'&beU2#E0Opn*2$&TcHR45A^@j+e` The problem is that there are also )]TJ /TT7 1 Tf 26.0338 0 TD 0.0428 Tc 0 Tw (capacitors)Tj /TT5 1 Tf 5.0662 0 TD 0.0197 Tc 0.1968 Tw [( and )]TJ /TT7 1 Tf 2.8 0 TD 0 Tc 0 Tw (unknown)Tj -33.9 -1.2 TD 0.001 Tc 0.0099 Tw (charge quantities)Tj /TT5 1 Tf 8 0 TD 0.0017 Tc 0.0167 Tw [( with which to deal. [TZZ?VJQA@BbFVL@i_;:0%7hO. e8V12+MXDuBU/Cm4t'@6LJd+_(b]C7KkXX]66S)'lpE8P8o7BJ2=T&ImIlrt5)j"? ?\pG/7(t8PP>oJXMUGF$Q?-[,[!6Xbf7Ikr;)0>Q2!6%uH&b8A#7"=N ?HojK[aJ1P?7(aGo9'&aK]U6unT-]X)5P"ci=NKspI-'DUbP8^8-l+5@j6ak/u By the same token, the charge )]TJ /TT7 1 Tf 15.3451 0 TD 0 Tc 0 Tw (q)Tj /TT5 1 Tf -36.3451 -1.6 TD 0.0017 Tc 0.0167 Tw (on one plate of a capacitor is proportional to the voltage )Tj /TT7 1 Tf 26.2313 0 TD 0 Tc 0 Tw (V)Tj 9 0 0 9 404.4296 621 Tm (c)Tj /TT5 1 Tf 10 0 0 10 408 626 Tm 0.0016 Tc 0.016 Tw [( across the capacitor)]TJ -27.3 -1.6 TD 0.0145 Tc 0.145 Tw (with the proportionality constant being the capacitance )Tj /TT7 1 Tf 27.7 0 TD 0 Tc 0 Tw (C)Tj /TT5 1 Tf 0.7891 0 TD 0.0151 Tc 0.151 Tw [( of the capacitor. )Tj ET endstream endobj 4 0 obj << /Type /Page /Parent 127 0 R /Resources 5 0 R /Contents 6 0 R /Thumb 85 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 5 0 obj << /ProcSet [ /PDF /Text ] /Font << /F2 134 0 R /F4 59 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 6 0 obj << /Length 8326 >> stream BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. ;a^[mgP)na8GrmZLP0mekBd`$+ )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 is, what)Tj -3 -1.25 TD (is it called, what are its units, and how is it calculated? )Tj ET 117 630 m 155.706 630 l S BT 10 0 0 10 117 631 Tm 0.0032 Tc 0.0361 Tw [(Solution)-26.2(: A decrease in frequency means less signal will pass through the circuit)]TJ 0 -1.3 TD 0.015 Tc 0.1503 Tw (\(remember, capacitors are )Tj /TT7 1 Tf 13.1925 0 TD 0.0158 Tc 0.158 Tw (high pass)Tj /TT5 1 Tf 4.706 0 TD 0.0114 Tc 0.1143 Tw [( filters\). )Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 1 i 117 588 m 155.706 588 l S BT 10 0 0 10 117 589 Tm 0.2021 Tw [(Solution)-29.4(:)-18.4( )]TJ 5.1561 0 TD 0.0184 Tc 0.1837 Tw (When the capacitors are totally charged, there will be )Tj /TT7 1 Tf 27.7215 0 TD 0.0297 Tc 0.2973 Tw (no current)Tj /TT5 1 Tf -32.8776 -1.3 TD 0.0028 Tc 0.0281 Tw [(through the circuit \(the charged capacitors will act as open circuits\). Ua/R/%.[:[Q-pY@8'>TcX*0:ocl7(u5,M,0? ,2YVn4U9eO1UC#4[!2k VUd5V@[!. "jZKN"ln0q^-Ou`-hU\l9IFnK8M[<<172KJ`"_8H-X\3-QV]"[&K1h@rD^MgK\-)D[9;`jXQ9)@!8cJ8m[:6H _M? f]KItk8(%`bt(4=;;l(p67Nl8hr&-l%,ko,i1ms%'='"Gq\K4=Dj5b.pDI=K2"SQ' )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 *$98=Mm!a3_)lE6R")DRLt>q@AMCE+!#0$6fjDnf-m?6!-W7(2%\nVP[\%E/gtK;0 @TB%@SlPGUmB8)X>)lVQqT-_;&?6mt`k+&EX[hO/^o:2RQ^>RL^"V!s_c-2)NL2s/ )Tj ET 139 500 m 177.706 500 l S BT 10 0 0 10 139 501 Tm 0.0036 Tc 0.0461 Tw [(Solution)-25.8(: Capacitance is the ratio of )]TJ /TT7 1 Tf 17.561 0 TD 0.0064 Tc 0.0636 Tw (charge on one plate)Tj /TT5 1 Tf 9.139 0 TD 0.0066 Tc 0.0663 Tw [( to )]TJ /TT7 1 Tf 1.6 0 TD 0.0045 Tc 0.0448 Tw (the voltage across the)Tj -28.3 -1.3 TD 0.0041 Tc 0 Tw (plates)Tj /TT5 1 Tf 2.7458 0 TD 0.0014 Tc 0.0141 Tw [(. @"c[kfW6&Z11FcG]KD7chrP6i7c7k9l[;r\cROB-Flt=6qY'NAb^0 \1!q"&qheG(;qM^;Aka*C'K95M&C8"YZ59h>&BU-KS"a`^H\6X@uI'2ZdORgc0h0o capacitances in their respective positions, as shown in the figure (b). a:>O"B%!D$!BcY6/=1);-MrZllt]\0&f.Lbl6mFJ;%]SS;JW8T)NW4b0Qt!^0aU$Z In this case, the voltage)Tj -26.5005 -1.3 TD 0.0097 Tc 0.0967 Tw [(has decreased while the capacitance has gone up. BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. Q#%n[C44,'3R4Jhuh" R;ib]#p4UU+l&LSaZ3[W%dIt;KsbR%PM'MXp>k`0,kk1UQ4$&\,o^,!paMj#J*a-HELt"H<0ob@6pI#B[H#h0u5lh C=Qg/5N)UYu 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. B>n+P&DP4u'\IE1D2``m*3;)nfgi-`k%'^3Z4\\4b4(pOXhmAJO-D2BP3K;#4anP+ e8V12+MXDuBU/Cm4t'@6LJd+_(b]C7KkXX]66S)'lpE8P8o7BJ2=T&ImIlrt5)j"? )Tj -25.1291 -1.6 TD 0.0004 Tw (--Meanwhile, the capacitors initially act like open circuits \(with no charge on)Tj -2.7 -1.2 TD 0.0026 Tc 0.0264 Tw (them, there is nothing to motivate them to do otherwise\), which means the initial)Tj T* 0 Tc 0 Tw (current )Tj /TT7 1 Tf 3.7202 0 TD (will)Tj /TT5 1 Tf 1.7798 0 TD ( flow freely through them and )Tj /TT7 1 Tf 14.1 0 TD (i)Tj 9 0 0 9 316.3301 605 Tm (1)Tj 10 0 0 10 321.3354 610 Tm ( = i)Tj 9 0 0 9 336 605 Tm (2)Tj /TT5 1 Tf 10 0 0 10 341.0054 610 Tm (. 8;V^n$ZK),(&lL.n(l6@OQ@Jq8FLRj!dP>"]FlEaliTT(Oq>\e:tX$N"GoM[1LO/+ )Tj ET 117 259 m 155.706 259 l S BT 10 0 0 10 117 260 Tm 0.0037 Tc 0.0566 Tw [(Solution)-25.7(: If capacitance )]TJ /TT7 1 Tf 11.7368 0 TD 0 Tc 0 Tw (C)Tj /TT5 1 Tf 0.7632 0 TD 0.0063 Tc 0.0631 Tw [( tells you how much )]TJ /TT7 1 Tf 9.9 0 TD 0.0075 Tc 0.0752 Tw (charge per volt)Tj /TT5 1 Tf 7.0383 0 TD 0.005 Tc 0.0502 Tw [( the cap can hold, a)]TJ -29.4383 -1.3 TD 0.002 Tc 0.0199 Tw (capacitor that is twice as large \()Tj /TT7 1 Tf 14.9296 0 TD 0.0162 Tc 0 Tw (2C)Tj /TT5 1 Tf 1.2704 0 TD 0.0023 Tc 0.0231 Tw [(\) will hold twice the charge. fp,_%#X:dM`5.U/"l")L-f:IJj@Ad]nqrXt:)9! )Tj ET 117 346 m 155.706 346 l S BT 10 0 0 10 117 347 Tm 0.0002 Tc 0.0017 Tw [(Solution)-29.2(: The charge on the capacitor is related to the voltage across the capacitor)]TJ 0 -1.3 TD 0 Tc 0 Tw (and the size of the capacitor by the relationship:)Tj 9.9 -2.4 TD ( C = Q/V or Q = CV. By the same token, the charge )]TJ /TT7 1 Tf 15.3451 0 TD 0 Tc 0 Tw (q)Tj /TT5 1 Tf -36.3451 -1.6 TD 0.0017 Tc 0.0167 Tw (on one plate of a capacitor is proportional to the voltage )Tj /TT7 1 Tf 26.2313 0 TD 0 Tc 0 Tw (V)Tj 9 0 0 9 404.4296 621 Tm (c)Tj /TT5 1 Tf 10 0 0 10 408 626 Tm 0.0016 Tc 0.016 Tw [( across the capacitor)]TJ -27.3 -1.6 TD 0.0145 Tc 0.145 Tw (with the proportionality constant being the capacitance )Tj /TT7 1 Tf 27.7 0 TD 0 Tc 0 Tw (C)Tj /TT5 1 Tf 0.7891 0 TD 0.0151 Tc 0.151 Tw [( of the capacitor. )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 (. )Tj ET 139 207 m 177.706 207 l S BT 10 0 0 10 139 208 Tm 0.0073 Tc 0.0823 Tw [(Solution)-22.1(: This is an interesting question. . 8;Z\6Mitt##i,I[6%8!oVm$_2Z'1\4]eIoo%uQ;9=HQ)p\Zl/-$_q^=<6ZioAmhP=iW+Bal_lJpP_6a32g@8DS]#kotAA2 't"4-HCJ>VL"2\0KkT4n("V#Ri'f @kuUiuDVgKXl;_LS.ffL$tcga)hmT@=JV^/QRd6`@eDcr.Sg)9@_HkWCuNmD7->]WX6)#/1fMb =O1*>2EjAJ`a^.G3)!^bnp.Zh>^HK$nH>H%)P4*c;?3QMn"_H &2G*e4JUqs.YmQ_I[nOQ$0O\!Uo_!Y$g'e70>]98r"6"Rdq /V2&:r9B6Mb$#NtQgPoub!XtC\B48BN[l*AEr:XO1<6"IrlB)1iuCQ>`tj[NNm/Qg BT /TT5 1 Tf 12 0 0 12 72 39 Tm 0 g /GS1 gs 0 Tc 0 Tw (900)Tj 10 0 0 10 252 710 Tm (i = V)Tj 9 0 0 9 274 705 Tm (R)Tj 10 0 0 10 280.4995 710 Tm (/R)Tj -2.85 -1.6 TD ( = \(120 volts\)/\(20 )Tj /TT1 1 Tf 8.5347 0 TD <009f>Tj /TT5 1 Tf 0.7681 0 TD (\))Tj -9.3027 -1.2 TD ( = 6 amps. 5d"$T;Q[j%+FZt?Vk=qL/b:IAGcAofOhXlX/"i*Y#. E,LbDf:IVUnP%AS0RdC1ja#QRHC%[Y#EU_"GQH')G?kH )Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 1 i 117 449 m 155.706 449 l S BT 10 0 0 10 117 450 Tm [(Solution)-29.4(: )]TJ /TT7 1 Tf 4.4557 0 TD ( )Tj /TT5 1 Tf 0.2443 0 TD (After a long period of time:)Tj -4.7 -2.5 TD (--The capacitors will be fully charged so that )Tj /TT7 1 Tf 20.8154 0 TD (i)Tj 9 0 0 9 328.4844 420 Tm (2)Tj 10 0 0 10 333.4897 425 Tm ( = 0)Tj /TT5 1 Tf 1.7178 0 TD (;)Tj -23.3667 -1.6 TD (--The currents )Tj /TT7 1 Tf 6.9048 0 TD (i)Tj 9 0 0 9 189.3779 404 Tm (1)Tj 10 0 0 10 194.3833 409 Tm ( )Tj /TT5 1 Tf 0.2617 0 TD (and )Tj /TT7 1 Tf 2.019 0 TD (i)Tj 9 0 0 9 220.5205 404 Tm (3)Tj /TT5 1 Tf 10 0 0 10 225.5259 409 Tm ( will be equal to one another. When the dielectric is inserted,)Tj T* 0.0037 Tc 0.0369 Tw [(it is actually pulled into the region between the plates. )CD$Vt19 More online conversion calculators at digi key. )Tj ET 135 98 m 173.706 98 l S BT 10 0 0 10 135 99 Tm 0.0015 Tc 0.0174 Tw [(Solution)-27.9(: The initial current through the circuit will be that of a resistor in series)]TJ 0 -1.3 TD 0 Tc 0 Tw (with a battery \(the uncharged caps will act like "shorts"\), or:)Tj ET endstream endobj 26 0 obj << /Type /Page /Parent 127 0 R /Resources 27 0 R /Contents 28 0 R /Thumb 99 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 27 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 28 0 obj << /Length 4754 >> stream B35O/V6#8>f/QYQb8,4.$1\qhX9M/TYi]ci$or5qBIRlBVp6n''8kAAg-5kl:JF.t 8;Z\7$W[?Q%%R3%0\9094p/6JpPA0NRAZ>;i\1]7JB5RCrrCbK)-8!N-1)?L[$=*] "d.CTlo>OFRKT)e@^-C6)UR(92Ur=P/B00(616#3XKT\`rGSbK+8mlN,?B`]mmdS- 14 \(Capacitors\))Tj 12 0 0 12 502 39 Tm (905)Tj ET /Cs6 CS 0 0 0 SCN 0 J 0 j 1 w 3.864 M []0 d 1 i 427 632.7 m 467.7 632.7 l 469.9 632.7 m 494.8 632.7 l 495 627.4 m 495 637.8 l 497.2 627.4 m 497.2 637.8 l 470 627.5 m 470 637.8 l 467.8 627.5 m 467.8 637.8 l S BT /F3 1 Tf 9 0 0 9 465.6 640.7578 Tm /Cs6 cs 0 0 0 scn (C)Tj ET 482.9 604.7 m 507.8 604.7 l 483 599.5 m 483 609.8 l 480.8 599.5 m 480.8 609.8 l 497 632.7 m 508 632.7 l 454.9 604.7 m 480.8 604.7 l 504.9 584.7 m 530.8 584.7 l 505 579.5 m 505 589.8 l 502.8 579.5 m 502.8 589.8 l 442 584.7 m 502.8 584.7 l 442 633 m 442 585 l 524 613.5 m 524 623.8 l 521.8 613.5 m 521.8 623.8 l 508 618.7 m 521.8 618.7 l 524 618.7 m 537.8 618.7 l 531 619 m 531 585 l 455 633 m 455 605 l 508 633 m 508 605 l S BT 9 0 0 9 519.5999 603.7578 Tm (C)Tj -4.5555 1 TD (C)Tj 1.5556 3.1111 TD (C)Tj 0.8889 -5.3333 TD (C)Tj 10 0 0 10 477 555.6754 Tm (FIGURE III)Tj ET q 408 548 132 104 re W n 2 w 537.1 552.7 m 473 552.7 l S Q q 75 449 471 67 re W n q 0.9833 0 0 1.017 0 0 cm 1.023 w 3.864 M 76.786 489.58 m 111.057 489.58 l 111.057 496.486 m 111.057 482.931 l 115.533 496.486 m 115.533 482.931 l 115.916 489.708 m 128.576 489.708 l 128.576 496.486 m 128.576 482.931 l 133.052 496.486 m 133.052 482.931 l 132.668 489.708 m 145.328 489.708 l 145.328 466.434 l 125.507 466.434 l 121.031 473.468 m 121.031 459.913 l 125.507 473.468 m 125.507 459.913 l 120.903 466.562 m 97.63 466.562 l 97.63 489.452 l 145.328 478.071 m 155.558 478.071 l 155.558 485.104 m 155.558 471.549 l 160.034 485.104 m 160.034 471.549 l 160.034 478.455 m 170.264 478.455 l 166.044 478.455 m 166.044 448.66 l 153.128 448.66 l 148.653 455.565 m 148.653 442.01 l 153.128 455.565 m 153.128 442.01 l 148.397 448.66 m 87.4 448.66 l 87.4 489.58 l 206.861 489.58 m 248.294 489.58 l 253.153 489.708 m 273.997 489.708 l 273.997 466.562 l 252.737 466.562 l 248.038 473.468 m 248.038 459.913 l 252.514 473.468 m 252.514 459.913 l 247.91 466.562 m 227.705 466.562 l 227.705 489.452 l 274.381 478.071 m 285.634 478.071 l 285.634 485.104 m 285.634 471.549 l 290.109 485.104 m 290.109 471.549 l 290.109 478.455 m 300.34 478.455 l 296.12 478.455 m 296.12 448.66 l 283.204 448.66 l 278.728 455.565 m 278.728 442.01 l 283.204 455.565 m 283.204 442.01 l 278.473 448.66 m 217.475 448.66 l 217.475 489.58 l 248.294 496.486 m 248.294 482.931 l 252.769 496.486 m 252.769 482.931 l 406.174 471.401 m 429.79 471.401 l 406.174 466.884 m 429.79 466.884 l 424.494 475.967 m 432.377 469.441 l 432.727 469.441 m 424.056 462.916 l 307.444 471.815 m 331.059 471.815 l 307.444 467.297 m 331.059 467.297 l 325.763 476.38 m 333.647 469.855 l 333.997 469.855 m 325.325 463.329 l 177.176 471.465 m 200.792 471.465 l 177.176 466.947 m 200.792 466.947 l 195.496 476.03 m 203.379 469.505 l 203.73 469.505 m 195.058 462.979 l 495.153 471.401 m 518.769 471.401 l 495.153 466.884 m 518.769 466.884 l 513.473 475.967 m 521.356 469.441 l 521.706 469.441 m 513.035 462.916 l 530.845 471.356 m 540.536 471.356 l 540.536 478.262 m 540.536 464.707 l 545.012 478.262 m 545.012 464.707 l 544.628 471.101 m 554.374 471.101 l 440.467 486.696 m 461.28 486.696 l 465.883 486.824 m 484.84 486.824 l 480.62 486.824 m 480.62 457.029 l 465.882 457.029 l 461.183 463.934 m 461.183 450.379 l 465.659 463.934 m 465.659 450.379 l 460.927 457.029 m 446.989 457.029 l 446.989 486.696 l S 461.28 493.602 m 461.28 480.047 l 465.755 493.602 m 465.755 480.047 l 340.902 485.948 m 358.804 485.948 l 375.684 492.725 m 375.684 479.17 l 380.16 492.725 m 380.16 479.17 l 380.16 486.076 m 394.482 486.076 l 390.262 486.076 m 390.262 456.28 l 372.455 456.28 l 367.756 463.185 m 367.756 449.631 l 372.231 463.185 m 372.231 449.631 l 367.5 456.28 m 347.423 456.28 l 347.423 485.948 l 358.804 492.853 m 358.804 479.298 l 363.28 492.853 m 363.28 479.298 l 363.792 486.331 m 375.602 486.331 l S Q Q BT /F2 1 Tf 8.0474 0 0 8.3232 108.2069 507.3395 Tm (C)Tj 2.1875 0.0313 TD (C)Tj 2.4165 -5.0405 TD (C)Tj -3.25 2.125 TD (C)Tj 4.2085 1.3843 TD (C)Tj 14.9165 -3.5405 TD (C)Tj -3.75 2.125 TD (C)Tj 4.7085 1.3843 TD (C)Tj -5.021 1.5532 TD (C/2)Tj 15 -4.1875 TD (C)Tj 0.9585 3.5093 TD (C)Tj -3.0835 -0.0093 TD (\(3/2\)C)Tj 13.5625 -3.4375 TD (C)Tj -0.9062 3.625 TD (\(3/5\)C)Tj 9.5938 -1.8125 TD (\(8/5\)C)Tj /F3 1 Tf 9 0 0 9 359.1 203.5577 Tm (120 volts)Tj 6.8889 -6.2222 TD (20)Tj ET q 0.8395 0 0 1.1912 0 0 cm 0.424 w 515.348 126.47 m 515.348 128.083 516.536 129.441 517.894 129.441 c 519.252 129.441 520.44 128.083 520.44 126.47 c 520.44 124.858 519.252 123.5 517.894 123.5 c 516.536 123.5 515.348 124.858 515.348 126.47 c s Q 1 1 1 scn 431.9 148.129 5.7 -3.033 re f q 0.8395 0 0 1.1912 0 0 cm 0.424 w 521.289 124.348 m 519.591 124.348 l 516.196 124.348 m 514.499 124.348 l S Q BT 9 0 0 9 409.1 268.5577 Tm 0 0 0 scn (switch closes)Tj 0 -1 TD ( at t=0)Tj 6.1111 -4.8889 TD (12 f)Tj ET 0.5 w 475 214 m 475.7 214.3 476.6 214.3 477 215 c 477.3 215.6 477 216.3 477 217 c 477 217.7 477 219.7 477 219 c 477 218.3 476.7 217.6 477 217 c 477.2 216.6 477.5 216.1 478 216 c 478.3 215.9 478.7 215.9 479 216 c 479.5 216.1 479.8 216.6 480 217 c 480.5 217.9 480 220 y 480 218.9 480 218.1 480 217 c 480 216.7 480 216.3 480 216 c S BT 10 0 0 10 479.5 139.4752 Tm (FIGURE IV)Tj ET q 350 132 190 148 re W n 2 w 536.6 136.5 m 475.5 136.5 l S Q 1 w 406.5 161.1 m 421.4 161.1 l 438.8 161.1 m 515 161.1 l 407.1 249.1 m 407.1 206.6 l 407.1 203.6 m 407.1 161.2 l 455.5 249.1 m 455.5 219.8 l 455.5 205 m 455.5 161.2 l 455.5 220.6 m 455.5 205 l 437.8 249.2 m 515 249.2 l 428.7 249.2 m 437.8 254.3 l S 0.5 w 432 255 m 432.6 254.6 433.4 254.2 433.9 253.6 c 434.6 252.7 435 251.8 435.2 250.6 c 435.3 249.8 435.2 249.2 435.2 248.4 c 435.2 248.4 m 435.8 251.4 l 435.2 248.4 m 434.6 250.6 l S 1 w 421.3 160.8 m 422.4 159 l 425 163 l 427.5 159 l 430.1 163 l 432.6 159 l 435.2 163 l 437.8 159 l 438.9 160.8 l 399 206.3 m 414.5 206.3 l 409.4 204.1 m 404.2 204.1 l 429 249 m 407 249 l 515.1 249.5 m 515.1 217 l 515.1 200 m 515.1 161 l 514.8 217.7 m 513 216.6 l 517 214 l 513 211.5 l 517 208.9 l 513 206.4 l 517 203.8 l 513 201.2 l 514.8 200.1 l S 0.5 w 412 217 m 412 234 l 412 234 m 409 227 l 412 234 m 415 227 l S BT 9 0 0 9 416.1 220.5577 Tm (i)Tj 8 0 0 8 419.1 215.6402 Tm (1)Tj 9 0 0 9 433.1 197.5577 Tm (i)Tj 8 0 0 8 436.1 192.6402 Tm (2)Tj ET 446 214 m 446 197 l 446 197 m 449 204 l 446 197 m 443 204 l S 482 244 m 499 244 l 499 244 m 492 247 l 499 244 m 492 241 l S BT 9 0 0 9 489.1 231.5577 Tm (i)Tj 8 0 0 8 492.1 226.6402 Tm (3)Tj 9 0 0 9 521.1 206.5577 Tm (30)Tj ET q 0.8395 0 0 1.1912 0 0 cm 0.424 w 634.472 175.998 m 634.472 177.611 635.66 178.969 637.018 178.969 c 638.376 178.969 639.565 177.611 639.565 175.998 c 639.565 174.386 638.376 173.028 637.018 173.028 c 635.66 173.028 634.472 174.386 634.472 175.998 c s Q 1 1 1 scn 531.9 207.129 5.7 -3.033 re f q 0.8395 0 0 1.1912 0 0 cm 0.424 w 640.413 173.876 m 638.716 173.876 l 635.321 173.876 m 633.624 173.876 l S Q BT 9 0 0 9 467.0999 188.5577 Tm 0 0 0 scn (6 f)Tj ET 473 187 m 473.7 187.3 474.6 187.3 475 188 c 475.3 188.6 475 189.3 475 190 c 475 190.7 475 192.7 475 192 c 475 191.3 474.7 190.6 475 190 c 475.2 189.6 475.5 189.1 476 189 c 476.3 188.9 476.7 188.9 477 189 c 477.5 189.1 477.8 189.6 478 190 c 478.5 190.9 478 193 y 478 191.9 478 191.1 478 190 c 478 189.7 478 189.3 478 189 c S 1 1 1 scn 452 220 8 -2 re f 451 192 8 -2 re f 1 w 450.2 220.1 m 460.6 220.1 l 450.2 217.9 m 460.6 217.9 l 450.2 192.1 m 460.6 192.1 l 450.2 189.9 m 460.6 189.9 l S BT /TT5 1 Tf 10 0 0 10 270 710 Tm 0 g (C)Tj 9 0 0 9 277.2217 705 Tm (new)Tj 10 0 0 10 294 710 Tm ( = k)Tj 9 0 0 9 312 705 Tm (d)Tj 10 0 0 10 317.168 710 Tm (C)Tj 9 0 0 9 324.3896 705 Tm (old)Tj 10 0 0 10 337 710 Tm (. )Tj -20.2 -2.8 TD (That means )Tj /TT7 1 Tf 5.8 0 TD (C)Tj 9 0 0 9 200.2217 677 Tm (new)Tj 10 0 0 10 216.7143 682 Tm ( = 1.6 C)Tj 9 0 0 9 252 677 Tm (old)Tj /TT5 1 Tf 10 0 0 10 265 682 Tm (. )Tj /TT6 1 Tf 12 0 0 12 99 614 Tm (c.\))Tj /TT5 1 Tf 1.25 0 TD ( What happens to the charge on the capacitor's plates? 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 ( + . \aP[!l`$7`19O%NeHZ&(j`A)`nW3/Jrk&_']f@;+P82st5A\WrcQ92;B2US+>^d+t )Tj 2.7 -1.2 TD 0.0063 Tc 0.0632 Tw (--When the switch is closed, the 30 )Tj /TT1 1 Tf 16.9461 0 TD 0 Tc 0 Tw <009f>Tj /TT5 1 Tf 0.7744 0 TD 0.0063 Tc 0.0632 Tw [( resistor is in parallel with the two series)-33.4(-)]TJ -20.4204 -1.2 TD 0.0028 Tc 0.0284 Tw [(connected capacitors. With an effectively diminished)]TJ T* 0 Tc 0 Tw (electric field across its plates, the plate voltage )Tj /TT7 1 Tf 21.9 0 TD (decreases)Tj /TT5 1 Tf 4.3 0 TD (. ?HojK[aJ1P?7(aGo9'&aK]U6unT-]X)5P"ci=NKspI-'DUbP8^8-l+5@j6ak/u @1MF.&ZQE&NOb[PEdQp1p`P%2/@VjdO'k$j`uaSYVU'3N&)_"=B(q@lLMu0(SE10, I-3Tcn(`!13UaYpL%]LHHUlNlL7m\oMUBM1c[AV-a.%r)+/^rDSYRA(q5\_u5BRBA 2k/(7.CHCL]e`Pj%. !&`dLW/iol8e[F37BkS/;$*jE0IYA$@*rD5;IiTl!NFV6d5H>um`$rRA+sLmkPrl= +;,uV"@3SN2>P.XPLK]2ddUQ!e$ClZtOT:0IriYHM-A0)VjGG4/)I/s&b5Qh+%I'J1g46HN:Y 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 At )]TJ /TT7 1 Tf 2.3467 0 TD 0.0077 Tc 0.0777 Tw (t = 2 seconds)Tj /TT5 1 Tf 6.1533 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 10 495 545 Tm (2)Tj /TT5 1 Tf 12 0 0 12 501 550 Tm (. BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. Nevertheless, that's the case. $a+tiqVZ&IieHqHX^HL[A,\7tL7d#bIGob>ej,MV;lI,s[X.4H8".d%HQP#3"\n$. 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. ;.pEmc'G3pu36ahPD+$7//l>CO(Eg[\NChfW4DFT*r^BJh]-sbeaF=qM7 P"j1iDFV5&dT$10;c>bl6(s)4ohNc4lF4Y06Xa=s%PM:9@CPhAW[k6pWTrPC?+RYA hQ:-oRkO15CCKgcJ@soV0's)Kl[6Lg9a5i0+L"pKlD8ZC(ZSW+C_2DHFg$dKXT]Am ],&P\iAPJ1DN'T?oVSZ,CHIBkD8jSDR4]uiT5Z@"@nPgX8Y4l_bl@&;>n b`7*,\RsORCs7t"`$Xi,gTmX0QSi2C'4R8M4""/RisRjb)MM';;/fF/q(bo%6[;:t when )Tj /TT7 1 Tf 4.7222 0 TD (V)Tj /TT5 1 Tf 0.7041 0 TD ( gets smaller, )Tj /TT7 1 Tf 6.4696 0 TD (C)Tj /TT5 1 Tf 0.7222 0 TD ( gets larger\). lgc9nD2;=PR=^%oZ%/$umeWTdEVN\6@nSm`duKa4$:Durc9Se]P\SU3fC-FJ3nW]B kgCBY6%+$.)SQ0bAN)k]U;gm&"Gc_5rpcC`L,FVtcC#+MKE. )Tj -4.3835 -1.2 TD 0.0002 Tc 0.0023 Tw (--With no initial voltage drop across the 30 )Tj /TT1 1 Tf 20.0474 0 TD 0 Tc 0 Tw <009f>Tj /TT5 1 Tf 0.7683 0 TD 0.0003 Tc 0.0022 Tw ( resistor, there will be no initial)Tj -23.5157 -1.2 TD 0 Tc 0 Tw (current through that resistor. [latex]{C_{\text{p}} = 1.000 \;\mu \text{F} + 5.000 \;\mu \text{F} + 8.000 \;\mu \text{F} = 14.000 \;\mu \text{F}}. `Dq+Z9ia]/+chGQh5I\,Y)%WS(UcDCCWMU>$N%]n;"SYC,:o/4,poG_&?c\N=h^t(ocABFGaJ(-(HaSJQ7L( )Tj -38 -1.6 TD (In short, the voltage across the capacitor won't change at all. 14 \(Capacitors\))Tj 12 0 0 12 502 39 Tm (891)Tj ET q 1 i 403 492 137 109 re W n q 0.9939 0 0 1.0062 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.026 w 3.864 M []0 d 490.369 523.386 m 490.369 502.356 l 493.959 517.231 m 493.959 509.024 l 489.343 513.64 m 436.513 513.64 l 436.513 513.64 m 436.513 562.495 l 542.814 562.88 m 542.814 514.153 l 542.685 513.64 m 494.857 513.64 l 489.984 562.623 m 498.704 562.623 l 501.14 569.547 l 505.628 555.827 l 510.5 569.676 l 515.117 555.699 l 519.733 569.547 l 524.349 555.827 l 529.221 569.676 l 534.094 555.699 l 536.787 562.88 l 542.814 562.88 l S Q Q BT /F2 1 Tf 10.1953 0 0 10.3213 512.5184 577.5381 Tm /Cs6 cs 0 0 0 scn (R)Tj -5.3045 -3.2968 TD (C)Tj 1.1625 -4.5 TD (100 volts)Tj -6.35 3.2625 TD (switch)Tj ET q 0.9939 0 0 1.0062 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.026 w 3.864 M []0 d 1 i 468.955 562.623 m 491.138 562.623 l 436.513 562.367 m 461.005 562.367 l S Q 1 1 1 scn 1 i 431.292 549.833 5.098 -12.128 re f q 0.9939 0 0 1.0062 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.026 w 3.864 M []0 d 436.77 534.157 m 431.384 546.466 l 441.417 542.584 m 434.237 542.584 430.75 540.84 428.083 535.916 c 428.083 535.916 m 430.102 541.081 l 428.083 535.916 m 432.667 538.26 l 441.417 542.584 m 435.231 544.415 l 441.417 542.584 m 436.77 539.286 l 461.518 572.753 m 461.518 551.724 l 468.57 572.753 m 468.57 551.724 l S Q BT 8.1563 0 0 8.2571 438.3014 592.6664 Tm 0 0 0 scn -0.0556 Tw (plate A)Tj 3.4375 -0.75 TD 0 Tw (plate B)Tj ET q 0.9939 0 0 1.0062 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 0.256 w 3.864 M []0 d 451.26 587.114 m 451.26 572.24 l 458.953 566.342 l 455.619 572.497 l 478.7 580.703 m 478.7 573.266 l 470.494 565.059 l 472.289 570.958 l 470.494 565.059 m 476.392 567.367 l 458.953 566.342 m 452.029 568.393 l S Q 0 G 0 J 0 j 1.206 w 10 M []0 d 185 700.2 m 444.69 700.2 l S BT /TT5 1 Tf 18 0 0 18 185 702 Tm 0 g (CHAPTER 14 -- CAPACITORS)Tj ET 144 656.2 m 485.042 656.2 l S BT 18 0 0 18 144 658 Tm (QUESTION & PROBLEM SOLUTIONS)Tj /TT6 1 Tf 12 0 0 12 90 593 Tm (14.1\))Tj /TT5 1 Tf 2.4167 0 TD ( You have a power supply whose low voltage)Tj -2.4167 -1.25 TD ("ground" terminal is attached to a resistor whose)Tj 0 -1.4167 TD (resistance is )Tj /TT7 1 Tf 6.0181 0 TD (R = 10)Tj 10 0 0 10 198.3984 566 Tm (4)Tj 12 0 0 12 204 561 Tm ( ohms)Tj /TT5 1 Tf 2.75 0 TD (. 93YV`@OQ9Y#aAiDk/QC#Bm9/4lLib4(MC5FgpXrVEJ;^464%,O8Z>s5U!HuKb0'kVDM<>j, )Tj -25.1291 -1.6 TD 0.0004 Tw (--Meanwhile, the capacitors initially act like open circuits \(with no charge on)Tj -2.7 -1.2 TD 0.0026 Tc 0.0264 Tw (them, there is nothing to motivate them to do otherwise\), which means the initial)Tj T* 0 Tc 0 Tw (current )Tj /TT7 1 Tf 3.7202 0 TD (will)Tj /TT5 1 Tf 1.7798 0 TD ( flow freely through them and )Tj /TT7 1 Tf 14.1 0 TD (i)Tj 9 0 0 9 316.3301 605 Tm (1)Tj 10 0 0 10 321.3354 610 Tm ( = i)Tj 9 0 0 9 336 605 Tm (2)Tj /TT5 1 Tf 10 0 0 10 341.0054 610 Tm (. 3U-3U^ee\YH-ho\.`*lgM2b1pZNmZD6KKR&:f endstream endobj 108 0 obj 580 endobj 109 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Width 76 /Height 99 /ColorSpace 123 0 R /BitsPerComponent 8 /Length 110 0 R >> stream )Tj 0 -1.2 TD 0.0143 Tc 0.1428 Tw (That means the voltage across the power supply will initially)Tj T* 0.0082 Tc 0.0821 Tw [(equal the voltage across the resistor. Unless you change the physical characteristics of the system, this)]TJ 0 -1.2 TD 0 Tc 0 Tw (will be a constant for a given capacitor. )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 [(. nH&3qrd*][%nAFDr\E6EZPsi=IiEf^qnC@9%8M]6n!+F`UDSQ20.0d4?V7m5-/,Nd )M_o$=qU:h&-fOG+ KVB-Y$:7T>^3J8X=iD:qWQ:jAKrSOcEhGp;.=*t)H7Ftb1"/3'OqV[!gq>fD^\@a% 0g[cd%8Z! Here the total capacitance is easier to find than in the series case. ot+b,ng;!KLij?.4C1!.14\Ch\->D5,9X1sp;nSieoSqq83@R3X%@N+Q,2`Q%:Vg_ )Tj ET 135 546 m 173.706 546 l S BT 10 0 0 10 135 547 Tm 0.0061 Tc 0.0682 Tw [(Solution)-23.3(: Again, capacitor combinations are the reverse of resistor combinations. 'Ubf3D6\uA3r0E%k1!/'7CA!-+D)3X`j$hso9Q@p`lVCDO!S6Xeu[b(B*T>B_#o8IrlL5kkT2L?g6ZeP3DeDhF/qG/T\\AI)8Ln;m`#b%!Vq> That is non-zero here, so the)]TJ T* 0.0145 Tc 0.1449 Tw [(single plate does have capacitance. !<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 f?/5VNtP:+b!&h*;ks;cUSET=R$5eFk!ek[M#4Ka.OdoJ11tj!q4l$cWY2 )Tj 1.8 -1.2 TD 0.004 Tc 0.04 Tw (As you know, the equivalent capacitance of a series combination of capacitors)Tj -1.8 -1.2 TD 0.0012 Tc 0.0122 Tw (is always )Tj /TT7 1 Tf 4.575 0 TD 0.0046 Tc 0 Tw (smaller)Tj /TT5 1 Tf 3.525 0 TD 0.0021 Tc 0.0208 Tw [( than the smallest capacitor in the combination. )Tj /TT6 1 Tf 12 0 0 12 94 617 Tm (b.\))Tj /TT5 1 Tf 1.3333 0 TD ( A long time after the switch is thrown \(i.e., by the time the caps are)Tj -3.1667 -1.25 TD (charged up fully\), how much charge is there on each plate? [$g;S67ShG^>"atp2DR2uFVQW;]]>/W&`P'B]k(2o*eidGf4Hm3Hc>;B7qb*fP5f#e^i N@.CuEa-:=^?Q=D%ZDbVNm_rXnU^BXH+3,XPiLi*_e3G&)Uj0=-`q's*^>.Xr&jr, ;qG_t26H-:#WmeF>1U,uD;!A^\$aSAFN-3e-9s]%^LXj"\FGF"K@A?hP+lg]47e/1.JB,ij1f_+?_)28c?QY?ph$)%^tce];@P2nbGD3qM0,D'"BF[p@\`"ZWgfDcp+Qr0I6ePa$MDJG\aRXUMi-i?UdJTS>ifSP=qWmP.s2AH<8*"?>l9hi#N H;Vm'PAY>P(r[ocN0M_GVKn7(O$F1e#o@8O>2eY$3oKo+1! "U.-sVN4/pVpCR-h.IP\NScB5HC?4I/ This statement is)]TJ T* 0 Tc 0 Tw (true. When the capacitor is)]TJ -27.3098 -1.6 TD 0.0119 Tc 0.1185 Tw (fully charged, the voltage across the capacitor will equal the voltage across the)Tj 0 -1.5 TD 0 Tc 0 Tw (power supply, and we can write )Tj /TT7 1 Tf 14.9 0 TD (q = \(10)Tj 9 0 0 9 315.6308 434 Tm (-6)Tj 10 0 0 10 323.6333 429 Tm ( f\)\(100 volts\) = 10)Tj 9 0 0 9 403 434 Tm (-4)Tj 10 0 0 10 411.0024 429 Tm ( coulombs)Tj /TT5 1 Tf 4.5998 0 TD (. ^j49NRQr7Jrs]!%ng P"j1iDFV5&dT$10;c>bl6(s)4ohNc4lF4Y06Xa=s%PM:9@CPhAW[k6pWTrPC?+RYA )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 (. q!77sO_jL<0@th()@CCIM6*?CY+U4eW':i$$a#0*0MTP'Jrqn#kg;*;(OG5o`lH/Q (I]RYoOQKCNg%IJ/(!U\P`7p$"\`_pWrStr0#?k]rR ipe=&?nV:=&L(NH$.UN6Q$mS`?`n\L0m.hQn8>j/K6PpD@V ;_`ADJ>RJBA+dZ&]q$JX)^Q@aU)-?5Y2CBMT3XK>uu (,(T0XO=`?XS>1C;Nj7TL)_Eca_c'ib$D;U*g+4(BB00* )Tj -15.6005 -2.8 TD [(Left inner loop:)-3707.7(V)]TJ 9 0 0 9 259.2217 122 Tm (o)Tj 10 0 0 10 264 127 Tm ( - q/C)Tj 9 0 0 9 297 122 Tm (eq)Tj 10 0 0 10 307 127 Tm ( - i)Tj 9 0 0 9 327.3711 122 Tm (1)Tj 10 0 0 10 332.3765 127 Tm (R)Tj 9 0 0 9 339.5981 122 Tm (20)Tj 10 0 0 10 349.6089 127 Tm ( = 0)Tj /F4 1 Tf 12 0 0 12 217.4687 108 Tm (\015)Tj /TT5 1 Tf 10 0 0 10 230 108 Tm ( 120 - q/\(4x10)Tj 9 0 0 9 303.1885 113 Tm (-6)Tj 10 0 0 10 311.1909 108 Tm (\) - 20i)Tj 9 0 0 9 340.4585 103 Tm (1)Tj 10 0 0 10 345.4639 108 Tm ( = 0. Unless you change the physical characteristics of the system, this)]TJ 0 -1.2 TD 0 Tc 0 Tw (will be a constant for a given capacitor. $EMXaN7o3Z_IOgT>/47BFi#>gUDcgm7*.0F's@F]JT[O;LpZ:q:j:p87mPFZd1H-m :OiDO#/8Oas4(@L endstream endobj 96 0 obj 899 endobj 97 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Width 76 /Height 99 /ColorSpace 123 0 R /BitsPerComponent 8 /Length 98 0 R >> stream Where does the energy go? 9QETgi/7\fgW,rFa7u/%'`T'N2kK8`^Y6M2(AGcVL\&e5"nE42/kRmh`Z-4A:7W4u6@]n1,&oV*EV>U:CG3gTF7eAG-%D%C(]$,F*CJ2Zp[( C0pY6XId0\o@Ymaf=M%YcKq"Jcj.aSI1:iLI,C4Sd)&uZD:-B!AK7nu$! 0=$%5AK5k[a!'U*? )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 NFF+b(N5;pZTsgs]L[,cT#$Sum52l*Z\RJCP4$s9n:8Qsj4;b]GV=F.D!s"F8MBJM od,YH597D)! `*)%3GSENp[8Mr1/`7T;NHchRKBIJr$H!K&3=o7#VALD5`3RTP kT! LbtjkO&NM9jhC>J35KUi(5efp*?oH]c6[M&3eUc\;%02/7/s.FA#\\aX!<5D(nd99 =0;AOCK;CNJQN/).&H*GOk-,SAnT"]]&23Jc..btr?8j$1,m-\AOHrk2S/Tp']l`l P$nqiS1(9Vim8+_ckA'"[Ih+OEqU)_V)epG>M_gc,^M*Y,Y-Q&g!=j1]!C; 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. Sg.WsZF'4^*Gh.W! )Tj ET 117 225 m 155.706 225 l S BT 10 0 0 10 117 226 Tm [(Solution)-29.4(: Knowing the charge on the 6 )]TJ /F4 1 Tf 12 0 0 12 301.625 226 Tm ()Tj /TT5 1 Tf 10 0 0 10 310 226 Tm (f cap, we can use )Tj /TT7 1 Tf 8.0366 0 TD (C = Q)Tj /TT5 1 Tf 2.6634 0 TD (/)Tj /TT7 1 Tf 0.3 0 TD (V)Tj /TT5 1 Tf 0.7041 0 TD ( to determine the)Tj -31.0041 -1.4 TD (voltage across the cap:)Tj 13.5 -2.4 TD (V)Tj 9 0 0 9 259.2217 183 Tm (6)Tj 10 0 0 10 264.2271 188 Tm ( = Q/C)Tj 9 0 0 9 293.6216 183 Tm (6)Tj 10 0 0 10 216 169 Tm [( )-3044.3( = \(4.8 x10)]TJ 9 0 0 9 311.2334 174 Tm (-4)Tj 10 0 0 10 319.2358 169 Tm ( C\)/\(6 x10)Tj 9 0 0 9 363.5083 174 Tm (-6)Tj 10 0 0 10 371.5107 169 Tm ( f\))Tj -11.9511 -1.2 TD ( = 80 volts. . IOBP.VYU/:-dDX%S%_>>7^2>YP4n,S!0.fK^56IRUEEN-Q,(%%@:#[$+%*`.^55X< `6;3+FU60%(N?p@:adK@=\/sQ.a^a``H0sO=lfI.5"Q\l$pkrb)FBZV+_KAE@`sCL )Tj ET endstream endobj 19 0 obj << /Type /Page /Parent 127 0 R /Resources 20 0 R /Contents 21 0 R /Thumb 95 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 20 0 obj << /ProcSet [ /PDF /Text ] /Font << /F2 134 0 R /F3 60 0 R /F4 59 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R /GS2 22 0 R >> /ColorSpace << /Cs6 138 0 R >> >> endobj 21 0 obj << /Length 12622 >> stream -*dFY&s9bH'r(I:qsi9$0iun)C0(iIeAH$'IAepo'_O_SOdg^lI,jVgI.=$c,=/), )Tj ET 135 136 m 173.706 136 l S BT 10 0 0 10 135 137 Tm 0.1228 Tw [(Solution)-29.4(:)-11.2( )]TJ 4.9903 0 TD 0.0112 Tc 0.1116 Tw (This question is just down right)Tj -4.9903 -1.3 TD 0 Tc 0 Tw (tricky. )Tj /TT6 1 Tf 12 0 0 12 94 288 Tm (b.\) )Tj /TT5 1 Tf 1.6021 0 TD ( How will the charge redistribute itself? 8;Z\7$'N1[#h/fKK3/@*P Is)]TJ /TT7 1 Tf -34.1667 -1.5 TD 0 Tc 0 Tw (i)Tj 10 0 0 10 76 509 Tm (2)Tj /TT5 1 Tf 12 0 0 12 82 514 Tm (/)Tj /TT7 1 Tf 0.2778 0 TD (i)Tj 10 0 0 10 89 509 Tm (1)Tj /TT5 1 Tf 12 0 0 12 95 514 Tm ( going to give you the same ratio as )Tj /TT7 1 Tf 16.5833 0 TD (i)Tj 10 0 0 10 298 509 Tm (8)Tj /TT5 1 Tf 12 0 0 12 304 514 Tm (/)Tj /TT7 1 Tf 0.2778 0 TD (i)Tj 10 0 0 10 311 509 Tm (4)Tj /TT5 1 Tf 12 0 0 12 317 514 Tm (? )Tj -38 -1.6 TD (In short, the voltage across the capacitor won't change at all. BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. >X$l6j@<=[9-3F'EnWh^cqZjjFWJM=ZX_7)4ss!VpF+ScflU+'ZJI!`CR*=?MUX5n )Tj /TT6 1 Tf 12 0 0 12 72 369 Tm (14.22\))Tj /TT5 1 Tf 3 0 TD ( What is the measure of a capacitor's net resistive nature? <8G"%UmSbE1$eO2$TB*V4l^c *@@UoAR%Vu+7('6pQ#!OZRM(DdP]DG0=U>9k )Tj ET 139 536 m 177.706 536 l S BT 10 0 0 10 139 537 Tm -0.0004 Tc [(Solution)-29.8(: If the voltage doubles, the charge on one plate will double and the)]TJ 0 -1.3 TD 0 Tc (ratio will stay the same. )Tj /TT6 1 Tf 12 0 0 12 72 369 Tm (14.22\))Tj /TT5 1 Tf 3 0 TD ( What is the measure of a capacitor's net resistive nature? If the first cap gets)]TJ /TT7 1 Tf -16.2 -1.2 TD 0 Tc 0 Tw (Q's)Tj /TT5 1 Tf 1.5 0 TD 0.0059 Tc 0.0592 Tw [( worth of charge, the second cap will get )]TJ /TT7 1 Tf 19.5203 0 TD 0.0286 Tc 0 Tw (2Q's)Tj /TT5 1 Tf 2.1797 0 TD 0.0066 Tc 0.0661 Tw [( worth of charge. )=bailTbC4")(H#8Gt`;8f]q*B6D1VKg'.``F*b*K?C75jms9`SNQf')jdh@*CktN nXTSOb$-k2?Wp\TgTdh@;SB*.Nqs2Dq81kLq;VRFMa).VdFr>"\__#@Rl,K'C.7:_ XQaXPPD1JGQpC=,"0XD>709FK2r$%+Lp+'`%]3jKQhHu!p[rZ@ .cBkX\R$sNb+UgFU,(./N/D4+RQ]K/eHX,YNP^]p]5iK)&M`(+5$N*>oR+nt[\-8b )Tj ET 0 G 0 J 0 j 0.67 w 10 M []0 d 121 679 m 159.706 679 l S BT 10 0 0 10 121 680 Tm 0.0013 Tc 0.0141 Tw [(Solution)-28.1(: From above, we've decided that the plate voltage stays the same but the)]TJ /TT7 1 Tf 0 -1.3 TD 0.007 Tc 0.0705 Tw (charge on each plate)Tj /TT5 1 Tf 9.7 0 TD 0.0712 Tw [( increases. )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. ( That is non-zero here, so the)]TJ T* 0.0145 Tc 0.1449 Tw [(single plate does have capacitance. +;,uV"@3SN2>P.XPLK]2ddUQ!e$ClZtOT:0IriYHM-A0)VjGG4/)I/s&b5Qh+%I'J1g46HN:Y ^$,i$^_KqQR`dsh=k0tqHL?dHc!RZ@Me8b$'RB'#[H;4$bqY);tW[uL/o$kk$t^V"$2.-60><9WRL )Tj ET 139 536 m 177.706 536 l S BT 10 0 0 10 139 537 Tm -0.0004 Tc [(Solution)-29.8(: If the voltage doubles, the charge on one plate will double and the)]TJ 0 -1.3 TD 0 Tc (ratio will stay the same. 8;Z\7$[0EA#ikn#j>uVI'#KP/H.fbdYO&B*&r-`D"Ejas)k#C>oCdD.C?L! That will be the pure, parallel capacitor)Tj T* (combination in the sketch. . A%uDaAUD%;`.$63g[3#BM(52WZ8b]nCc@@n.H*QLSaA!m;ZRg8O7BN:D;r4gpcUgU`+LI3 ]hG/>@8.g )]TJ /TT5 1 Tf 3.0429 0 TD 0.0139 Tc 0.1387 Tw [( \) increases its)]TJ -31.4 -1.6 TD 0.004 Tc 0.0402 Tw (equivalent resistance when a resistor is added, a )Tj /TT7 1 Tf 23.3 0 TD 0.0038 Tc 0 Tw (parallel)Tj /TT5 1 Tf 3.6398 0 TD 0.0023 Tc 0.023 Tw [( capacitance combination)]TJ -26.9398 -1.2 TD 0.0009 Tc 0 Tw (\(i.e., )Tj /TT7 1 Tf 2.3 0 TD 0 Tc (C)Tj 9 0 0 9 165.2727 501 Tm 0.0038 Tc (equ)Tj 10 0 0 10 179.8722 506 Tm 0.0006 Tc 0.0055 Tw [( = C)]TJ 9 0 0 9 198.8441 501 Tm 0 Tc 0 Tw (1)Tj 10 0 0 10 203.8495 506 Tm 0.0006 Tc 0.0055 Tw [( + C)]TJ 9 0 0 9 222.8214 501 Tm 0 Tc 0 Tw (2)Tj 10 0 0 10 227.8268 506 Tm 0.0007 Tc 0.003 Tw ( + . Some capacitors are only marked 01 or 001 mostly in these cases the values are given in uf. )S)flo)*mK%[DH&7SU9A/[J,`LkW.2R+5]8im:EL1,_&`J)[5:GA%gGjIQquO,;muf^*c/kX@8)!3Nc, )Tj -19.6127 -2.7 TD (Each capacitor will hold 4.8x10)Tj 9 0 0 9 261.2871 274 Tm (-4)Tj 10 0 0 10 269.2896 269 Tm ( coulombs per plate when fully charged. j`%'/+fTa&m+eC2h1ROF16bH24S? XQaXPPD1JGQpC=,"0XD>709FK2r$%+Lp+'`%]3jKQhHu!p[rZ@ 9fV(G2d`U#1Q::sq9YXCi>I@XR>VZiq^\KP?AKT[FI>@@i !rU1l7.h#d.IAh"h#W#FuLtG&j/K In other words, you will end up with what)]TJ T* 0 Tc 0 Tw (looks like two equal sized capacitors in series with one another. *G)"jqYC4teTQ&/RD,q"gHZeFm)$+]abd batterys voltage. qa#*TGV@.o$_l"CiOlID5+aK['*\db]#_.3@1#._0%Cg:`qcS?qHRh "pfU&)X5LQpmp/G?Ancs]sRf6>^k]8>lNmbMhB[^A@^O00J'q?h)b/aNTXX) (="RnVm"q\pnT;4RA,[>Y_ML+92[$!1sRSX8~> endstream endobj 69 0 obj << /Type /FontDescriptor /Ascent 985 /CapHeight 0 /Descent -216 /Flags 70 /FontBBox [ -156 -215 1048 969 ] /FontName /JAEEPE+CenturySchoolbook-Italic /ItalicAngle -15 /StemV 0 /FontFile2 70 0 R >> endobj 70 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 6625 /Length1 7772 >> stream )Tj /TT6 1 Tf 12 0 0 12 99 614 Tm (c.\))Tj /TT5 1 Tf 1.25 0 TD ( What happens to the charge on the capacitor's plates? )Tj /TT6 1 Tf 12 0 0 12 94 360 Tm (b.\))Tj /TT5 1 Tf 1.3333 0 TD ( How will the )Tj /TT7 1 Tf 6.7227 0 TD (charge)Tj /TT5 1 Tf 3.0273 0 TD ( on the capacitor )Tj /TT7 1 Tf 7.9443 0 TD (change)Tj /TT5 1 Tf 3.2223 0 TD (? fQIQ(+cLu\+ieP-CTY5&LUO2,_R[ubbQ!2^! 3U-3U^ee\YH-ho\.`*lgM2b1pZNmZD6KKR&:f endstream endobj 108 0 obj 580 endobj 109 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Width 76 /Height 99 /ColorSpace 123 0 R /BitsPerComponent 8 /Length 110 0 R >> stream In fact, each)Tj -18.2 -1.2 TD 0.0176 Tc 0.1764 Tw (plate is now )Tj /TT7 1 Tf 6.6 0 TD 0 Tc 0 Tw (d)Tj /TT5 1 Tf 0.6108 0 TD (/)Tj /TT7 1 Tf 0.2892 0 TD (4)Tj /TT5 1 Tf 0.6047 0 TD 0.015 Tc 0.1504 Tw [( units apart. )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. )Tj /TT6 1 Tf 12 0 0 12 94 113 Tm (b.\) )Tj /TT5 1 Tf 1.6021 0 TD ( What is the initial current in the circuit? aV1:qroqbBCs/,UF'!3K#C.=Sn8tP>UTUa%?T?HN!%=J5hF"3WG9m#%$]f"1N.J'2 )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. . Once)Tj -15.2373 -1.25 TD (charged to its maximum possible )Tj /TT7 1 Tf 15.5 0 TD (Q)Tj /TT5 1 Tf 0.7778 0 TD (, the capacitor's plates are separated by a)Tj -16.2778 -1.25 TD (factor of four \(that is, the distance between the plates is quadrupled\) while the)Tj T* (capacitor is)Tj /TT7 1 Tf 5.2778 0 TD ( kept hooked to the power supply)Tj /TT5 1 Tf 14.8888 0 TD (. 0F(QKUGnTl[^"4;NAd)#R*_h$G2e? 5j0$7*u$)tcJcSjU@=Y\ADDpDjtZS%G:!?K.0%i#. )]TJ -33.3187 -1.2 TD 0.0124 Tc 0.1241 Tw [(Note that this is just what you would expect. 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 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 (. )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. cM8I#%Z0dcqeVn>P-a1.heb`E->f[bBpXpE1kG9dZiX4/6Wl@^^F94N,U?3cKIWjQ ;.pEmc'G3pu36ahPD+$7//l>CO(Eg[\NChfW4DFT*r^BJh]-sbeaF=qM7 )Tj ET 112 497 m 150.706 497 l S BT 10 0 0 10 112 498 Tm 0.0034 Tc 0.0382 Tw [(Solution)-26(: Current in a charging circuit follows an exponential function. "(&f/V)!2'Lo^e8>KeE\jXqt#o.-l#INZajEIjS(Zl )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 /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? :563CaV7N8XE&mk=KQ#:c&"@?RBsH=YdU5r(^dAuQ=C1>qtm;IS_g5gEA;C@gae*e@JlX`5r>,LCJV`L\>VTJ]6pGW;cZ*:]@L)0&;EtT That means the)]TJ -2.7 -1.2 TD 0 Tc 0 Tw (capacitors initially have no voltage drop across them. If the capacitance is halved, the time constant will halve and the)]TJ 0 -1.2 TD 0.0032 Tc 0.0316 Tw (capacitor will take )Tj /TT7 1 Tf 9 0 TD 0.0049 Tc 0.0489 Tw (less time)Tj /TT5 1 Tf 4.0534 0 TD 0.0033 Tc 0.0332 Tw [( to charge to 63%. "frO*EW7kK*bp_a_\q :^c!5\ks!&_d9\S2577cN~> endstream endobj 148 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 24650 /Length1 26380 >> stream ]`.P>GHf! g7aB=*!+)*GEq8b`h;-07*dS,^0+tIrKO' )Tj ET 117 630 m 155.706 630 l S BT 10 0 0 10 117 631 Tm 0.0032 Tc 0.0361 Tw [(Solution)-26.2(: A decrease in frequency means less signal will pass through the circuit)]TJ 0 -1.3 TD 0.015 Tc 0.1503 Tw (\(remember, capacitors are )Tj /TT7 1 Tf 13.1925 0 TD 0.0158 Tc 0.158 Tw (high pass)Tj /TT5 1 Tf 4.706 0 TD 0.0114 Tc 0.1143 Tw [( filters\). h^[!@? )Tj T* 0.0022 Tc 0.022 Tw (When the capacitors are fully charged, the current through the circuit will be )Tj /TT7 1 Tf 36.4 0 TD 0 Tc 0 Tw (i)Tj 9 0 0 9 502.3981 405 Tm (1)Tj 10 0 0 10 507.5064 410 Tm 0.0181 Tc ( =)Tj -37.2506 -1.6 TD 0 Tc (i)Tj 9 0 0 9 138.4241 389 Tm (3)Tj 10 0 0 10 143.5704 394 Tm 0.0037 Tc 0.0365 Tw [( = 2.4 amps)]TJ /TT5 1 Tf 5.4612 0 TD 0.0045 Tc 0.0445 Tw [(, as calculated above. Once)]TJ T* 0.0011 Tc 0.0109 Tw (discharged, the switch flips back to charging mode and the capacitor recharges \(this is)Tj T* 0.0064 Tc 0.0641 Tw (why it usually takes a few seconds before you can take)Tj T* 0 Tc 0 Tw (the next flash picture\). !c^IH)aqJ*-nSh`<07[Gn7\!m()3Ibd/#67@mHkH-q]C4KqX^D4a1Ba['o_Pm[X;A 14 \(Capacitors\))Tj 12 0 0 12 502 39 Tm (893)Tj ET q 1 i 466 623 108 108 re W n q 1.0007 0 0 0.9993 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.029 w 3.864 M []0 d 524.597 659.111 m 524.597 638.015 l 519.966 652.937 m 519.966 644.704 l 519.451 649.335 m 466.453 649.335 l 466.453 649.335 m 466.453 698.345 l 573.093 698.989 m 573.093 649.849 l 572.964 649.335 m 524.983 649.335 l 466.196 698.345 m 474.943 698.345 l 477.387 705.292 l 481.89 691.528 l 486.778 705.42 l 491.409 691.399 l 496.04 705.292 l 500.67 691.528 l 505.559 705.42 l 510.447 691.399 l 513.148 698.603 l 519.194 698.603 l 518.422 698.86 m 541.191 698.86 l 548.137 698.86 m 573.093 698.86 l 540.805 709.794 m 540.805 688.698 l 547.88 709.794 m 547.88 688.698 l S Q Q BT /F2 1 Tf 10.298 0 0 10.2839 487.3683 720.6207 Tm /Cs6 cs 0 0 0 scn (V)Tj 8.2384 0 0 8.2271 492.9034 717.407 Tm (R)Tj 6.425 0.0874 TD (c)Tj 10.298 0 0 10.2839 539.8879 719.8494 Tm (V)Tj -2.5 -8.6875 TD (V)Tj 8.2384 0 0 8.2271 519.8069 627.0373 Tm (o)Tj ET q 1.0007 0 0 0.9993 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 0.257 w 3.864 M []0 d 1 i 471.37 705.176 m 474.663 707.851 475.589 714.128 481.352 714.128 c 484.233 714.128 485.673 712.07 488.863 712.07 c 491.024 712.07 492.362 713.408 493.185 714.437 c 515.257 705.176 m 511.964 707.851 511.038 714.128 505.276 714.128 c 502.395 714.128 500.954 712.07 497.764 712.07 c 495.603 712.07 494.266 713.408 493.442 714.437 c 522.439 707.491 m 525.732 710.166 526.658 716.443 532.42 716.443 c 535.302 716.443 536.742 714.385 539.932 714.385 c 542.093 714.385 543.431 715.723 544.254 716.752 c 566.326 707.491 m 563.033 710.166 562.107 716.443 556.345 716.443 c 553.464 716.443 552.023 714.385 548.833 714.385 c 546.672 714.385 545.334 715.723 544.511 716.752 c S Q 0 G 0 J 0 j 0.67 w 10 M []0 d 1 i 135 709 m 173.706 709 l S BT /TT5 1 Tf 10 0 0 10 135 710 Tm 0 g 0.0021 Tc 0.0239 Tw [(Solution)-27.3(: Notice that at any point in time, the voltage across the)]TJ 0 -1.3 TD 0.0064 Tc 0.0638 Tw (battery must equal the voltage )Tj /TT7 1 Tf 15.0028 0 TD 0 Tc 0 Tw (V)Tj 9 0 0 9 292.3195 692 Tm (c)Tj /TT5 1 Tf 10 0 0 10 296 697 Tm 0.007 Tc 0.0704 Tw [( across the capacitor added to)]TJ -16.1 -1.6 TD 0.0044 Tc 0.0438 Tw (the voltage )Tj /TT7 1 Tf 5.5305 0 TD 0 Tc 0 Tw (V)Tj 9 0 0 9 198 676 Tm (R)Tj /TT5 1 Tf 10 0 0 10 205 681 Tm 0.0048 Tc 0.048 Tw [( across the resistor. )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? )=bailTbC4")(H#8Gt`;8f]q*B6D1VKg'.``F*b*K?C75jms9`SNQf')jdh@*CktN rh[6^L4M&,9nUG9dhIY(X&2SS2KHn+n9V7X>/TaBq>Dk`c?T(G*j9gA*c+WIi(f^9 s)m`^"Fr+X[.0ko2ne@`-W3'F4ierY[$:qW+g:ATRf@E-oZhYQ5=#HX] 8;Z\7!Kr'h#i,H0ORLt)_m8K?U.IkgESG30D&,ZMTk5r! 9"ag[%BfDZ62RJo&EF%0#k9/;rXMK92lX$W=ZT*epA$[5=r9?;6"9crH!2*. ()?,Q B3)_KMT? )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. P)ZbDL[-A-W!EtTTgHb\cqYUTN`530\Ad)E*5NZ8%cKC-).UN+&ego?9KV(U*2/EIKCg9r()[MK J*`_#5[U9f""#_Ql%k7)UI#f;Z47c_g8_M]oiAC-5dP^fQ@s>JN/+hfoIW"g'K8!n !rU1l7.h#d.IAh"h#W#FuLtG&j/K *J_VfiBYhO!oW38RE 14 \(Capacitors\))Tj 12 0 0 12 502 39 Tm (901)Tj /TT6 1 Tf -32.5 55.75 TD (d.\))Tj /TT5 1 Tf 1.334 0 TD ( How much energy does the 6 )Tj /F4 1 Tf 14.2181 0 TD ()Tj /TT5 1 Tf 0.6979 0 TD (f capacitor hold when completely)Tj -18.0833 -1.3333 TD (charged? Multiple connections of capacitors act like a single equivalent capacitor. )Tj ET 121 600 m 159.706 600 l S BT 10 0 0 10 121 601 Tm 0.1495 Tw [(Solution)-29.4(:)-13.6( A)-13.6(s)-13.6( )]TJ 6.2584 0 TD 0.0136 Tc 0.1359 Tw (was pointed out in )Tj /TT7 1 Tf 9.5994 0 TD 0.0235 Tc 0.2346 Tw (Part 11a)Tj /TT5 1 Tf 4.4241 0 TD 0.0164 Tc 0.1642 Tw (, the charge on the plates)Tj -20.2818 -1.3 TD 0 Tc 0 Tw (increases. Where does that removed charge go? eH`Kc,:fP%S>QL2VmqX)_/Uou0?c5T0pe`bns#uu116NUd. *;8Y-))RU&-0[8b0;j>s@ca$o_ 14 \(Capacitors\))Tj 12 0 0 12 502 39 Tm (907)Tj 10 0 0 10 148 710 Tm [( )-566.5(Right inner loop: )-2744.8(-i)]TJ 9 0 0 9 276.4795 705 Tm (3)Tj 10 0 0 10 281.4849 710 Tm (R)Tj 9 0 0 9 288.7065 705 Tm (30)Tj 10 0 0 10 298.7173 710 Tm ( + q/C)Tj 9 0 0 9 331 705 Tm (eq)Tj 10 0 0 10 341 710 Tm ( = 0)Tj /F4 1 Tf 12 0 0 12 235.4687 691 Tm (\015)Tj /TT5 1 Tf 10 0 0 10 248 691 Tm ( -30i)Tj 9 0 0 9 291 686 Tm (3)Tj 10 0 0 10 296.0054 691 Tm ( + q/\(4x10)Tj 9 0 0 9 341.3472 696 Tm (-6)Tj 10 0 0 10 349.3496 691 Tm (\) = 0. (%Mu09P1LocIECBkTQTUT\uVHF-@5DaY2\`n2GT,O<6qBPn\Mbj8:1H,X#[(&aQ<9 m)8Y>K+o:m*]Coo657ll[(sI.jJ)_BaM9'3RX\lIJ&b\\Lf2=,! Calculate the effective capacitance in series and parallel given individual capacitances. 9VaDQrZ%u&riFK23^-B[aXQZB6W7"L.N^#O-QAnFiri%$]"uZT%krofqgh``"QtTp 'bALo/V[(JRQENl>,_5Gidc-L.XTa5U,H&II(i&I7)c&ItO/5U$Nc )Tj ET 135 98 m 173.706 98 l S BT 10 0 0 10 135 99 Tm 0.0015 Tc 0.0174 Tw [(Solution)-27.9(: The initial current through the circuit will be that of a resistor in series)]TJ 0 -1.3 TD 0 Tc 0 Tw (with a battery \(the uncharged caps will act like "shorts"\), or:)Tj ET endstream endobj 26 0 obj << /Type /Page /Parent 127 0 R /Resources 27 0 R /Contents 28 0 R /Thumb 99 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 27 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 28 0 obj << /Length 4754 >> stream b\'^n,b]n+*G;YtEa6Wd\IPHN2PrN9@j^N>7\)gggI=o4SiZ`R. )Tj ET 117 111 m 155.706 111 l S BT 10 0 0 10 117 112 Tm 0.26 Tw [(Solution)-29.4(:)-23.6( )]TJ 5.2771 0 TD 0.0236 Tc 0.2364 Tw (Knowing the dielectric constant allows us to determine the new)Tj -5.2771 -1.3 TD 0 Tc 0 Tw (capacitance knowing the old capacitance. The sum of the charge on BOTH plates is )Tj /TT7 1 Tf 27.6 0 TD (zero)Tj /TT5 1 Tf 1.8506 0 TD (. *7](L0dQP[k?HKJpt5>L7@+Fu[o&pZphujSSO+ZVn4K3rU`aB\:L[+! odAf(PrCa'`@P`C$*4-\R&1^#6MDs#duYn$Bc_Y:Y)dieJ8*eBg:Ggn[TU=F>m28L Nevertheless, if the)]TJ T* 0.0037 Tc 0.0371 Tw (capacitance goes down with the insertion of a conductor between the plates, we)Tj T* 0.0115 Tc 0.1155 Tw [(are done In short, what we need to determine before doing anything else is)]TJ T* 0 Tc 0 Tw (what a conductor will do to the capacitance when placed between the plates. Remembering that)]TJ T* 0.0065 Tc 0.0651 Tw (current ceases in capacitor circuits only when the voltage across the capacitor is)Tj T* 0.0011 Tc 0.0108 Tw (the same as the voltage across the power supply, this voltage difference creates an)Tj T* 0.0074 Tc 0.0739 Tw [(electric field in the wire that motivates current to flow. 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