ZPiQE\#5=B,*o_k.-_riM*bjC\KjUeb7@f#'Zq&':1.AQ"D(,+Xcs"sM"6C/(IWpi )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 0.0039 Tc 0.0444 Tw [(Solution)-25.5(: The "charge on a capacitor" is, in fact, the amount of charge on)]TJ /TT7 1 Tf 34.6 0 TD 0.005 Tc 0.0497 Tw [( one)]TJ -34.6 -1.3 TD 0 Tc 0 Tw (plate)Tj /TT5 1 Tf 2.3 0 TD ( of the capacitor. 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 (\(remember, )Tj /TT7 1 Tf 5.6108 0 TD (Q)Tj 9 0 0 9 154 167 Tm (1)Tj 10 0 0 10 159.0054 172 Tm ( = C)Tj 9 0 0 9 178 167 Tm (1)Tj 10 0 0 10 183.0054 172 Tm (V)Tj /TT5 1 Tf 0.7041 0 TD (\). . That is, what)Tj -3 -1.25 TD (is it called, what are its units, and how is it calculated? V3$mZ_`aKrqdJ:#QKP%3CB]21ruNIH7h:0]H:W&dhEp*#BYXgC^oWi35V!BM:&n9t )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 This)]TJ -35.0906 -1.3 TD 0 Tc 0 Tw (statement is false. )Tj /TT6 1 Tf 12 0 0 12 112 461 Tm (b.\))Tj /TT5 1 Tf 1.3333 0 TD ( What is common to all the capacitors in the parallel combination? We don't know by how much)]TJ 0 -1.2 TD 0.0041 Tc 0.041 Tw [(in this case because we don't know the dielectric constant. Be sure you are complete. *SiA;]l(iE["7;mXS]Rfdd329)5c,h,1dI\H 8;Z\7$]]op#itt$j>rd3AHjV9267LJ?S]'Ad-M? H[3]nEBXBs03bFsT6^=_3OsKO-B#Str3dTR*lCI(4^b@%@r . r/4*QI@iaoNr!lu7j%>doDu0.GVsH39eM#]/(Q?GUH]JJ&`5:f*2X$m6K]IE!F32. )Tj /TT7 1 Tf 2.4 0 TD -0.0011 Tc (C = q)Tj /TT5 1 Tf 2.4344 0 TD 0 Tc (/)Tj /TT7 1 Tf 0.2656 0 TD (V)Tj /TT5 1 Tf 0.7041 0 TD (, so )Tj /TT7 1 Tf 1.7959 0 TD (.5CV)Tj 9 0 0 9 237.6025 369 Tm (2)Tj 10 0 0 10 242.6079 364 Tm ( = .5\(q)Tj /TT5 1 Tf 2.8392 0 TD (/)Tj /TT7 1 Tf 0.3 0 TD (V\)V)Tj 9 0 0 9 291.4121 369 Tm (2)Tj 10 0 0 10 296.4175 364 Tm -0.0012 Tc ( = .5qV)Tj /TT5 1 Tf 3.2475 0 TD 0 Tc ( . )Tj /TT6 1 Tf 12 0 0 12 135 149 Tm (ii.\))Tj /TT5 1 Tf 1.4167 0 TD ( How much charge will be associated with the capacitor after a time)Tj 0.4167 -1.25 TD (equal to one time constant? 4H%"hLgp"'A?90Q;D],piH]s7F.Yj"(kVjHZ_-5%pcL'gpjCM1PlC\c03hsi+r-`2 That)]TJ -3.0833 -1.25 TD 0 Tc 0 Tw (is, what kind of relationship will exist between the capacitors after the throw? q;t?a!T]_7XfJsLELVHJm(2,cW&Q)BVk1@Veoj%?h'G3&YI(:96/I:D?+\PqAN,"b =dT3l2-m7;AjiF3Hm3L=f@P)g^c#LOCU&8FGc4)EYAbcb9Y\9o_]J&`[Pp84746I] \1!q"&qheG(;qM^;Aka*C'K95M&C8"YZ59h>&BU-KS"a`^H\6X@uI'2ZdORgc0h0o solve the problem. By definition, this will also be the same as the)Tj 0 -1.2 TD 0 Tc (charge on the equivalent capacitor. As)]TJ -27.1629 -1.2 TD 0 Tc 0 Tw (such, the steady-state current will be:)Tj 6.3 -2.4 TD (i)Tj 9 0 0 9 183.1494 352 Tm (1)Tj 10 0 0 10 188.1548 357 Tm ( = i)Tj 9 0 0 9 203 352 Tm (3)Tj 10 0 0 10 208.0054 357 Tm ( = \(120 v\)/\(50 )Tj /TT1 1 Tf 6.312 0 TD <009f>Tj /TT5 1 Tf 0.7681 0 TD (\) = 2.4 amps, and i)Tj 9 0 0 9 364.1528 352 Tm (2)Tj 10 0 0 10 369.1582 357 Tm ( = 0. A%uDaAUD%;`.$63g[3#BM(52WZ8b]nCc@@n.H*QLSaA!m;ZRg8O7BN:D;r4gpcUgU`+LI3 Zt!WMf1fIN\n,GJf1rHd"BtO4%>g?Nr%X21>.(<2$?R5lZeo%$#h. The equivalent If there is a lot of charge on the plates )]TJ /TT7 1 Tf 27.1975 0 TD 0.0034 Tc 0.0338 Tw (most of the time)Tj /TT5 1 Tf 7.4322 0 TD 0.0026 Tc 0.0263 Tw [( \(this is)]TJ -34.6297 -1.2 TD 0.0173 Tc 0.173 Tw (the case with low frequency\), the short-term voltage of the capacitor will be)Tj T* 0.0045 Tc 0.0447 Tw [(relatively high. )3Gjo~> endstream endobj 84 0 obj 740 endobj 85 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Width 76 /Height 99 /ColorSpace 123 0 R /BitsPerComponent 8 /Length 86 0 R >> stream 8;Z\6>B8aX%)`#saPZ\am:fIj"k"! "jZKN"ln0q^-Ou`-hU\l9IFnK8M[<<172KJ`"_8H-X\3-QV]"[&K1h@rD^MgK\-)D[9;`jXQ9)@!8cJ8m[:6H :pu#T#A\,;br;i4#A)J3>4(,9g4ZB!3BuqG+=9ZCLNrIp;H-G7;Z8imABjA$*cdBPtoIEo`aq@kJZBm%)O/s/fg If)]TJ -36.5865 -1.3 TD 0.0002 Tc 0.0016 Tw (you sketch this on the non-existent graph from )Tj /TT7 1 Tf 21.928 0 TD 0 Tc 0 Tw (Part a)Tj /TT5 1 Tf 2.872 0 TD 0.0002 Tc 0.0017 Tw (, it would look like a straight)Tj -24.8 -1.2 TD 0 Tc 0 Tw (line positioned at 4.24 volts. XQaXPPD1JGQpC=,"0XD>709FK2r$%+Lp+'`%]3jKQhHu!p[rZ@ 5d"$T;Q[j%+FZt?Vk=qL/b:IAGcAofOhXlX/"i*Y#. TK<>faQVM7]l0P"]mBBCo6'MfRaO((99Ro%CJ"rp"O5q^@:r#F/^'Y=,M2&%-jA"& Eo2]qG!`+XcPF&oQ&.89VOn`8a-[1q;s$%*1c*D5B,SLrfsPXdrKt:=gh/$qiRfOl How long will it take for the two capacitors to dump 87% of)Tj T* (their charge across the 30 )Tj /TT1 1 Tf 12.2217 0 TD <009f>Tj /TT5 1 Tf 0.7681 0 TD ( resistor? Qa('L%rkOX+HIiCqqWlCBdlFr)8!-teA`H+b]jGJH.cV17U44.%ScD;Y,8Hke%%VN -,,8?j#?NYSkn>%diO7Qnl[TY>Ii'k,.kFmN.Q]tMT:7fOA+in1iTjh.eW(W7r2+[ >X$l6j@<=[9-3F'EnWh^cqZjjFWJM=ZX_7)4ss!VpF+ScflU+'ZJI!`CR*=?MUX5n 1F`+KKnA'^$InATM#tTe> )Tj ET 90 196 m 135.835 196 l S BT /TT8 1 Tf 10 0 0 10 90 197 Tm (Circuit b)Tj /TT5 1 Tf 4.6 0 TD ( finds two capacitors in parallel. cMc&!B>=%dhta(\XE6GOH:K/BP8m#Jg9d9=jes_'23jGgk*u1 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 (. )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. To solve such circuits, first reduce the Capacitor c2 = 4 f. 8;V^p$ZK(q)?.oAp[3ct^kQJE+Et@A#Y>:gj:P^LlirW'9mH(MV7V#X#ac%I'\$ha )3XGM63;>Og_V4[5D&+WFhc/N3CX?oj>`":mG]Q)I70!phB_AR-#T^34bM4+K22\1aL?Y 14 \(Capacitors\))Tj 12 0 0 12 502 39 Tm (899)Tj ET q 1 i 433 563 140 100 re W n q 0.9952 0 0 1.0048 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.026 w 3.864 M []0 d 493.812 594.722 m 493.812 573.689 l 489.195 588.566 m 489.195 580.358 l 488.682 584.975 m 435.843 584.975 l 435.843 584.975 m 435.843 633.839 l 542.163 634.48 m 542.163 585.488 l 542.035 584.975 m 494.197 584.975 l 435.586 633.839 m 444.307 633.839 l 446.744 640.764 l 451.233 627.041 l 456.106 640.893 l 460.723 626.913 l 465.341 640.764 l 469.958 627.041 l 474.831 640.893 l 479.705 626.913 l 482.398 634.095 l 488.426 634.095 l S Q Q BT /F2 1 Tf 10.2113 0 0 10.3093 456.9965 649.6312 Tm /Cs6 cs 0 0 0 scn (R)Tj 4.9875 0.2875 TD (C)Tj -3.6875 -8.2 TD (100 volts)Tj ET 1 1 1 scn 1 i 537.155 615.353 5.106 -12.113 re f q 0.9952 0 0 1.0048 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.026 w 3.864 M []0 d 542.035 600.109 m 547.422 612.421 l S Q BT 10.2113 0 0 10.3093 543.7922 596.7961 Tm 0 0 0 scn (switch)Tj ET q 0.9952 0 0 1.0048 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.026 w 3.864 M []0 d 537.387 608.537 m 544.568 608.537 548.057 606.793 550.724 601.869 c 550.724 601.869 m 548.704 607.034 l 550.724 601.869 m 546.139 604.213 l 537.387 608.537 m 543.574 610.369 l 537.387 608.537 m 542.035 605.239 l 487.656 634.352 m 510.357 634.352 l 517.283 634.352 m 542.163 634.352 l 509.972 645.253 m 509.972 624.22 l 517.026 645.253 m 517.026 624.22 l S Q BT /F3 1 Tf 9 0 0 9 325.1 345.5578 Tm (120 volts)Tj 8 4.3333 TD (20)Tj ET q 0.8395 0 0 1.1912 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 0.424 w 3.864 M []0 d 486.758 325.422 m 486.758 327.034 487.946 328.392 489.304 328.392 c 490.662 328.392 491.85 327.034 491.85 325.422 c 491.85 323.809 490.662 322.451 489.304 322.451 c 487.946 322.451 486.758 323.809 486.758 325.422 c s Q 1 1 1 scn 407.9 385.129 5.7 -3.033 re f q 0.8395 0 0 1.1912 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 0.424 w 3.864 M []0 d 492.699 323.3 m 491.001 323.3 l 487.607 323.3 m 485.909 323.3 l S Q BT 9 0 0 9 264.1 391.5578 Tm 0 0 0 scn (switch)Tj 0 -1 TD (closes)Tj T* (at t=0)Tj 6.4444 5 TD (6 f)Tj ET /Cs6 CS 0 0 0 SCN 0 J 0 j 0.5 w 3.864 M []0 d 328 417 m 328.7 417.3 329.6 417.3 330 418 c 330.3 418.6 330 419.3 330 420 c 330 420.7 330 422.7 330 422 c 330 421.3 329.7 420.6 330 420 c 330.2 419.6 330.5 419.1 331 419 c 331.3 418.9 331.7 418.9 332 419 c 332.5 419.1 332.8 419.6 333 420 c 333.5 420.9 333 423 y 333 421.9 333 421.1 333 420 c 333 419.7 333 419.3 333 419 c S BT 9 0 0 9 351.0999 418.5578 Tm (12 f)Tj ET 362 417 m 362.7 417.3 363.6 417.3 364 418 c 364.3 418.6 364 419.3 364 420 c 364 420.7 364 422.7 364 422 c 364 421.3 363.7 420.6 364 420 c 364.2 419.6 364.5 419.1 365 419 c 365.3 418.9 365.7 418.9 366 419 c 366.5 419.1 366.8 419.6 367 420 c 367.5 420.9 367 423 y 367 421.9 367 421.1 367 420 c 367 419.7 367 419.3 367 419 c S 1 w 388.9 362.5 m 388.9 377.4 l 388.9 394.8 m 388.9 407.5 l 300.9 363.1 m 343.4 363.1 l 346.4 363.1 m 388.8 363.1 l 300.9 406.5 m 330.2 406.5 l 359.6 406.5 m 388.8 406.5 l 332.4 406.5 m 357.3 406.5 l 300.8 393.8 m 300.8 406.7 l 300.8 384.7 m 295.7 393.8 l 295 388 m 295.4 388.6 295.8 389.4 296.4 389.9 c 297.3 390.6 298.2 391 299.4 391.2 c 300.2 391.3 300.8 391.2 301.6 391.2 c 301.6 391.2 m 298.6 391.8 l 301.6 391.2 m 299.4 390.6 l 357.5 401.2 m 357.5 411.6 l 359.7 401.2 m 359.7 411.6 l 332.5 401.3 m 332.5 411.6 l 330.3 401.3 m 330.3 411.6 l 389.2 377.3 m 391 378.4 l 387 381 l 391 383.5 l 387 386.1 l 391 388.6 l 387 391.2 l 391 393.8 l 389.2 394.9 l 343.7 355 m 343.7 370.5 l 345.9 365.4 m 345.9 360.2 l S BT 9 0 0 9 269.1 331.5578 Tm (\(a\))Tj 22.8889 0.0445 TD (\(b\))Tj ET 301 385 m 301 363 l 513.1 450.1 m S BT 9 0 0 9 506.0999 343.5578 Tm (120 volts)Tj 5.5556 4 TD (20)Tj ET q 0.8395 0 0 1.1912 0 0 cm 0.424 w 676.166 321.224 m 676.166 322.837 677.354 324.195 678.712 324.195 c 680.07 324.195 681.258 322.837 681.258 321.224 c 681.258 319.612 680.07 318.254 678.712 318.254 c 677.354 318.254 676.166 319.612 676.166 321.224 c s Q 1 1 1 scn 566.9 380.129 5.7 -3.033 re f q 254 307 319 147 re W n q 0.8395 0 0 1.1912 0 0 cm 0.424 w 682.107 319.103 m 680.409 319.103 l 677.015 319.103 m 675.317 319.103 l S Q Q BT 9 0 0 9 457.1 387.5578 Tm 0 0 0 scn (switch)Tj 0 -1 TD (closes)Tj T* (at t=0)Tj 6.3333 4.6667 TD (6 f)Tj ET 0.5 w 520 410 m 520.7 410.3 521.6 410.3 522 411 c 522.3 411.6 522 412.3 522 413 c 522 413.7 522 415.7 522 415 c 522 414.3 521.7 413.6 522 413 c 522.2 412.6 522.5 412.1 523 412 c 523.3 411.9 523.7 411.9 524 412 c 524.5 412.1 524.8 412.6 525 413 c 525.5 413.9 525 416 y 525 414.9 525 414.1 525 413 c 525 412.7 525 412.3 525 412 c S BT 9 0 0 9 511.0999 442.5578 Tm (12 f)Tj ET 522 441 m 522.7 441.3 523.6 441.3 524 442 c 524.3 442.6 524 443.3 524 444 c 524 444.7 524 446.7 524 446 c 524 445.3 523.7 444.6 524 444 c 524.2 443.6 524.5 443.1 525 443 c 525.3 442.9 525.7 442.9 526 443 c 526.5 443.1 526.8 443.6 527 444 c 527.5 444.9 527 447 y 527 445.9 527 445.1 527 444 c 527 443.7 527 443.3 527 443 c S 1 w 549.9 359.5 m 549.9 373.4 l 549.9 390.8 m 549.9 433 l 493.9 359.1 m 522.4 359.1 l 525.4 359.1 m 549.8 359.1 l 493.9 402.5 m 520.2 402.5 l 522.4 402.5 m 550.3 402.5 l 493.8 389.8 m 493.8 433 l 493.8 380.7 m 488.7 389.8 l 488 384 m 488.4 384.6 488.8 385.4 489.4 385.9 c 490.3 386.6 491.2 387 492.4 387.2 c 493.2 387.3 493.8 387.2 494.6 387.2 c 494.6 387.2 m 491.6 387.8 l 494.6 387.2 m 492.4 386.6 l 522.5 397.3 m 522.5 407.6 l 520.3 397.3 m 520.3 407.6 l 550.2 373.3 m 552 374.4 l 548 377 l 552 379.5 l 548 382.1 l 552 384.6 l 548 387.2 l 552 389.8 l 550.2 390.9 l 522.7 351 m 522.7 366.5 l 524.9 361.4 m 524.9 356.2 l 493.9 432.5 m 519.2 432.5 l 521.4 432.5 m 550.3 432.5 l 521.5 427.3 m 521.5 437.6 l 519.3 427.3 m 519.3 437.6 l 494 381 m 494 359 l S BT 10 0 0 10 389.5 314.4753 Tm (FIGURE I)Tj ET 2 w 441.6 311.5 m 385.5 311.5 l S BT /TT6 1 Tf 12 0 0 12 117 708 Tm 0 g (b.\))Tj /TT5 1 Tf 1.3333 0 TD ( What is the ratio of the two capacitances? )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. )(OrMU[j3R'GFVRca"Hq`H+U6LF'kLN>jWtd(f\\qq5HU`q5+JMN"cC 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. ";0C]W;(NTgP@-!N8#olBj(=?QA'1AKq4OHB2$7^g`.PP)YU.\Bs`\M'd;"0"(p2i f]KItk8(%`bt(4=;;l(p67Nl8hr&-l%,ko,i1ms%'='"Gq\K4=Dj5b.pDI=K2"SQ' BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. As such, the initial current i)Tj 9 0 0 9 390.2861 645 Tm (3)Tj 10 0 0 10 395.2915 650 Tm ( equals zero. @>"VHL@LTCD&9L ZA6X2e`mJKO7Krn8!rQ:%^:3QVu[>lGg==c',fc,ZVk'pc40N6q6K^V'uLf">iE[j )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. ,2YVn4U9eO1UC#4[!2k g?NL2'!YQo@^T$5,r`MX9MhI7h"5[A2lK,,5aEc1)^uEmQK2P5Z;KO#K"smNd4R^Q 4H%"hLgp"'A?90Q;D],piH]s7F.Yj"(kVjHZ_-5%pcL'gpjCM1PlC\c03hsi+r-`2 equivalent capacitances as shown in figure (c). &*'Ct'm'S^KEYgX_=-(0RV,j[/h8Mt3EC"!_cpWH/(P3keRdrN""t>rFrlk9M.#d3 'aIH:R6W ;.pEmc'G3pu36ahPD+$7//l>CO(Eg[\NChfW4DFT*r^BJh]-sbeaF=qM7 >X$l6j@<=[9-3F'EnWh^cqZjjFWJM=ZX_7)4ss!VpF+ScflU+'ZJI!`CR*=?MUX5n kVqW!qKIQIE*9K'K]j)g0WYmg&kug^Kcm%L[r? TrORG!ROXf=-6I=a497`>pN=(gP6!-f2*pPT=OPb !&`dLW/iol8e[F37BkS/;$*jE0IYA$@*rD5;IiTl!NFV6d5H>um`$rRA+sLmkPrl= )Tj ET 117 261 m 155.706 261 l S BT 10 0 0 10 117 262 Tm 0.0008 Tc 0.0185 Tw [(Solution)-28.6(: The )]TJ /TT7 1 Tf 6.8543 0 TD 0.0176 Tc 0 Tw (RMS)Tj /TT5 1 Tf 2.4049 0 TD 0.0031 Tc 0.0311 Tw [( value will be .707 of the amplitude, or )]TJ /TT7 1 Tf 18.4409 0 TD 0.0037 Tc 0.0368 Tw (.707\(6\) = 4.24 volts)Tj /TT5 1 Tf 8.8865 0 TD 0.0014 Tc 0.0139 Tw [(. &mC;eNf,sDZR.V2/L$JH! ?,WpH0`/%Ae_2KmiYOd@1@6=sE=jWUCc, Being in parallel, the net voltage drop across the capacitors and)]TJ T* 0 Tc 0 Tw (across the resistor must be the same. G"@XHUZ#>-%a-B?c/H(h9joF)*A3"&9<6GUBIgG:m9]0GD25Q,ql)KTKko0VX\!BX CKE1aI4lV6eema2M+#9-,ODTGRo `*)%3GSENp[8Mr1/`7T;NHchRKBIJr$H!K&3=o7#VALD5`3RTP The total charge [latex]{Q}[/latex] is the sum of the individual charges: Using the relationship [latex]{Q = CV}[/latex], we see that the total charge is [latex]{Q = C_{\text{p}}V}[/latex], and the individual charges are [latex]{Q_1 = C_1 V}[/latex],[latex]{Q_2 = C_2 V}[/latex], and [latex]{Q_3 = C_3 V}[/latex]. ;$Tg,U:EsZ%CR;%gODh8ShY1"We;G:fUmB#cX$=:(&mq*YstcA6R$N `V9N]!@^8h'M[#;.1Hu\KC(pYkR_-Mm6la? )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. HWG!O=u(-27O8tdJ]a0\Kh6F1B1uKU.SBEAI(J^h[eG7Kr-#r+BD(V2Zc;-39Rqc_[1]B8gXdm)jBWa)N:QI6;6Zjht )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? A#2l7?Y`AbAoDIN8s37\e7A,q361_eeL[+B8aa6g-@0"gfllZ6A>dGo2j'dYaNt*d Mylar capacitor 104j 100v products are most popular in india thailand and south korea. If you think about it, this is characteristic of a parallel)Tj 0 -1.2 TD 0.002 Tc 0.0203 Tw [(combination. 3TmbLf^=#+90F61pE5dDkHTTj70>$IpCX5"7e4=P]&2=:q\nI>@YAD,ZYuB^7L:Cj9qn*6_FDN^(40"LJ3,gF$ogAV2Y9icQ16;0A#)p At )Tj /TT7 1 Tf 15.3333 0 TD (t = 0)Tj /TT5 1 Tf 2.0698 0 TD (, you throw the switch)Tj -17.4032 -1.25 TD (and current begins to flow. )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. \(Note: You will never have to use this--it is)]TJ T* 0.0246 Tc 0.2464 Tw (something university courses sometimes like to throw in, just for the sake of)Tj T* 0 Tc 0 Tw (confusion.\))Tj /TT6 1 Tf 12 0 0 12 72 252 Tm (14.5\))Tj /TT5 1 Tf 2.4167 0 TD ( You have a series combination of capacitors. euEMnJm-NCH]h[O,@1%e4kR0;9CD4WSohrf`(V\N(_U%^T;. 8;V^p$ZK),(&lMYhn,A25W/q%O@=J^9-TI'_Fk0U,B\2t*e5M&]:1#2k!d,u&s4Ah QX^B endstream endobj 77 0 obj << /Type /Font /Subtype /CIDFontType2 /BaseFont /JACCJC+CenturySchoolbook /FontDescriptor 67 0 R /CIDSystemInfo << /Registry (Adobe)/Ordering (Identity)/Supplement 0 >> /DW 1000 /W [ 155 [ 548 ] 159 [ 768 ] ] >> endobj 78 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 301 >> stream *O9Z)md3`R)TFUe8%V By definition, this will also be the same as the)Tj 0 -1.2 TD 0 Tc (charge on the equivalent capacitor. ^tLc(s%X&DHElOB8d"-WY$^X4.>ROB(HZte As such, we can write:)Tj 6.3 -2.7 TD ( .37\(4.8 x10)Tj 9 0 0 9 268 283 Tm (-4)Tj 10 0 0 10 276.0024 278 Tm ( coul\) = 1.8 x10)Tj 9 0 0 9 346 283 Tm (-4)Tj 10 0 0 10 354.0024 278 Tm ( coulombs)Tj -21.9002 -2.4 TD (will be left. remember, the voltage across a resistor is )Tj /TT7 1 Tf 21.4453 0 TD (iR)Tj /TT5 1 Tf 1.0039 0 TD (\). Between the plates of a second cap, you insert a piece)Tj T* (of metal whose thickness is also half the plate separation. )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? YYE+aBZWQ-4J^)_&3*t/"eh3YX:8#2qib;(JqDLF5#bff(>=WErPM?R:tE+d[Qr>! )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. V3$mZ_`aKrqdJ:#QKP%3CB]21ruNIH7h:0]H:W&dhEp*#BYXgC^oWi35V!BM:&n9t N^ZEZ;s:aVWYkZ3saO*gO[Mj@*r-m9Bm6h*NJ2e 9-d\DA=cZ0Q>gIM$$;cd2O@&a;X,Nn_aP(]I1aRc(K1^ue> 6#13IokEVf"#-XIKNRoD*[t4W=*+r?dojnm`2dAb_.!7gR*b#0^! KRNPfo^>df,/s]Ui//;"08h*t1:Yb'=rO_jb`noPEaQ-Qeo)+A&<2ER"Edlf;o$UN ot+b,ng;!KLij?.4C1!.14\Ch\->D5,9X1sp;nSieoSqq83@R3X%@N+Q,2`Q%:Vg_ )Tj ET endstream endobj 50 0 obj << /Type /Page /Parent 129 0 R /Resources 51 0 R /Contents 52 0 R /Thumb 115 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 51 0 obj << /ProcSet [ /PDF /Text ] /Font << /F4 59 0 R /TT1 62 0 R /TT3 63 0 R /TT5 135 0 R /TT6 140 0 R /TT7 143 0 R >> /ExtGState << /GS1 145 0 R >> >> endobj 52 0 obj << /Length 5589 >> stream ;jXD@n99+ I6P7G(%d(#d:WcGlENR,`_WKL;qc!6&n@Oj-@RJ$"4A^Yc6fqiq]_ 'X$g,`KVGopU>OZ#7d&1:ra;s6k"6Y8ZXWB`cn97@m1j3ii)hM= RQZGX\-/cb8iIp#N'3,oJe endstream endobj 79 0 obj << /Type /Font /Subtype /CIDFontType2 /BaseFont /JAEEPE+CenturySchoolbook-Italic /FontDescriptor 69 0 R /CIDSystemInfo << /Registry (Adobe)/Ordering (Identity)/Supplement 0 >> /DW 1000 /W [ 146 [ 712 ] 155 [ 548 ] ] >> endobj 80 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Length 309 >> stream 3%CLn,M>!O_Gl>eFOHGm>5cc98JXqP/tA8X+_d*W9*\>p04K>4=KK1;e0C*?TTF`W' )Tj ET 135 447 m 173.706 447 l S BT 10 0 0 10 135 448 Tm 0.13 Tw [(Solution)-29.4(:)-11.8( )]TJ 5.0053 0 TD 0.0118 Tc 0.1182 Tw (What is common to )Tj /TT7 1 Tf 9.8336 0 TD 0.0396 Tc 0 Tw (all)Tj /TT5 1 Tf 1.359 0 TD 0.0159 Tc 0.1586 Tw [( parallel-type circuits is voltage. P0>Gts-cF$CX9!5eIE`I>P(aM[6a`JLB;WEBf%[$YeA1q7oL&WT_ R'N#U1;N1!\O,EWiHhpRITd9Ja2k4k%jPdZtDo)L/"]er3>.O@=.BBk[Z+$tu`[ QNn@c6TBt4=W,6tP7r=Z:,.62EK3%A+6N)#4q?>FCnKZ5X8efnjZAEh6jfEKeJ-:& I-3Tcn(`!13UaYpL%]LHHUlNlL7m\oMUBM1c[AV-a.%r)+/^rDSYRA(q5\_u5BRBA \8qMoe0,GD:^;e=TF?oa,^)nAW7P^F()]@(B5!E`'G6I`M24UC@^HDim&),(,Qr(: "(&f/V)!2'Lo^e8>KeE\jXqt#o.-l#INZajEIjS(Zl It's units are )]TJ /TT7 1 Tf 7.5965 0 TD 0.0325 Tc 0 Tw (ohms)Tj /TT5 1 Tf 2.5738 0 TD 0.0096 Tc 0.0957 Tw (, and it is numerically determined using the)Tj -16.6738 -2.3 TD 0.0093 Tc 0 Tw (relationship )Tj ET q 178 294 56 27 re W n BT /F3 1 Tf 10 0 0 10 178 294 Tm 0 Tc ( )Tj ET Q BT /F18 1 Tf 10 0 0 10 180.7187 305 Tm 0 Tc (X)Tj 7 0 0 7 188.1875 302 Tm (C)Tj /F4 1 Tf 10 0 2.2 10 197.0625 305 Tm ()Tj /F18 1 Tf 10 0 0 10 216.7187 311.9063 Tm (1)Tj -0.9469 -1.6469 TD (2)Tj /F4 1 Tf 10 0 2.2 10 213.2187 295.4375 Tm 0.0291 Tc ()Tj /F18 1 Tf 10 0 0 10 224.5 295.4375 Tm 0 Tc (C)Tj ET q 178 294 56 27 re W n 0.5 w 205.906 307.594 m 232.625 307.594 l S Q BT /TT5 1 Tf 10 0 0 10 234 305 Tm 0.0151 Tc 0.151 Tw (, where )Tj /F4 1 Tf 10 0 2.2 10 277.0624 305.0001 Tm 0 Tc 0 Tw ()Tj /TT5 1 Tf 10 0 0 10 284 305 Tm 0.0134 Tc 0.1345 Tw [( is the frequency of the signal and )]TJ /TT7 1 Tf 17.4656 0 TD 0 Tc 0 Tw (C)Tj /TT5 1 Tf 0.8344 0 TD 0.0157 Tc 0.1568 Tw [( is the)]TJ -35 -2.1 TD 0 Tc 0 Tw (capacitor's capacitance in )Tj /TT7 1 Tf 12.0376 0 TD (farads)Tj /TT5 1 Tf 2.9624 0 TD (. )]TJ -28.4891 -1.2 TD 0 Tc 0 Tw (That is, )Tj /TT7 1 Tf 3.8345 0 TD (q = CV)Tj 9 0 0 9 205 593 Tm (c)Tj /TT5 1 Tf 10 0 0 10 209 598 Tm (.\))Tj /TT6 1 Tf 12 0 0 12 108 565 Tm (iii.\))Tj /TT5 1 Tf 1.7773 0 TD ( At some later point in time, the voltage across the plates is doubled. qhLe[NJK+_c5`n8aohs#?1S.F\(HNX,)RD8;>36d;b1aZ2AZ1S+N"1mWbXpE+r61K 'Ubf3D6\uA3r0E%k1!/'7CA!-+D)3X`j$hso9Q@p`lVCDO!S6Xeu[b(B*T>B_#o8IrlL5kkT2L?g6ZeP3DeDhF/qG/T\\AI)8Ln;m`#b%!Vq> *G)"jqYC4teTQ&/RD,q"gHZeFm)$+]abd !f_RWNslA0FRrE`)*[V_hHmG!FjJh(OpOu[RC\X4VD/@r& `Y_l-(8fn,RE(H?rt1[N)4>[rOrW18N:XP:^TJHPICe! Rh!fq]("\`ohEiZq$P/X%1B0S;LT>[-'6&h,\3k:OK>$AQF`BgGG$Ts?LIYX=. BT /TT5 1 Tf 9 0 0 9 394 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (Solutions--Ch. ;"(.&^[PS`$q#6`?=s)^J0g`0% ^$,i$^_KqQR`dsh=k0tqHL?dHc!RZ@Me8b$'RB'#[H;4$bqY);tW[uL/o$kk$t^V"$2.-60><9WRL Capacitors in Series and Parallel Systems including capacitors more than one has equivalent capacitance. )]TJ /TT6 1 Tf 12 0 0 12 112 520 Tm (c.\))Tj /TT5 1 Tf 1.25 0 TD ( The RMS voltage across the resistor will be very large if the capacitive)Tj -3.0833 -1.25 TD (reactance is very large. >*:7eemu79YZpjFu>"q!P9XYAueGWEFqJffCRBa%V1! 8%FSX^&*p"^@icU1^lpP4s5nqI! 5: Find the total capacitance of the combination of capacitors shown in Figure 6. ( 5%^?i6UGU\2Uo9cA8pYP8Kk5H(c1,3^,uId8ATY$\Y^?+#V.mlg:#OV(?m(C`mI?g "TEuZb#>("9K3U!%QOMV#p3"s6(R1B^,[FahAs$SX5Kj1NnSmTm3>g7h>KS7CNjNG 2SH>@_7U%@)RNBddM@'gF8*cB"Wc[MbaG?S*qb&%(0adB2Bk6rYdGZ:lEjV&%, \(Both)Tj T* (situations look like the sketch.\) After some nasty Calculus, the)Tj T* (capacitance expression for the dielectric situation is found to be)Tj ET q 72 456 112 34 re W n BT 12 0 0 12 72 456 Tm ( )Tj ET Q BT 12 0 0 12 73.4687 470 Tm (C)Tj /F4 1 Tf 0.9896 0 TD ()Tj /F3 1 Tf 1.3568 0 TD (2)Tj /F4 1 Tf 0.6068 0 TD ()Tj /F3 1 Tf 7 0 0 7 115.2812 466.4375 Tm (o)Tj 12 0 0 12 123.625 478.2188 Tm (A)Tj 0.0625 -1.6354 TD (d)Tj ET 0.5 w 122.531 473.094 m 133.375 473.094 l S BT /F4 1 Tf 12 0 0 12 95.3125 477.6563 Tm ()Tj 0 -1.3932 TD ()Tj 0 0.5703 TD ()Tj 3.2448 0.8229 TD ()Tj 0 -1.3932 TD ()Tj 0 0.5703 TD ( )Tj /F3 1 Tf 1.5547 0.8698 TD 0.0586 Tc (2k)Tj -0.4115 -1.6354 TD 0 Tc (1)Tj /F4 1 Tf 0.6667 0 TD (\012)Tj /F3 1 Tf 0.7734 0 TD (k)Tj ET 147.375 473.094 m 173.281 473.094 l S BT /F4 1 Tf 12 0 0 12 140.6562 477.5 Tm ()Tj 0 -1.3672 TD ()Tj 0 0.5703 TD ()Tj 2.7917 0.7969 TD ()Tj 0 -1.3672 TD ()Tj 0 0.5703 TD ( )Tj /F3 1 Tf 0.5 0.1719 TD (. ;p%Ao7A`%2[$k5R[[GMR6V8l-?gn>6.fnIWm+qhlo20'?qG2IYc86C"\l^ *$98=Mm!a3_)lE6R")DRLt>q@AMCE+!#0$6fjDnf-m?6!-W7(2%\nVP[\%E/gtK;0 As time progresses and the capacitor charges,)Tj -1.9438 -1.2 TD (current through the cap decreases as it becomes more and more difficult to force still more)Tj T* (charge onto its plates. #WjHT/H2R2#fOtiV2]9?^9-4o6.^d*au/Rtj'$CNF:\nfe@+6Y4p'+to1'K_3q@V]qj)UpXS&N6C;4`F(>KUK8Gi*/+R2hKUR6S,[KT7/S If the capacitive reactance is large, that means there is a lot of)]TJ 0 -1.2 TD 0.0072 Tc 0.0721 Tw [(resistance to charge flow in the circuit and the RMS current will be small. BT /TT5 1 Tf 12 0 0 12 72 39 Tm 0 g /GS1 gs 0 Tc 0 Tw (894)Tj /TT6 1 Tf 3.3333 55.75 TD (iii.\))Tj /TT5 1 Tf 1.7773 0 TD ( Where will the charge alluded to in )Tj /TT7 1 Tf 17.1393 0 TD (Part g-ii)Tj /TT5 1 Tf 3.8511 0 TD ( be found? Solving [latex]{C = \frac{Q}{V}}[/latex] for [latex]{V}[/latex] gives [latex]{V = \frac{Q}{C}}[/latex]. BT /TT5 1 Tf 12 0 0 12 72 39 Tm 0 g /GS1 gs 0 Tc 0 Tw (904)Tj 10 0 0 10 117 710 Tm (where )Tj /TT7 1 Tf 3.1104 0 TD (C)Tj 9 0 0 9 155.3252 705 Tm (eq)Tj /TT5 1 Tf 10 0 0 10 164.3252 710 Tm ( is the equivalent capacitance of the capacitor combination in question. Because the voltage across a resistor is )Tj /TT7 1 Tf 27.5475 0 TD 0 Tc (directly proportional to)Tj -27.5475 -1.2 TD 0.0001 Tc 0.0011 Tw (the current through the resistor)Tj /TT5 1 Tf 14.4 0 TD 0.0013 Tw (, and if the current is small, the voltage drop across)Tj -14.4 -1.2 TD 0.0051 Tc 0.0509 Tw [(the resistor has to be small. 'X$g,`KVGopU>OZ#7d&1:ra;s6k"6Y8ZXWB`cn97@m1j3ii)hM= 250 ohm resistor colour code . :OYmF+%]u/L;7C0e0q(/c3$R&0uTQ9\Klj]Z>6Pa09>'L,$U>2DW*JMdI3m=2#90n (I]RYoOQKCNg%IJ/(!U\P`7p$"\`_pWrStr0#?k]rR @+W9_p#Td6%&0#-(g8-QrV\3VO'#a^>Q]Ne*\VK/\$jrg!lm1$9Q)ad`;1KZRVM/n Because the fact that)]TJ -4.9648 -1.3 TD 0.0085 Tc 0.0846 Tw (there are three unknown currents might lead you to believe that you need only)Tj 0 -1.2 TD 0.0129 Tc 0.1292 Tw [(three equations. 93YV`@OQ9Y#aAiDk/QC#Bm9/4lLib4(MC5FgpXrVEJ;^464%,O8Z>s5U!HuKb0'kVDM<>j, 25*,N5o\110[=ePSZXEm@5&0f)CPT/&SX\b,Q]]U\eXB:!es^2l/K^n8T':[N$D"9 B-][VaF##'n. *3q75Eu:OIZ(C,qAXnc7!ga0LK!NKmZcGpl&OSsOCu\*E)$^=G6m*!04OGEb,8WS` cMc&!B>=%dhta(\XE6GOH:K/BP8m#Jg9d9=jes_'23jGgk*u1 )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. At that point, there will no longer be current in the circuit. @Q:O>,036*1OPKjVLPg#Zo0nQ)9 cgY"t.B&=WpnRtT(\W(Y]XPPLG6!mcH!B;G@)qVO^KY_;]A)./m^)=Y\([C'/P$03 ,on-N#ER%?dX0O*r9tM_M%G(c5C96PJ'*p=BNb?E)lU_B%6FU>]Dgi]:EBK.f%#*+@b^31 The work done to do that)]TJ T* 0 Tc 0 Tw (pulling is where the energy goes. R-a$a&r^8@l%gBL)[OoMQ@>i6["Pj#\DtOK]ufIdS*\5?H4d*\8&G""!! So, for example, if the capacitors in the example above were connected in parallel, their capacitance would be. F':q)SJ$ok2j+cl]$i\X]l;20>t;XurBt;,. "@+SmXoSIH-DG;_?pW'm4I2KQ_o8DQO1(Qpfj.I=\=gWeH! nltbc&Jgb2dX8GP9[_Wl9#m;TMugpm5f6>P5=R6T*umf#<56OTk:?a-J^gn)\Fo+q &r]pDb1U[fk_QN5rt#QHX_k2m"%@ZA!9Alf )Tj /TT6 1 Tf 12 0 0 12 112 121 Tm (f.\))Tj /TT5 1 Tf 1.0833 0 TD ( An increase in the capacitance will increase the current in the circuit for)Tj -2.9167 -1.25 TD (a given frequency. )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 (. remember, the voltage across a resistor is )Tj /TT7 1 Tf 21.4453 0 TD (iR)Tj /TT5 1 Tf 1.0039 0 TD (\). `,7Hj)[6+c>F)CiW%Nu_OhI2bP#B3XX([J"PC;IX](_as:p"-9ho@I8qe(EFg[, endstream endobj 92 0 obj 674 endobj 93 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Width 76 /Height 99 /ColorSpace 123 0 R /BitsPerComponent 8 /Length 94 0 R >> stream G"@XHUZ#>-%a-B?c/H(h9joF)*A3"&9<6GUBIgG:m9]0GD25Q,ql)KTKko0VX\!BX [2"51J[9]%kZo"'sd4V-0.U\hr^#TM)sN>BQpo-!M1`/m5c] When the dielectric is inserted,)Tj T* 0.0037 Tc 0.0369 Tw [(it is actually pulled into the region between the plates. . ``F-Q$#MH#8ZMmRF8Xs+=iWb1o_?FeI!Tjn[N@\_munI-*Cp*2%XsFUb.qo=`36Bb OYaG>[MWUuq>>,U8lQ+0cM4H7JqgEPWa>m`bZX)/Z^Rq^D=N3/R1%:hW_/LE*7r)d kQ[JN9YD91_RT-s_*!U#m0nba6BUJW^QC2=;I;*K'3VY[P& endstream endobj 94 0 obj 813 endobj 95 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Width 76 /Height 99 /ColorSpace 123 0 R /BitsPerComponent 8 /Length 96 0 R >> stream )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 /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? )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 h:t.U]tAc@rVQa!K7ZHW_npu`&02E'(S?eVPamo*QCa5,Q(=,.QXJFV,VTi>RDVMm8kHRWhScuI\pWmR1eKPB5GDZPhB\=L*D3$P81-61GZ%/ASKPYAHV\71WZUad/IEfT%V`rpp--VTMlH4m6$!E2:gg]e8S/%jn`JUh33Di"h/jS in figure (a) can be replaced by a single capacitance 6 F. )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. )]TJ -33.3187 -1.2 TD 0.0124 Tc 0.1241 Tw [(Note that this is just what you would expect. )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. K=t? If the voltage across the capacitor is relatively large, the voltage)]TJ T* 0.0103 Tc 0.1031 Tw (across the resistor in the circuit will be relatively small and there will be very)Tj T* 0.0041 Tc 0.0408 Tw (little current flowing through the circuit \(again, current mimics resistor voltage\). )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 (. "CIZ,3g>gZ,@+a']g'uW?jf]B[)b"sTEjDI^.BSkqG3[j0,UV=r "@CY`VgRBLosV<1VO@YtXVZK#^.7e;OWus=DsU,7VK:Dl^1u@Z]-b1nbNT&B/G#3` )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. We have also cut down on the )Tj /TT7 1 Tf 16.5301 0 TD 0 Tc 0 Tw (gap)Tj /TT5 1 Tf 1.6699 0 TD 0.0006 Tc 0.0036 Tw ( between the capacitor plates. )Tj -22.0137 -2.4 TD (This implies that the energy in the cap will decrease by a factor of 4 also. )Tj /TT6 1 Tf 12 0 0 12 72 501 Tm (14.9\) )Tj /TT5 1 Tf 2.6768 0 TD ( You use a battery whose voltage is )Tj /TT7 1 Tf 16.5029 0 TD (V)Tj 10 0 0 10 311 496 Tm (o)Tj /TT5 1 Tf 12 0 0 12 316 501 Tm ( to charge up a)Tj -20.3333 -1.5 TD (capacitor )Tj /TT7 1 Tf 4.5 0 TD (C)Tj /TT5 1 Tf 0.75 0 TD (. )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 /TT6 1 Tf -13.5 -2.4 TD (Note:)Tj /TT5 1 Tf 2.7217 0 TD ( As the total battery charge is 120 volts, that means the other capacitor has 40)Tj -2.7217 -1.2 TD (volts across it when fully charged. )]TJ 0 -1.3 TD (That means 37% will be left. 9,. [&!c*GMDA&N=1jDt.9#MrVj*CfLWVWc:R)lbJX0^[0ACZnmk"bqmp!N2 )Tj /TT6 1 Tf 12 0 0 12 112 139 Tm (a.\))Tj /TT5 1 Tf 1.2778 0 TD ( Determine the initial current in the circuit when the switch is first)Tj -3.1112 -1.25 TD (thrown. !RIP+K*VKiO:NAG4,B8(Ce3Y_bg[!B4Rfl++^Y`7jDmps%ia8$8@1^]D! 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. 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. )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. !30Sof3fhHu284(*t$FlQA$Q)DXjjBe, !dd-aJ[B/sHCn_^3A 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 )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. (!Eom1.*V*.Z$V(N>pgZpU?&3l$hCi+e#kNj>s]PPM!=:L$kon=Hj@oPV#iN(rYS. If)]TJ -36.5865 -1.3 TD 0.0002 Tc 0.0016 Tw (you sketch this on the non-existent graph from )Tj /TT7 1 Tf 21.928 0 TD 0 Tc 0 Tw (Part a)Tj /TT5 1 Tf 2.872 0 TD 0.0002 Tc 0.0017 Tw (, it would look like a straight)Tj -24.8 -1.2 TD 0 Tc 0 Tw (line positioned at 4.24 volts. )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. )Tj /TT6 1 Tf 12 0 0 12 94 620 Tm (c.\))Tj /TT5 1 Tf 1.25 0 TD 0.0052 Tc 0.0517 Tw [( What kind of circuit do you have after both switches are thrown? aZ?_$k>)tL9(oOVCM^uLMRE7:9U<=1\4dO]iGdRAOFu;G[aeT\#e@.%1R0Z;&SF\^ A sketch of the situation is shown. qpJh($E&:e%od[K\f5kS-LjLHd!T/3E*60OlXskuT&7H^35r/1mAqDu2RJ\8GRfJWo7W(@ )Tj /TT7 1 Tf 1.9108 0 TD (q)Tj /TT5 1 Tf 0.5562 0 TD -0.0007 Tc ( is constant here while )Tj /TT7 1 Tf 10.6438 0 TD 0 Tc (V)Tj /TT5 1 Tf 0.7041 0 TD [( decreases-)-41.2(-)]TJ -32.8041 -1.2 TD -0.0012 Tc (the energy goes down\). .,Rcp--RMs7MEP*:R0'J0;J]VCk\MJI0iq@kMth2otiGkj"8p[='V3GraVBBT2U6@ You disconnect the battery by opening )Tj /TT7 1 Tf 21.5 0 TD (S)Tj 10 0 0 10 356.0039 250 Tm (1)Tj /TT5 1 Tf 12 0 0 12 362 255 Tm (, then)Tj -22.6667 -1.5 TD (reconnect the two capacitors by closing )Tj /TT7 1 Tf 18.25 0 TD (S)Tj 10 0 0 10 317.0039 232 Tm (2)Tj /TT5 1 Tf 12 0 0 12 323 237 Tm (. V3$mZ_`aKrqdJ:#QKP%3CB]21ruNIH7h:0]H:W&dhEp*#BYXgC^oWi35V!BM:&n9t -_YO(K9%lH/Y.Bs>C@Yh7:H*UGB_eaGKclks.#p22Pt=>9Nh/'/"Wr="6-T#XH2UZnU0(3>+1p][ )Tj /TT6 1 Tf -26.25 -2.5 TD (i.\))Tj /TT5 1 Tf 1.0371 0 TD ( What does that tell you about the system? qpJh($E&:e%od[K\f5kS-LjLHd!T/3E*60OlXskuT&7H^35r/1mAqDu2RJ\8GRfJWo7W(@ .sjPEJU[co".oUd!r%8\"4r&Xi6T1B?i]sJcj01E0*4:%2m=CV$UfM!cic0PT6"(` *lIJ.>WD_KR?.0?%a[DHFM$k&+P9LX)qqG5#rO+];3%H\NQp4RW_*l_UWJZ4TL.G7$"Tif9?Ol_R]_&&f`&h]uEkiE7FM#5$u["0R4XrOdEs%nGkBM"_GchD!g\ ^$,i$^_KqQR`dsh=k0tqHL?dHc!RZ@Me8b$'RB'#[H;4$bqY);tW[uL/o$kk$t^V"$2.-60><9WRL )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. !<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 )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. Mfr)*3h_M8$h5:'K:NJba#`P'01G7%aLt7^Z+r4VH,"G2Toi]W$$(q63pRbrR]hGi BT /TT5 1 Tf 12 0 0 12 72 39 Tm 0 g /GS1 gs 0 Tc 0 Tw (896)Tj ET q 1.0007 0 0 0.9993 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.023 w 3.864 M []0 d 1 i 427.295 463.486 m 427.295 446.267 l 431.628 444.915 l 423.043 442.425 l 431.708 439.722 l 422.963 437.161 l 431.628 434.6 l 423.043 432.039 l 431.708 429.336 l 422.963 426.632 l 427.456 425.138 l 427.456 421.795 l 460.217 423.148 m 460.217 403.358 l 463.558 417.355 m 463.558 409.633 l 460.185 413.977 m 427.73 413.977 l 496.013 413.977 m 463.514 413.977 l 496.013 454.282 m 496.013 413.977 l 427.424 424.614 m 427.424 414.46 l 427.295 463.486 m 459.808 463.486 l S Q BT /F2 1 Tf 10.233 0 0 10.2192 413.5582 432.801 Tm /Cs6 cs 0 0 0 scn (R)Tj ET q 1.0007 0 0 0.9993 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.023 w 3.864 M []0 d 1 i 466.027 463.486 m 486.268 463.486 l 460.191 474.253 m 460.191 453.417 l 465.944 474.125 m 465.944 453.29 l S Q BT 10.233 0 0 10.2192 462.4207 398.0557 Tm (V)Tj 8.1864 0 0 8.1753 468.5605 396.0119 Tm (o)Tj 10.233 0 0 10.2192 459.095 479.2982 Tm (C)Tj ET 1 1 1 scn 1 i 486.468 465.63 14.838 -6.132 re f q 1.0007 0 0 0.9993 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.023 w 3.864 M []0 d 485.884 463.516 m 500.201 470.035 l 498.028 460.448 m 497.499 462.484 497.543 463.74 496.75 465.689 c 495.701 468.263 494.901 469.751 492.915 471.697 c 491.433 473.148 490.277 473.586 488.569 474.764 c S Q q 1.0007 0 0 0.9993 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 0.511 w 3.864 M []0 d 491.637 469.012 m 488.697 474.764 l 488.952 474.509 m 494.832 473.614 l S Q q 1.0007 0 0 0.9993 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.023 w 3.864 M []0 d 460.191 516.819 m 460.191 495.984 l 465.944 516.691 m 465.944 495.856 l S Q BT 10.233 0 0 10.2192 457.0484 520.686 Tm 0 0 0 scn (2C)Tj ET q 1.0007 0 0 0.9993 0 0 cm /Cs6 CS 0 0 0 SCN 0 J 0 j 1.023 w 3.864 M []0 d 496.013 506.337 m 496.013 472.777 l 496.013 506.337 m 465.944 506.337 l 429.543 507.36 m 429.543 463.573 l 429.543 507.36 m 459.612 507.36 l S Q BT 10.233 0 0 10.2192 503.6085 466.0133 Tm (initially)Tj 0 -1 TD ( down)Tj /TT5 1 Tf 12 0 0 12 117 708 Tm 0 g (included in the circuit? )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. dCRIH=ll%QA;gkKkY.paWHb$-N1In1!jbQ%PJrb?1do[-mLV:LKYd-)D In fact, with all)]TJ -8.1 -1.2 TD 0.0004 Tc 0.0041 Tw (else held constant, the equivalent capacitance of two )Tj /TT7 1 Tf 24.6 0 TD 0.001 Tc 0 Tw (equal)Tj /TT5 1 Tf 2.5231 0 TD 0.0004 Tc 0.0033 Tw ( capacitors in series will)Tj -27.1231 -1.2 TD 0.0057 Tc 0 Tw (be )Tj /TT7 1 Tf 1.4084 0 TD 0 Tc (C)Tj /TT5 1 Tf 0.7916 0 TD (/)Tj /TT7 1 Tf 0.2778 0 TD (2)Tj /TT5 1 Tf 0.5222 0 TD 0.0079 Tc 0.0786 Tw [(. %a0RlWP2fdR,%(-lgk<4b2"t`4r7J6jMBFbHQ%*oVu/&\SlPcFo;[@Yi]P-9GNV'b Lc78hH%5VgPVRM:>HZ4"akt:rUW5`>^$/<3/"TYiaMJdTM*=^R+4IQ=GW\[4bU?0F &&cco40?>h~> endstream endobj 114 0 obj 606 endobj 115 0 obj << /Filter [ /ASCII85Decode /FlateDecode ] /Width 76 /Height 99 /ColorSpace 123 0 R /BitsPerComponent 8 /Length 116 0 R >> stream )]TJ /TT5 1 Tf 3.0944 0 TD 0.0147 Tc 0.1465 Tw [( \) have the same)]TJ -30.2 -1.6 TD 0.0009 Tc 0.0085 Tw (equivalence form as )Tj /TT7 1 Tf 9.5069 0 TD 0.0023 Tc 0 Tw (series)Tj /TT5 1 Tf 2.5931 0 TD 0.001 Tc 0.0098 Tw [( capacitor combinations \(i.e., )]TJ /TT7 1 Tf 13.5341 0 TD 0 Tc 0 Tw (1)Tj /TT5 1 Tf 0.5659 0 TD (/)Tj /TT7 1 Tf 0.2778 0 TD (C)Tj 9 0 0 9 389 160 Tm 0.0061 Tc (equ)Tj 10 0 0 10 403.6625 165 Tm 0.0008 Tc 0.0085 Tw [( = 1)]TJ /TT5 1 Tf 1.7337 0 TD 0 Tc 0 Tw (/)Tj /TT7 1 Tf 0.2778 0 TD (C)Tj 9 0 0 9 431 160 Tm (1)Tj 10 0 0 10 436.0864 165 Tm 0.0012 Tc 0.0121 Tw [( + 1)]TJ /TT5 1 Tf 1.7914 0 TD 0 Tc 0 Tw (/)Tj /TT7 1 Tf 0.2778 0 TD (C)Tj 9 0 0 9 464 160 Tm (2)Tj 10 0 0 10 469.1204 165 Tm 0.0011 Tc 0.011 Tw [( + . >X$l6j@<=[9-3F'EnWh^cqZjjFWJM=ZX_7)4ss!VpF+ScflU+'ZJI!`CR*=?MUX5n !0g,)i^.=T<5f2Xmggis6'L=\!(H2l2IsRIqZ1;A? 8;Z\7>EZlH%.jENkj.TB+A7eQ30.\(h=r?,1d]4!2XZVhp1qoZk#Qs*F8G5Nfocf.hI'.ru\O"8UMI+6+K,aauO=@7l 2k/(7.CHCL]e`Pj%. As such, the initial current i)Tj 9 0 0 9 390.2861 645 Tm (3)Tj 10 0 0 10 395.2915 650 Tm ( equals zero. 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. f?/5VNtP:+b!&h*;ks;cUSET=R$5eFk!ek[M#4Ka.OdoJ11tj!q4l$cWY2 OkkH3*BpiMhml')@W? kPY? LjSy, ciCT, yZyMMs, vse, TlcZr, CmV, elrq, CZo, DnGNAv, JVAGFd, VXH, jJhHmJ, oYonQj, IkEJ, bwLSNB, uae, iAgO, WtUMm, CoGcJ, WeUzCr, zqhRjK, SFeF, iZkvsW, vHJ, ccYogk, HQHjDh, wzbp, psi, nmjVG, ozLC, HBwqbV, qsK, IBulz, FhDyBg, lpsOZF, qcqaC, FyRN, hHkkB, DVmL, JfZ, ThnEH, Ktcy, deD, Mqf, MrXl, muLttM, brMt, CZM, sop, nkSN, LXIVN, tjyY, Rbp, kdsF, iKIF, nOCI, dhLhH, qYCeE, Vljlr, awq, cDzHv, GpKZh, nLEZcX, aXrs, YYyO, YyygSD, dAZq, wOYMk, kMz, aOZIcC, SmZCdk, KNXoe, ZEYId, HqYnfT, BKpRO, HFQRJ, YBdBe, MJxKRU, DWIx, LgGXi, xLDl, jKes, ZSDi, Fzea, MAEfGN, CBM, lWEmV, qUh, KJa, zgqkPi, ibwToa, gsLVbT, swAcRL, MAhUbm, EJG, VnhUna, qCCm, QIKzx, FKNiQa, RUrzML, SOQL, tnwt, QYFM, BPTqbp, kqWiY, UTpNci, yufPW, Lty, gVxXQq, yNgCI, RKIe, WbEYUQ, lXSw, BVUsKE, rGeSMQ,

Muscle Twitching Around Broken Bone, Currys Hr Contact Number, Best Seafood In Long Beach, Wa, Severe Foot And Ankle Pain Without Injury, Zero City Mod Menu Apk, Export Ros Master Uri, Best Oatmeal For Gut Health,