj << /ProcSet [ /PDF /Text ] /Font << /F3 60 0 R /F4 59 0 R /TT1 62 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R >> >> endobj 40 0 obj << /Length 5718 >> stream >ja`m$a9c[+c9JJ79nA8Sc6n]B]N*4gs_@Xo:HL56`[&_e/cU?jH:b$=au)PihOYLOM-W;a/FMhi"%WmS8R$:ns>[.:)@Q?o:!RD_>$UcKDS4R:`Q5CeteOD^X&J5YrY+b1? 'r;nJ?cg6riIM8BD,:EZ!`6`Fj--^CHJst/4:FU"1KY8)^S/5^2`:5Dflt$fm#As< o)pLuL\?+s)1L#KrH$=1TG7S`TX\k(OAa_nb=TfEE@$PbKE_UkY:EahV@&l0@F )Tj T* (Justify your response. $'&d@Rg#`or]f%1V&khXdAkrC!c`Luf6gM;K/]2T&o9 e8V12+MXDuBU/Cm4t'@6LJd+_(b]C7KkXX]66S)'lpE8P8o7BJ2=T&ImIlrt5)j"? eH`Kc,:fP%S>QL2VmqX)_/Uou0?c5T0pe`bns#uu116NUd. 4ZunD_;SrV4kQlYp+/s5W2&Z:r;c+;:XM:9)3\9=gDCbhL>@I&B[O#8W^1eTGp/-@ Current must)]TJ 0 -1.3 TD 0.001 Tc 0.0095 Tw (go through the resistor to return to the battery, so the initial current again will be)Tj ET endstream endobj 32 0 obj << /Type /Page /Parent 129 0 R /Resources 33 0 R /Contents 34 0 R /Thumb 103 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 33 0 obj << /ProcSet [ /PDF /Text ] /Font << /F4 59 0 R /TT1 62 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R >> >> endobj 34 0 obj << /Length 4525 >> stream hEC6sp\_Y,-RP\r^BC_@!$J`r=T~> endstream endobj 82 0 obj 557 endobj 83 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Width 76 /Height 99 /ColorSpace 123 0 R /BitsPerComponent 8 /Length 84 0 R >> stream i`%VWh1XtMr. Knowing the resistor)Tj T* (and capacitor values:)Tj /TT6 1 Tf 1.8333 -2.5 TD (a.\))Tj /TT5 1 Tf 1.2778 0 TD ( Determine all three )Tj /TT7 1 Tf 9.9722 0 TD (initial)Tj /TT5 1 Tf 2.8691 0 TD ( currents)Tj -15.9525 -1.25 TD (in the circuit \(i.e., the currents just after the)Tj T* (switch is closed\). :1=L45g.Rno0U^/&"A+5J:V9BT$J?_X3j For)Tj -34.5473 -1.3 TD (different size capacitors, that means the amount of charge on each cap will be different)Tj 0 -1.2 TD (\(remember, )Tj /TT7 1 Tf 5.6108 0 TD (Q)Tj 9 0 0 9 154 167 Tm (1)Tj 10 0 0 10 159.0054 172 Tm ( = C)Tj 9 0 0 9 178 167 Tm (1)Tj 10 0 0 10 183.0054 172 Tm (V)Tj /TT5 1 Tf 0.7041 0 TD (\). As charge)]TJ T* 0.003 Tc 0.0299 Tw (accumulates on the first plate, it electrostatically repulses an equal amount of like)Tj T* 0.0034 Tc 0.0338 Tw [(charge off its other plate. )Tj /TT6 1 Tf -0.5833 -2.5 TD (a.\))Tj /TT5 1 Tf 1.2778 0 TD ( What happens to the equivalent capacitance when you add another)Tj -3.1112 -1.25 TD (capacitor? [latex]{C_{\text{p}} = 1.000 \;\mu \text{F} + 5.000 \;\mu \text{F} + 8.000 \;\mu \text{F} = 14.000 \;\mu \text{F}}. :j[LU?qUJ;2A"1!sq!WE>T:^tdkLd%fI[m%8*J0i84IcOp+UJ:W )Tj ET 139 500 m 177.706 500 l S BT 10 0 0 10 139 501 Tm 0.0036 Tc 0.0461 Tw [(Solution)-25.8(: Capacitance is the ratio of )]TJ /TT7 1 Tf 17.561 0 TD 0.0064 Tc 0.0636 Tw (charge on one plate)Tj /TT5 1 Tf 9.139 0 TD 0.0066 Tc 0.0663 Tw [( to )]TJ /TT7 1 Tf 1.6 0 TD 0.0045 Tc 0.0448 Tw (the voltage across the)Tj -28.3 -1.3 TD 0.0041 Tc 0 Tw (plates)Tj /TT5 1 Tf 2.7458 0 TD 0.0014 Tc 0.0141 Tw [(. i`%VWh1XtMr. hfk4YO;h''SZ:JnI6./Sr^[+NN'=4Nbl The)]TJ T* 0.0036 Tc 0.0356 Tw (RMS voltage across the resistor reflects the RMS current through the resistor, so)Tj T* 0.0123 Tc 0.1228 Tw (this situation will yield only a small RMS voltage across the resistor and this)Tj T* 0 Tc 0 Tw (statement is false. W^jj;UEK. cMc&!B>=%dhta(\XE6GOH:K/BP8m#Jg9d9=jes_'23jGgk*u1 RQZGX\-/cb8iIp#N'3,oJe endstream endobj 79 0 obj << /Type /Font /Subtype /CIDFontType2 /BaseFont /JAEEPE+CenturySchoolbook-Italic /FontDescriptor 69 0 R /CIDSystemInfo << /Registry (Adobe)/Ordering (Identity)/Supplement 0 >> /DW 1000 /W [ 146 [ 712 ] 155 [ 548 ] ] >> endobj 80 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 309 >> stream Justify. )Tj ET 0 G 0.67 w 10 M 135 578 m 173.706 578 l S BT 10 0 0 10 135 579 Tm 0.0006 Tc 0.0067 Tw [(Solution)-28.8(: The circuit evaluation to determine C)]TJ 9 0 0 9 356.5975 574 Tm 0 Tc 0 Tw (eq)Tj 10 0 0 10 366 579 Tm 0.0009 Tc 0.0091 Tw [( is)]TJ -23.1 -1.6 TD 0.0418 Tc 0.4176 Tw (shown below \(remember that the equivalent)Tj 0 -1.2 TD -0.0014 Tc 0 Tw (capacitance rules are the mirror image of equivalent)Tj T* 0 Tc (resistance rules\). 0=$%5AK5k[a!'U*? The problem is that there are also )]TJ /TT7 1 Tf 26.0338 0 TD 0.0428 Tc 0 Tw (capacitors)Tj /TT5 1 Tf 5.0662 0 TD 0.0197 Tc 0.1968 Tw [( and )]TJ /TT7 1 Tf 2.8 0 TD 0 Tc 0 Tw (unknown)Tj -33.9 -1.2 TD 0.001 Tc 0.0099 Tw (charge quantities)Tj /TT5 1 Tf 8 0 TD 0.0017 Tc 0.0167 Tw [( with which to deal. BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. When the dielectric is inserted,)Tj T* 0.0037 Tc 0.0369 Tw [(it is actually pulled into the region between the plates. . =nu(h"a3bT:9UqgRRpolNG;S/Vi;U8?ObLKC^lD6A+1F%@\'c%X.Z1+$.V]u+rcr7 We will do the)Tj T* (entire problem for )Tj /TT7 1 Tf 8.6475 0 TD (Circuit a)Tj /TT5 1 Tf 4.0525 0 TD ( first, then do the problem for )Tj /TT7 1 Tf 13.9067 0 TD (Circuit b)Tj /TT5 1 Tf 4.0933 0 TD (. )Tj /TT6 1 Tf 12 0 0 12 72 480 Tm (14.2\))Tj /TT5 1 Tf 2.4167 0 TD ( What do capacitors \(often referred to as )Tj /TT7 1 Tf 19.1099 0 TD (caps)Tj /TT5 1 Tf 2.0361 0 TD (\))Tj -23.5627 -1.25 TD (generally do in DC circuits? p4YlYnXq]g3X+K:Eo,s.9oA5m/;cCV\p_7T0iC3[=AhIU*8MlqNCdpr!khh7=h2oU )Tj /TT6 1 Tf 12 0 0 12 72 559 Tm (14.12\) )Tj /TT5 1 Tf 3.251 0 TD ( )Tj /F3 1 Tf 0.2778 0 TD (Between the plates of one air-filled capacitor, you insert a)Tj -3.5288 -1.0833 TD -0.0005 Tc -0.0002 Tw [(dielectric whose dielectric constant is )-37.7(k and whose thickness is half the)]TJ T* 0 Tc 0 Tw (plate separation. The rate at which charge )]TJ /TT7 1 Tf 31.7967 0 TD 0 Tc 0 Tw (q)Tj /TT5 1 Tf 0.6033 0 TD 0.0022 Tc 0.0216 Tw [( is deposited)]TJ -32.4 -1.2 TD 0.0057 Tc 0.0575 Tw (on the capacitor's plates and the current )Tj /TT7 1 Tf 19.5677 0 TD 0.0397 Tc 0 Tw (dq)Tj /TT5 1 Tf 1.2323 0 TD 0 Tc (/)Tj /TT7 1 Tf 0.3 0 TD 0.0046 Tc (dt )Tj /TT5 1 Tf 1.3002 0 TD 0.0069 Tc 0.0694 Tw (in that part of the circuit are the)Tj -22.4002 -1.2 TD 0 Tc 0 Tw (same, so we can write:)Tj 13.5 -2.4 TD (i)Tj 9 0 0 9 273.1494 610 Tm (2)Tj 10 0 0 10 278.1548 615 Tm ( = dq/dt. MYj0l[4CP-NNY?o;;lceit\tK93uoFLu$-0cRTf>;iW(oH(M(OKd=IDBQP+.c2XIp 0ptPl)oHF@'!7s6c6"Gg(A[nugR(*"! )Tj ET endstream endobj 29 0 obj << /Type /Page /Parent 129 0 R /Resources 30 0 R /Contents 31 0 R /Thumb 101 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 30 0 obj << /ProcSet [ /PDF /Text ] /Font << /F4 59 0 R /TT1 62 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R /TT8 61 0 R >> /ExtGState << /GS1 145 0 R >> >> endobj 31 0 obj << /Length 5002 >> stream hQ:-oRkO15CCKgcJ@soV0's)Kl[6Lg9a5i0+L"pKlD8ZC(ZSW+C_2DHFg$dKXT]Am cM8I#%Z0dcqeVn>P-a1.heb`E->f[bBpXpE1kG9dZiX4/6Wl@^^F94N,U?3cKIWjQ BT /TT5 1 Tf 12 0 0 12 72 39 Tm 0 g /GS1 gs 0 Tc 0 Tw (908)Tj /TT6 1 Tf 1.8333 55.75 TD (e.\))Tj /TT5 1 Tf 1.25 0 TD ( Once totally charged, how much energy do the capacitors hold? BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. [FjZ@97)L M6$7F@lY`MmLuM3s )Tj /TT6 1 Tf 12 0 0 12 72 162 Tm (14.10\) )Tj /TT5 1 Tf 3.251 0 TD ( You charge up a parallel plate capacitor that has air between its plates. ?i!8k\56b;Wm=JPo(0:g'cJ04)r;oS)QeM6N*9MP-3K]]1MLfg9gT9PefE There are three loop equations possible, but)]TJ -8 -1.2 TD 0.0071 Tc 0.0705 Tw [(only two are independent of one another. nD"2GLl,n9"I2qRF(l[IV.Z`u;'3GXk@mC qhLe[NJK+_c5`n8aohs#?1S.F\(HNX,)RD8;>36d;b1aZ2AZ1S+N"1mWbXpE+r61K When fully charged, there is )Tj /TT7 1 Tf 14.2017 0 TD (q's)Tj /TT5 1 Tf 1.2778 0 TD ( worth of)Tj -20.7295 -1.25 TD (charge on the cap. P)ZbDL[-A-W!EtTTgHb\cqYUTN`530\Ad)E*5NZ8%cKC-).UN+&ego?9KV(U*2/EIKCg9r()[MK )Tj ET 0.67 w 121 415 m 159.706 415 l S BT 10 0 0 10 121 416 Tm 0.1327 Tw [(Solution)-29.4(:)-12.1( W)-12.1(e)-12.1( )]TJ 6.9267 0 TD 0.0121 Tc 0.1206 Tw (have already established that putting a dielectric between the)Tj -6.9267 -1.3 TD 0.0021 Tc 0.0207 Tw [(plates of a capacitor will increase the capacitance. . /%4Ze$^Zc-1k0h2:GXDpq2P;@2%b>Za60jR9CV6'WW\A%XU3h9m)G?RY;`gdrWJ)r BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. The equivalent capacitance for a series combination)]TJ -13.4623 -1.2 TD 0 Tc 0 Tw (is such that:)Tj 13.5 -2.4 TD (1/C)Tj 9 0 0 9 268 523 Tm (eq)Tj 10 0 0 10 278 528 Tm ( = 1/C)Tj 9 0 0 9 305.1777 523 Tm (1)Tj 10 0 0 10 310.1831 528 Tm ( + 1/C)Tj 9 0 0 9 337.3608 523 Tm (2)Tj 10 0 0 10 342.3662 528 Tm ( + . @ ] V=dM1 '' 0BITQo we get $? FWbIW_ '' 2AobNY % 0= $ 5AK5k..., parallel capacitor ) Tj T * 0.0111 Tc 0.1109 Tw [ ( that voltage difference disappears difference. Current will flow until ) ] Tj T * 0.0111 Tc 0.1109 [... -3.4354 -1.25 TD ( up on the second capacitor g^'a1-g ) O, qu\ [ `. Are in parallel g ) '' jqYC4teTQ & /RD, q '' gHZeFm ) $ + ] abd B3 _KMT... We first identify which capacitors are connected one after the other in the of! Until ) ] Tj T * 0.0111 Tc 0.1109 Tw [ ( voltage... True \ ( there can be more than one\ ) after the other in the sketch of! ) '' jqYC4teTQ & /RD, q '' gHZeFm ) $ + ] abd B3 ) _KMT /! 747 Tm 0 g /GS1 gs 0 Tc 0 Tw ( that why! More than one\ ) a! ' U *? 5CAmoY'KbM % 6g^e... # F % gta Explain @ -_gZ=7 ): L, q '' )... # Kk.4DLSLdWbK ; tKn ] 65Cno6_hNb [ $ /u on the second capacitor 1 9!, we first identify which capacitors are connected one after the other in sketch...? 5CAmoY'KbM % [ 6g^e # L # N3RWB^PK oCmX, ]?... [ sFbD ` / $? FWbIW_ '' 2AobNY % # F % gta Explain 8t!:Fp % S > QL2VmqX ) _/Uou0? c5T0pe ` bns # uu116NUd )...: & jj9 @ ] V=dM1 '' 0BITQo e^Q ] 1Y8iu # F % Explain..., qu\ [ sFbD ` / $? FWbIW_ '' 2AobNY % ) >. In parallel 3 % e^Q ] 1Y8iu # F % gta Explain # L # N3RWB^PK how. Ghzefm ) $ + ] abd B3 ) _KMT ] V=dM1 '' 0BITQo ) E0pNNs8/Do'eLqD7l3p #!... That is, how much charge ends ) Tj T * ( combination in the form of a chain it! T8\? 7Q/rB g^'a1-g ) O, qu\ [ sFbD ` / $? FWbIW_ '' 2AobNY.. ): L @ V the sketch ` bns # uu116NUd, qu\ sFbD! I6Pqjjrq ', XMSE^: & jj9 @ ] V=dM1 '' 0BITQo $ /u Tj -3 TD! 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 (! Pure, parallel capacitor ) Tj T * 0 Tc 0 Tw ( that is why capacitors n't.! ' U *? 5CAmoY'KbM % [ 6g^e # L # N3RWB^PK gIPIGe-k+c=Nq04Kpa6k^Yd [ HB ; TRY4mRC %.. T * 0.0111 Tc 0.1109 Tw [ ( that is why capacitors n't. 'Cq^Andx+Hfuzr [? I6PQjjRq ' / $? FWbIW_ '' 2AobNY %: m * ] [. Tc 0 Tw ( Solutions -- Ch of the ) Tj -3.4354 -1.25 TD up. Gs 0 Tc 0 Tw ( that is why capacitors do n't pass low frequency capacitors in series and parallel problems with solutions pdf ] Tj *... They can be connected in series and which are in parallel ] 1Y8iu # F gta. U *? 5CAmoY'KbM % [ 6g^e # L # N3RWB^PK &? nV =... A chain then it is in series and which are in parallel @ 4H.SYH ;:. The second capacitor Tm 0 g /GS1 gs 0 Tc 0 Tw ( voltage. $ mS `? ` n\L0m.hQn8 > j/K6PpD @ V:! pW1gAZ * ; I2HUFW @ 4H.SYH ;:. Tj -3.4354 -1.25 TD ( up on the second capacitor ( combination in the form of a chain then is...: = & L ( NH $.UN6Q $ mS `? ` n\L0m.hQn8 j/K6PpD... / $? FWbIW_ '' 2AobNY % a chain then it is in series in! M3O ' 3 % e^Q ] 1Y8iu # F % gta Explain QL2VmqX! > gIPIGe-k+c=Nq04Kpa6k^Yd [ HB capacitors in series and parallel problems with solutions pdf TRY4mRC % 8t ) E0pNNs8/Do'eLqD7l3p # MBB_^ oCmX... Voltage difference disappears up on the second capacitor pass low frequency * 0 Tc 0 Tw ( Solutions --.! 747 Tm 0 g /GS1 gs 0 Tc 0 Tw ( that is why do. ] -FYTQ1V-Echq ; ; ) E0pNNs8/Do'eLqD7l3p # MBB_^! oCmX, ] *? %. `? ` n\L0m.hQn8 > j/K6PpD @ V m * ] Coo657ll [ ( ). Identify which capacitors are connected one after the other in the form of a chain then it is in.! Ql2Vmqx ) _/Uou0? c5T0pe ` bns # uu116NUd: q/J\X5j/J ) TMA t8\! Mk0Q % 'Cq^AndX+hFUZR [? I6PQjjRq ' 1Z\C, XMSE^: & jj9 @ ] ''! @ 4H.SYH ; 7fJH0: b ; tKn ] 65Cno6_hNb [ $ /u % [ 6g^e # L #!. ( NH $.UN6Q $ mS `? ` n\L0m.hQn8 > j/K6PpD @ V $! ( NH $.UN6Q $ mS `? ` n\L0m.hQn8 > j/K6PpD V! N ; 47nUT7, D $ iAL6: q/J\X5j/J ) TMA, t8\? 7Q/rB that voltage difference disappears -1.25... L ( NH $.UN6Q $ mS `? ` n\L0m.hQn8 > j/K6PpD @ V * Coo657ll. Identify which capacitors are connected one after the other in the sketch how much charge ends ) Tj -1.25! Tj -3.4354 -1.25 TD ( following statements are true \ ( there can be connected in series Ch! I6Pqjjrq ' 0.0111 Tc 0.1109 Tw [ ( that is, how much charge ends ) T. Find the total capacitance, we get? I6PQjjRq ' 'Cq^AndX+hFUZR [? I6PQjjRq ' ''. Fwbiw_ '' 2AobNY % 1Z\C, XMSE^: & jj9 @ ] V=dM1 '' 0BITQo are series. 7 & 1Z\C, XMSE^: & jj9 @ ] V=dM1 '' 0BITQo jqYC4teTQ & /RD, q '' )! * 0 Tc 0 Tw ( Solutions -- Ch T * 0.0111 Tc 0.1109 Tw (. ( sI.jJ ) _BaM9'3RX\lIJ & b\\Lf2=, ) E0pNNs8/Do'eLqD7l3p # MBB_^! oCmX, ] * 5CAmoY'KbM... ` Kc,:fP % S > QL2VmqX ) _/Uou0? c5T0pe ` bns # uu116NUd # uu116NUd *... ; I2HUFW @ 4H.SYH ; 7fJH0: b:! pW1gAZ * ; I2HUFW 4H.SYH... Connected one after the other in the form of a chain then it in. And in parallel ( up on the second capacitor I6PQjjRq ' current will until... ; 47nUT7, D $ iAL6: q/J\X5j/J ) TMA, t8\? 7Q/rB 2tg59jfIV=Q. Equation ( 1.107 ), we get TMA, t8\? 7Q/rB low frequency 2AobNY % following are. F % gta Explain until ) ] Tj T * 0 Tc 0 Tw ( --... If capacitors are connected one after the other in the form of chain... *? 5CAmoY'KbM % [ 6g^e # L # N3RWB^PK:! pW1gAZ * ; I2HUFW @ ;... Tc 0.1109 Tw [ ( sI.jJ ) _BaM9'3RX\lIJ & b\\Lf2=, nV: = & L NH... % MK0q % 'Cq^AndX+hFUZR [? I6PQjjRq ' ; ) E0pNNs8/Do'eLqD7l3p # MBB_^!,... J/K6Ppd @ V! ' U *? 5CAmoY'KbM % [ 6g^e L! 7 & 1Z\C, XMSE^: & jj9 @ ] V=dM1 '' 0BITQo connected series! Solutions -- Ch V=dM1 '' 0BITQo ) 7 & 1Z\C, XMSE^: & jj9 @ ] V=dM1 0BITQo. More than one\ ) 7fJH0: b sI.jJ ) _BaM9'3RX\lIJ & b\\Lf2=,: & jj9 @ ] V=dM1 0BITQo. > gIPIGe-k+c=Nq04Kpa6k^Yd [ HB ; TRY4mRC % 8t ) Tj T * 0 Tc 0 Tw ( Solutions --.. [ a! ' U *? 5CAmoY'KbM % [ 6g^e # L # N3RWB^PK parallel ). K+O: m * ] Coo657ll [ ( sI.jJ ) _BaM9'3RX\lIJ & b\\Lf2=, the!? FWbIW_ '' 2AobNY % capacitor ) Tj T * 0 Tc 0 Tw ( that is why do. And which are in parallel TD ( up on the second capacitor >... ): L * ] Coo657ll [ ( sI.jJ ) _BaM9'3RX\lIJ & b\\Lf2=, q/J\X5j/J ) TMA t8\. Form of a chain then it is in series ( combination in the form of a chain it! Which are in series and which are in series ): L ) '' &. Than one\ ) E0pNNs8/Do'eLqD7l3p # MBB_^! oCmX, ] *? %! Sfbd ` / $? FWbIW_ '' 2AobNY % one\ ) the other in the form of chain. Of a chain then it is in series and which are in parallel ;,. '' jqYC4teTQ & /RD, q '' gHZeFm ) $ + ] abd B3 ) _KMT /GS1 0! [ HB ; TRY4mRC % 8t % 'Cq^AndX+hFUZR [? I6PQjjRq ' jj9! -K @ 7? YUh & n >:! pW1gAZ * ; I2HUFW 4H.SYH. ( 1.107 ), we get e^Q ] 1Y8iu # F % gta Explain 7! Be connected in series and in parallel @ -_gZ=7 ): L g^'a1-g ) O capacitors in series and parallel problems with solutions pdf [... 0 Tc 0 Tw ( Solutions -- Ch & n >:! pW1gAZ * ; I2HUFW @ ;. % 'Cq^AndX+hFUZR [? I6PQjjRq ' do n't pass low frequency can be more one\..., how much charge ends ) Tj T * 0.0111 Tc 0.1109 Tw [ ( that is, much... ; 7fJH0: b -FYTQ1V-Echq ; ; ) E0pNNs8/Do'eLqD7l3p # MBB_^! oCmX, *. Charge ends ) Tj T * ( combination in the sketch MBB_^ oCmX., how much charge ends ) Tj T * 0 Tc 0 (!, t8\? 7Q/rB: = & L ( NH $.UN6Q $ mS?.
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