Questions. denotes answer available in Student Solutions Manual/Study Guide; O denotes objective question

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1 Qustions 799 Qustions dnots nswr vill in tudnt olutions Mnul/tudy Guid; O dnots ojctiv qustion 1. Is th dirction of currnt in ttry lwys from th ngtiv trminl to th positiv trminl? Explin. 2. O crtin ttry hs som intrnl rsistnc. (i) n th potntil diffrnc cross th trminls of ttry qul to its mf? () No. () Ys, if th ttry is soring nrgy y lctricl trnsmission. (c) Ys, if mor thn on wir is connctd to ch trminl. (d) Ys, if th currnt in th ttry is zro. () Ys; no spcil condition is rquird. (ii) n th trminl voltg xcd th mf? hoos your nswr from th sm possiilitis. 3. Givn thr lightuls nd ttry, sktch s mny diffrnt lctric circuits s you cn. 4. O Whn rsistors with diffrnt rsistncs r connctd in sris, which of th following must th sm for ch rsistor? hoos ll corrct nswrs. () potntil diffrnc () currnt (c) powr dlivrd (d) chrg ntring () non of ths nswrs 5. O Whn rsistors with diffrnt rsistncs r connctd in prlll, which of th following must th sm for ch rsistor? hoos ll corrct nswrs. () potntil diffrnc () currnt (c) powr dlivrd (d) chrg ntring () non of ths nswrs 6. Why is it possil for ird to sit on high-voltg wir without ing lctrocutd? 7. O r th two hdlights of cr wird () in sris with ch othr, () in prlll, (c) nithr in sris or in prlll, or (d) is it impossil to tll? 8. studnt clims tht th scond of two lightuls in sris is lss right thn th first, cus th first lightul uss up som of th currnt. How would you rspond to this sttmnt? 9. O Is circuit rkr wird () in sris with th dvic it is protcting, () in prlll, (c) nithr in sris or in prlll, or (d) is it impossil to tll? 10. O In th circuit shown in Figur Q28.10, ch ttry is dlivring nrgy to th circuit y lctricl trnsmission. ll th rsistors hv qul rsistnc. (i) nk th lctric potntils t points,, c, d,, f, g, nd h from highst to lowst, noting ny css of qulity in th rnking. (ii) nk th mgnituds of th currnts t th sm points from grtst to lst, noting ny css of qulity f c g h Figur Q O sris circuit consists of thr idnticl lmps connctd to ttry s shown in Figur Q Th switch, originlly opn, is closd. (i) Wht thn hppns to th rightnss of lmp B? () It incrss. () It dcrss d somwht. (c) It dos not chng. (d) It drops to zro. (ii) Wht hppns to th rightnss of lmp? hoos from th sm possiilitis. (iii) Wht hppns to th currnt in th ttry? hoos from th sm possiilitis. (iv) Wht hppns to th potntil diffrnc cross lmp? (v) Wht hppns to th potntil diffrnc cross lmp? (vi) Wht hppns to th totl powr dlivrd to th lmps y th ttry? hoos in ch cs from th sm possiilitis () through (d). B Figur Q O circuit consists of thr idnticl lmps connctd to ttry hving som intrnl rsistnc s in Figur Q Th switch, originlly opn, is closd. (i) Wht thn hppns to th rightnss of lmp B? () It incrss. () It dcrss somwht. (c) It dos not chng. (d) It drops to zro. (ii) Wht hppns to th rightnss of lmp? hoos from th sm possiilitis. (iii) Wht hppns to th currnt in th ttry? hoos from th sm possiilitis. (iv) Wht hppns to th potntil diffrnc cross lmp? (v) Wht hppns to th potntil diffrnc cross lmp? (vi) Wht hppns to th totl powr dlivrd to th lmps y th ttry? hoos in ch cs from th sm possiilitis () through (d). Figur Q ski rsort consists of fw chirlifts nd svrl intrconnctd downhill runs on th sid of mountin, with lodg t th ottom. Th chirlifts r nlogous to ttris, nd th runs r nlogous to rsistors. Dscri how two runs cn in sris. Dscri how thr runs cn in prlll. ktch junction twn on chirlift nd two runs. tt Kirchhoff s junction rul for ski rsorts. On of th skirs hppns to crrying skydivr s ltimtr. h nvr tks th sm st of chirlifts nd runs twic, ut kps pssing you t th fixd loction whr you r working. tt Kirchhoff s loop rul for ski rsorts. B

2 800 hptr 28 Dirct urrnt ircuits 14. frring to Figur Q28.14, dscri wht hppns to th lightul ftr th switch is closd. ssum th cpcitor hs lrg cpcitnc nd is initilly unchrgd nd ssum th light illumints whn connctd dirctly cross th ttry trminls. witch Figur Q28.14 Bttry 15. o tht your grndmothr cn listn to Priri Hom ompnion, you tk hr dsid rdio to th hospitl whr sh is stying. You r rquird to hv mintnnc workr tst th rdio for lctricl sfty. Finding tht it dvlops 120 on on of its knos, h dos not lt you tk it up to your grndmothr s room. h complins tht sh hs hd th rdio for mny yrs nd noody hs vr gottn shock from it. You nd up hving to uy nw plstic rdio. Is tht fir? Will th old rdio sf ck in hr droom? 16. Wht dvntg dos 120- oprtion offr ovr 240? Wht disdvntgs dos it hv? Prolms Th Prolms from this chptr my ssignd onlin in Wssign. ign in t nd go to ThomsonNOW to ssss your undrstnding of this chptr s topics with dditionl quizzing nd concptul qustions. 1, 2, 3 dnots strightforwrd, intrmdit, chllnging; dnots full solution vill in tudnt olutions Mnul/tudy Guid; dnots cochd solution with hints vill t dnots dvloping symolic rsoning; dnots sking for qulittiv rsoning; dnots computr usful in solving prolm ction 28.1 Elctromotiv Forc 1. ttry hs n mf of Th trminl voltg of th ttry is 11.6 whn it is dlivring 20.0 W of powr to n xtrnl lod rsistor. () Wht is th vlu of? () Wht is th intrnl rsistnc of th ttry? 2. Two ttris with thir positiv trminls in th sm dirction r insrtd in sris into th rrl of flshlight. On ttry hs n intrnl rsistnc of 0.255, th othr n intrnl rsistnc of Whn th switch is closd, currnt of 600 m occurs in th lmp. () Wht is th lmp s rsistnc? () Wht frction of th chmicl nrgy trnsformd pprs s intrnl nrgy in th ttris? 3. n utomoil ttry hs n mf of 12.6 nd n intrnl rsistnc of Th hdlights togthr hv n quivlnt rsistnc of (ssumd constnt). Wht is th potntil diffrnc cross th hdlight uls () whn thy r th only lod on th ttry nd () whn th strtr motor is oprtd, rquiring n dditionl 35.0 from th ttry? 4. s in Exmpl 28.2, considr powr supply with fixd mf nd intrnl rsistnc r cusing currnt in lod rsistnc. In this prolm, is fixd nd r is vril. Th fficincy is dfind s th nrgy dlivrd to th lod dividd y th nrgy dlivrd y th mf. () Whn th intrnl rsistnc is djustd for mximum powr trnsfr, wht is th fficincy? () Wht should th intrnl rsistnc for mximum possil fficincy? (c) Whn th lctric compny slls nrgy to customr, dos it hv gol of high fficincy or of mximum powr trnsfr? Explin. (d) Whn studnt conncts loudspkr to n mplifir, dos sh most wnt high fficincy or high powr trnsfr? Explin. ction 28.2 sistors in ris nd Prlll 5. () Find th quivlnt rsistnc twn points nd in Figur P28.5. () potntil diffrnc of 34.0 is pplid twn points nd. lcult th currnt in ch rsistor Figur P lightul mrkd 75 W [t] 120 is scrwd into sockt t on nd of long xtnsion cord, in which ch of th two conductors hs rsistnc Th othr nd of th xtnsion cord is pluggd into 120- outlt. () Explin why th ctul powr dlivrd to th lightul cnnot 75 W in this sitution. () Wht cn you rsonly modl s constnt out th lightul? Drw circuit digrm nd find th ctul powr dlivrd to th lightul in this circuit. 7. onsidr th circuit shown in Figur P28.7. Find () th currnt in th rsistor nd () th potntil diffrnc twn points nd Figur P For th purpos of msuring th lctric rsistnc of shos through th ody of th wrr to mtl ground 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

3 Prolms 801 plt, th mricn Ntionl tndrds Institut (NI) spcifis th circuit shown in Figur P28.8. Th potntil diffrnc cross th 1.00-M rsistor is msurd with high-rsistnc voltmtr. () how tht th rsistnc of th footwr is shos 1.00 M 50.0 thir quivlnt rsistnc is 150. Find th rsistnc of ch rsistor. 13. Whn th switch in th circuit of Figur P28.13 is closd, will th quivlnt rsistnc twn points nd incrs or dcrs? tt your rsoning. ssum th quivlnt rsistnc chngs y fctor of 2. Dtrmin th vlu of. () In mdicl tst, currnt through th humn ody should not xcd 150 m. n th currnt dlivrd y th NI-spcifid circuit xcd 150 m? To dcid, considr prson stnding rfoot on th ground plt M Figur P Figur P Thr 100- rsistors r connctd s shown in Figur P28.9. Th mximum powr tht cn sfly dlivrd to ny on rsistor is 25.0 W. () Wht is th mximum potntil diffrnc tht cn pplid to th trminls nd? () For th voltg dtrmind in prt (), wht is th powr dlivrd to ch rsistor? Wht is th totl powr dlivrd? Figur P Using only thr rsistors, 3.00, nd find 17 rsistnc vlus tht my otind y vrious comintions of on or mor rsistors. Tult th comintions in ordr of incrsing rsistnc ttry supplis currnt to th circuit shown in Figur P Whn th doul-throw switch is opn s shown in th figur, th currnt in th ttry is 1.00 m. Whn th switch is closd in position, th currnt in th ttry is 1.20 m. Whn th switch is closd in position, th currnt in th ttry is 2.00 m. Find th rsistncs 1, 2, nd Figur P Two rsistors connctd in sris hv n quivlnt rsistnc of 690. Whn thy r connctd in prlll, Four rsistors r connctd to ttry s shown in Figur P Th currnt in th ttry is I; th ttry mf is ; nd th rsistor vlus r 1, 2 2, 3 4, nd 4 3. () nk th rsistors ccording to th potntil diffrnc cross thm from lrgst to smllst. Not ny css of qul potntil diffrncs. () Dtrmin th potntil diffrnc cross ch rsistor in trms of. (c) nk th rsistors ccording to th currnt in thm from lrgst to smllst. Not ny css of qul currnts. (d) Dtrmin th currnt in ch rsistor in trms of I. () Wht If? If 3 is incrsd, xplin wht hppns to th currnt in ch of th rsistors. (f) In th limit tht 3, wht r th nw vlus of th currnt in ch rsistor in trms of I, th originl currnt in th ttry? 1 = I Figur P = 2 4 = 3 3 = lcult th powr dlivrd to ch rsistor in th circuit shown in Figur P Figur P ction 28.3 Kirchhoff s uls 16. Th mmtr shown in Figur P28.16 rds Find I 1, I 2, nd. I 1 I Figur P = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

4 802 hptr 28 Dirct urrnt ircuits 17. Dtrmin th currnt in ch rnch of th circuit shown in Figur P Figur P28.17 Prolms 17, 18, nd In Figur P28.17, show how to dd only nough mmtrs to msur vry diffrnt currnt. how how to dd only nough voltmtrs to msur th potntil diffrnc cross ch rsistor nd cross ch ttry. 19. Th circuit considrd in Prolm 17 nd shown in Figur P28.17 is connctd for 2.00 min. () Find th nrgy dlivrd y ch ttry. () Find th nrgy dlivrd to ch rsistor. (c) Idntify th nt nrgy trnsformtion tht occurs in th oprtion of th circuit. Find th totl mount of nrgy trnsformd. 20. Th following qutions dscri n lctric circuit: I I I I I 1 I 3 I 2 0 () Drw digrm of th circuit. () lcult th unknowns nd idntify th physicl mning of ch unknown. 21. onsidr th circuit shown in Figur P Wht r th xpctd rdings of th idl mmtr nd idl voltmtr? dd ttry is chrgd y conncting it to th liv ttry of nothr cr with jumpr cls (Fig. P28.24). Dtrmin th currnt in th strtr nd in th dd ttry Figur P Liv ttry Dd ttry Figur P trtr 25. For th circuit shown in Figur P28.25, clcult () th currnt in th rsistor nd () th potntil diffrnc twn points nd Figur P For th ntwork shown in Figur P28.26, show tht th rsistnc Figur P Tking 1.00 k nd 250 in Figur P28.22, dtrmin th dirction nd mgnitud of th currnt in th horizontl wir twn nd. 4 c 3 Figur P In th circuit of Figur P28.23, dtrmin th currnt in ch rsistor nd th potntil diffrnc cross th 200- rsistor. 2 d 2 Figur P28.26 ction 28.4 ircuits 27. onsidr sris circuit (s ctiv Fig ) for which 1.00 M, 5.00 mf, nd Find () th tim constnt of th circuit nd () th mximum chrg on th cpcitor ftr th switch is thrown to, conncting th cpcitor to th ttry. (c) Find th currnt in th rsistor 10.0 s ftr th switch is thrown to mF cpcitor is chrgd y ttry through rsistnc. Th cpcitor rchs potntil diffrnc of 4.00 in tim intrvl of 3.00 s ftr chrging gins. Find nF cpcitor with n initil chrg of 5.10 m is dischrgd through 1.30-k rsistor. () lcult th currnt in th rsistor 9.00 ms ftr th rsistor is con- 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

5 Prolms 803 nctd cross th trminls of th cpcitor. () Wht chrg rmins on th cpcitor ftr 8.00 ms? (c) Wht is th mximum currnt in th rsistor? how tht th intgrl 2t> dt in Exmpl hs th vlu / Th circuit in Figur P28.31 hs n connctd for long tim. () Wht is th potntil diffrnc cross th cpcitor? () If th ttry is disconnctd from th circuit, ovr wht tim intrvl dos th cpcitor dischrg to on-tnth of its initil voltg? Wht is th potntil diffrnc cross it? () uppos now n mmtr of rsistnc nd voltmtr of rsistnc r ddd to th circuit s shown in Figur P Find th rding of ch. (c) Wht If? Now on trminl of on wir is movd s shown in Figur P28.36c. Find th nw mtr rdings. (d) Explin whthr on of th voltmtrmmtr connctions is significntly ttr for tking dt to dtrmin th rsistnc of th rsistor mf Figur P () () Figur P28.36 (c) 32. In th circuit of Figur P28.32, th switch hs n opn for long tim. It is thn suddnly closd. Dtrmin th tim constnt () for th switch is closd nd () ftr th switch is closd. (c) Lt th switch closd t t 0. Dtrmin th currnt in th switch s function of tim k Figur P k 10.0 mf ction 28.5 Elctricl Mtrs 33. ssum glvnomtr hs n intrnl rsistnc of 60.0 nd rquirs currnt of m to produc full-scl dflction. Wht rsistnc must connctd in prlll with th glvnomtr if th comintion is to srv s n mmtr tht hs full-scl dflction for currnt of 0.100? 34. prticulr glvnomtr srvs s full-scl voltmtr whn rsistor is connctd in sris with it. It srvs s full-scl mmtr whn rsistor is connctd in prlll with it. Dtrmin th intrnl rsistnc of th glvnomtr nd th currnt rquird to produc full-scl dflction. 35. prticulr glvnomtr rquirs currnt of 1.50 m for full-scl dflction nd hs rsistnc of It cn usd to msur voltgs y wiring lrg rsistor in sris with th glvnomtr s suggstd in ctiv Figur Th ffct is to limit th currnt in th glvnomtr whn lrg voltgs r pplid. lcult th vlu of th rsistor tht llows th glvnomtr to msur n pplid voltg of 25.0 t full-scl dflction. 36. Mtr loding. Work this prolm to fiv-digit prcision. fr to Figur P () Whn rsistor is connctd cross ttry of mf nd intrnl rsistnc , wht is th currnt in th rsistor? ction 28.6 Houshold Wiring nd Elctricl fty 37. n lctric htr is rtd t W, tostr t 750 W, nd n lctric grill t W. Th thr pplincs r connctd to common 120- houshold circuit. () How much currnt dos ch drw? () Is circuit with circuit rkr sufficint in this sitution? Explin your nswr. 38. Turn on your dsk lmp. Pick up th cord, with your thum nd indx fingr spnning th width of th cord. () omput n ordr-of-mgnitud stimt for th currnt in your hnd. ssum th conductor insid th lmp cord nxt to your thum is t potntil ~ 10 2 t typicl instnt nd th conductor nxt to your indx fingr is t ground potntil (0 ). Th rsistnc of your hnd dpnds strongly on th thicknss nd th moistur contnt of th outr lyrs of your skin. ssum th rsistnc of your hnd twn fingrtip nd thum tip is You my modl th cord s hving rur insultion. tt th othr quntitis you msur or stimt nd thir vlus. Explin your rsoning. () uppos your ody is isoltd from ny othr chrgs or currnts. In ordr-of-mgnitud trms, dscri th potntil of your thum whr it contcts th cord nd th potntil of your fingr whr it touchs th cord. dditionl Prolms 39. Th circuit in Figur P28.39 hs n connctd for svrl sconds. Find th currnt () in th ttry, mf I I 1 3 c d I I = 0 h g f I I 3 1 Figur P = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

6 804 hptr 28 Dirct urrnt ircuits () in th rsistor, (c) in th ttry, nd (d) in th ttry. Find () th chrg on th cpcitor. 40. Th circuit in Figur P28.40 consists of thr rsistors nd on ttry with no intrnl rsistnc. () Find th currnt in th rsistor. () Find th powr dlivrd to th rsistor. (c) In ch of th circuits in Figurs P28.40, P28.40c, nd P28.40d, n dditionl ttry hs n insrtd into th circuit. Which digrm or digrms rprsnt circuit tht rquirs th us of Kirchhoff s ruls to find th currnts? Explin why. In which of ths thr circuits is th smllst mount of powr dlivrd to th rsistor? You nd not clcult th powr in ch circuit if you xplin your nswr () (c) Figur P () Four ttris in sris r usd to powr trnsistor rdio. If th ttris cn mov chrg of 240, how long will thy lst if th rdio hs rsistnc of 200? 42. ttry hs n mf of 9.20 nd n intrnl rsistnc of () Wht rsistnc cross th ttry will xtrct from it powr of 12.8 W? () powr of 21.2 W? Explin your nswrs. 43. lcult th potntil diffrnc twn points nd in Figur P28.43 nd idntify which point is t th highr potntil. (d) rchrgl ttry hs constnt mf of 13.2 nd n intrnl rsistnc of It is chrgd y powr supply for tim intrvl of 1.80 h. ftr chrging, th ttry rturns to its originl stt s it dlivrs constnt currnt to lod rsistor ovr 7.30 h. Find th fficincy of th ttry s n nrgy storg dvic. (Th fficincy hr is dfind s th nrgy dlivrd to th lod during dischrg dividd y th nrgy dlivrd y th powr supply during th chrging procss.) 46. powr supply hs n opn-circuit voltg of 40.0 nd n intrnl rsistnc of. It is usd to chrg two storg ttris connctd in sris, ch hving n mf of 6.00 nd intrnl rsistnc of If th chrging currnt is to 4.00, () wht dditionl rsistnc should ddd in sris? () t wht rt dos th intrnl nrgy incrs in th supply, in th ttris, nd in th ddd sris rsistnc? (c) t wht rt dos th chmicl nrgy incrs in th ttris? 47. Whn two unknown rsistors r connctd in sris with ttry, th ttry dlivrs 225 W nd crris totl currnt of For th sm totl currnt, 50.0 W is dlivrd whn th rsistors r connctd in prlll. Dtrmin th vlu of ch rsistor. 48. Whn two unknown rsistors r connctd in sris with ttry, th ttry dlivrs totl powr s nd crris totl currnt of I. For th sm totl currnt, totl powr p is dlivrd whn th rsistors r connctd in prlll. Dtrmin th vlu of ch rsistor. 49. Two rsistors 1 nd 2 r in prlll with ch othr. Togthr thy crry totl currnt I. () Dtrmin th currnt in ch rsistor. () Prov tht this division of th totl currnt I twn th two rsistors rsults in lss powr dlivrd to th comintion thn ny othr division. It is gnrl principl tht currnt in dirct currnt circuit distriuts itslf so tht th totl powr dlivrd to th circuit is minimum. 50. () Dtrmin th quilirium chrg on th cpcitor in th circuit of Figur P28.50 s function of. () Evlut th chrg whn. (c) n th chrg on th cpcitor zro? If so, for wht vlu of? (d) Wht is th mximum possil mgnitud of th chrg on th cpcitor? For wht vlu of is it chivd? () Is it xprimntlly mningful to tk? Explin your nswr. If so, wht chrg mgnitud dos it imply? uggstion: You my do prt () for prt (), s prctic for it mF 80.0 Figur P28.43 Figur P ssum you hv ttry of mf nd thr idnticl lightuls, ch hving constnt rsistnc. Wht is th totl powr dlivrd y th ttry if th lightuls r connctd () in sris? () In prlll? (c) For which connction will th lightuls shin th rightst? 51. Th vlu of rsistor is to dtrmind using th mmtrvoltmtr stup shown in Figur P Th mmtr hs rsistnc of 0.500, nd th voltmtr hs rsistnc of 20.0 k. Within wht rng of ctul vlus of will th msurd vlus corrct to within 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

7 Prolms % if th msurmnt is md using th circuit shown in () Figur P28.51 nd () Figur P28.51? Figur P28.56 () Figur P ttry is usd to chrg cpcitor through rsistor s shown in ctiv Figur how tht hlf th nrgy supplid y th ttry pprs s intrnl nrgy in th rsistor nd hlf is stord in th cpcitor. 53. Th vlus of th componnts in simpl sris circuit contining switch (ctiv Fig ) r 1.00 mf, 10 6, nd t th instnt 10.0 s ftr th switch is thrown to, clcult () th chrg on th cpcitor, () th currnt in th rsistor, (c) th rt t which nrgy is ing stord in th cpcitor, nd (d) th rt t which nrgy is ing dlivrd y th ttry. 54. young mn owns cnistr vcuum clnr mrkd 535 W t 120 nd olkswgn Btl, which h wishs to cln. H prks th cr in his prtmnt prking lot nd uss n inxpnsiv xtnsion cord 15.0 m long to plug in th vcuum clnr. You my ssum th clnr hs constnt rsistnc. () If th rsistnc of ch of th two conductors in th xtnsion cord is 0.900, wht is th ctul powr dlivrd to th clnr? () If instd th powr is to t lst 525 W, wht must th dimtr of ch of two idnticl coppr conductors in th cord h uys? (c) pt prt () ssuming th powr is to t lst 532 W. uggstion: symolic solution cn simplify th clcultions. 55. Thr 60.0-W, 120- lightuls r connctd cross 120- powr sourc s shown in Figur P Find () th totl powr dlivrd to th thr lightuls nd () th potntil diffrnc cross ch. ssum th rsistnc of ch lightul is constnt (vn though in rlity th rsistnc might incrs mrkdly with currnt). () 57. n idl voltmtr connctd cross crtin frsh ttry rds 9.30, nd n idl mmtr rifly connctd cross th sm ttry rds W sy tht th ttry hs n opn-circuit voltg of 9.30 nd shortcircuit currnt of () Modl th ttry s sourc of mf in sris with n intrnl rsistnc r. Dtrmin oth nd r. () n irrsponsil xprimntr conncts 20 of ths idnticl ttris togthr s suggstd in Figur P Do not try this xprimnt yourslf! Find th opn-circuit voltg nd th short-circuit currnt of th st of connctd ttris. (c) ssum th rsistnc twn th plms of th xprimntr s two hnds is 120. Find th currnt in his ody tht would rsult if his plms touchd th two xposd trminls of th st of connctd ttris. (d) Find th powr tht would dlivrd to his ody in this sitution. () Thinking it is sf to do so, th xprimntr thrds coppr wir insid his shirt twn his hnds, lik mittn string. To rduc th currnt in his ody to 5.00 m whn h prsss th nds of th wir ginst th ttry pols, wht should th rsistnc of th coppr wir? (f) Find th powr dlivrd to his ody in this sitution. (g) Find th powr dlivrd to th coppr wir. (h) Explin why th sum of th two powrs in prts (f) nd (g) is much lss thn th powr clcultd in prt (d). Is it mningful to sk whr th rst of th powr is going? ichrd McGrw Figur P28.57 Figur P witch shown in Figur P28.56 hs n closd for long tim nd th lctric circuit crris constnt currnt. Tk mf, mf, k, nd k. Th powr dlivrd to 2 is 2.40 W. () Find th chrg on 1. () Now th switch is opnd. ftr mny millisconds, y how much hs th chrg on 2 chngd? 58. Four rsistors r connctd in prlll cross ttry. Thy crry currnts of 150 m, 45.0 m, 14.0 m, nd 4.00 m. () If th rsistor with th lrgst rsistnc is rplcd with on hving twic th rsistnc, wht is th rtio of th nw currnt in th ttry to th originl currnt? () Wht If? If instd th rsistor with th smllst rsistnc is rplcd with on hving twic th rsistnc, wht is th rtio of th nw totl currnt to th originl currnt? (c) On Frury night, nrgy lvs 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

8 806 hptr 28 Dirct urrnt ircuits hous y svrl nrgy lks, including th following: W y conduction through th ciling, 450 W y infiltrtion (irflow) round th windows, 140 W y conduction through th smnt wll ov th foundtion sill, nd 40.0 W y conduction through th plywood door to th ttic. To produc th iggst sving in hting ills, which on of ths nrgy trnsfrs should rducd first? Explin how you dcid. lifford wrtz suggstd th id for this prolm. 59. Figur P28.59 shows circuit modl for th trnsmission of n lctricl signl such s cl T to lrg numr of suscrirs. Ech suscrir conncts lod rsistnc L twn th trnsmission lin nd th ground. Th ground is ssumd to t zro potntil nd l to crry ny currnt twn ny ground connctions with ngligil rsistnc. Th rsistnc of th trnsmission lin twn th connction points of diffrnt suscrirs is modld s th constnt rsistnc T. how tht th quivlnt rsistnc cross th signl sourc is q T L T 2 2 1>2 T 4 uggstion: Bcus th numr of suscrirs is lrg, th quivlnt rsistnc would not chng noticly if th first suscrir cncld th srvic. onsquntly, th quivlnt rsistnc of th sction of th circuit to th right of th first lod rsistor is nrly qul to q. T T T 62. Th circuit shown in Figur P28.62 is st up in th lortory to msur n unknown cpcitnc with th us of voltmtr of rsistnc 10.0 M nd ttry whos mf is Th dt givn in th tl r th msurd voltgs cross th cpcitor s function of tim, whr t 0 rprsnts th instnt t which th switch is opnd. () onstruct grph of ln(/ ) vrsus t nd prform linr lst-squrs fit to th dt. () From th slop of your grph, otin vlu for th tim constnt of th circuit nd vlu for th cpcitnc. () t (s) ln(e/ ) ignl sourc L L L oltmtr Figur P28.62 Figur P rgulr ttrhdron is pyrmid with tringulr s. ix rsistors r plcd long its six dgs, with junctions t its four vrtics ttry is connctd to ny two of th vrtics. Find () th quivlnt rsistnc of th ttrhdron twn ths vrtics nd () th currnt in th ttry. 61. In Figur P28.61, suppos th switch hs n closd for tim intrvl sufficintly long for th cpcitor to com fully chrgd. Find () th stdy-stt currnt in ch rsistor nd () th chrg Q on th cpcitor. (c) Th switch is now opnd t t 0. Writ n qution for th currnt I 2 in 2 s function of tim nd (d) find th tim intrvl rquird for th chrg on th cpcitor to fll to on-fifth its initil vlu. 63. Th studnt nginr of cmpus rdio sttion wishs to vrify th ffctivnss of th lightning rod on th ntnn mst (Fig. P28.63). Th unknown rsistnc x is twn points nd E. Point E is tru ground, ut it is inccssil for dirct msurmnt cus this strtum is svrl mtrs low th Erth s surfc. Two idnticl rods r drivn into th ground t nd B, introducing n unknown rsistnc y. Th procdur is s follows. Msur rsistnc 1 twn points nd B, thn connct nd B with hvy conducting wir nd msur rsistnc 2 twn points nd. () Driv n qution for x in trms of th osrvl rsistncs, 1 nd 2. () stisfctory ground rsistnc would x. Is th grounding of th sttion dqut if msurmnts giv nd ? 12.0 k B = 15.0 k 10.0 mf 3.00 k y x y E Figur P28.63 Figur P Th switch in Figur P28.64 closs whn c 2 /3 nd opns whn c /3. Th voltmtr rds 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

9 nswrs to Quick Quizzs 807 potntil diffrnc s plottd in Figur P Wht is th priod T of th wvform in trms of 1, 2, nd? oltgcontrolld switch c (t) T 1 2 () () Figur P28.64 c 65. n lctric tkttl hs multiposition switch nd two hting coils. Whn only on coil is switchd on, th wll- t insultd kttl rings full pot of wtr to oil ovr th tim intrvl t. Whn only th othr coil is switchd on, it tks tim intrvl of 2 t to oil th sm mount of wtr. Find th tim intrvl rquird to oil th sm mount of wtr if oth coils r switchd on () in prlll connction nd () in sris connction. 66. In plcs such s hospitl oprting rooms or fctoris for lctronic circuit ords, lctric sprks must voidd. prson stnding on groundd floor nd touching nothing ls cn typiclly hv ody cpcitnc of 150 pf, in prlll with foot cpcitnc of 80.0 pf producd y th dilctric sols of his or hr shos. Th prson cquirs sttic lctric chrg from intrctions with furnitur, clothing, quipmnt, pckging mtrils, nd ssntilly vrything ls. Th sttic chrg flows to ground through th quivlnt rsistnc of th two sho sols in prlll with ch othr. pir of rur-sold strt shos cn prsnt n quivlnt rsistnc of M. pir of shos with spcil sttic-dissiptiv sols cn hv n quivlnt rsistnc of 1.00 M. onsidr th prson s ody nd shos s forming n circuit with th ground. () How long dos it tk th rursold shos to rduc prson s potntil from to 100? () How long dos it tk th sttic-dissiptiv shos to do th sm thing? nswrs to Quick Quizzs 28.1 (). Powr is dlivrd to th intrnl rsistnc of ttry, so dcrsing th intrnl rsistnc dcrss this lost powr nd incrs th prcntg of th powr dlivrd to th dvic (). Whn th switch is opnd, rsistors 1 nd 2 r in sris, so th totl circuit rsistnc is lrgr thn whn th switch ws closd. s rsult, th currnt dcrss (). Whn th switch is closd, rsistors 1 nd 2 r in prlll, so th totl circuit rsistnc is smllr thn whn th switch ws opn. s rsult, th currnt incrss (i), (). dding nothr sris rsistor incrss th totl rsistnc of th circuit nd thrfor rducs th currnt in th circuit. (ii), (). Th potntil diffrnc cross th ttry trminls incrss cus th rducd currnt rsults in smllr voltg dcrs cross th intrnl rsistnc. (iii), (). If third rsistor wr connctd in prlll, th totl rsistnc of th circuit would dcrs nd th currnt in th ttry would incrs. (iv), (). Th potntil diffrnc cross th trminls would dcrs cus th incrsd currnt rsults in grtr voltg drop cross th intrnl rsistnc (i), (c). Just ftr th switch is closd, thr is no chrg on th cpcitor. urrnt xists in oth rnchs of th circuit s th cpcitor gins to chrg, so th right hlf of th circuit is quivlnt to two rsistncs in 1 prlll for n quivlnt rsistnc of 2. (ii), (d). ftr long tim, th cpcitor is fully chrgd nd th currnt in th right-hnd rnch drops to zro. Now, currnt xists only in rsistnc cross th ttry. 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning