CHAPTER 18: Electric Currents. Answers to Questions

Transcription

1 CHTE : Elecric Currens nswers Quesins. mpere-hurs measures charge. The ampere is a charge per uni ime, an he hur is a ime, s he pruc is charge. mpere-hur f charge is 6 Culmbs f charge.. n he circui (n in he baery), elecrns flw frm high penial energy (a he negaive erminal) lw penial energy (a he psiive erminal). nsie he baery, he chemical reacin es wrk n he elecrns ake hem frm lw penial energy high penial energy ( he negaive erminal). mre chemical escripin says ha he chemical reacin aking place a he negaive elecre leaves elecrns behin n he erminal, an he psiive ins creae a he negaive elecre pull elecrns ff he psiive elecre.. Baery energy is wha is being use up. s charges leave he baery erminal, hey have a relaively high penial energy. Then as he charges mve hrugh he flashligh bulb, hey lse penial energy. The baery uses a chemical reacin replace he penial energy f he charges, by lwering he baery s chemical penial energy. When a baery is use up, i is unable give penial energy charges.. The ne erminal f he baery (usually he negaive ne) is cnnece he meal chassis, frame, an engine blck f he car. This means ha all vlages use fr elecrical evices in he car are measure wih respec he car s frame. ls, since he frame is a large mass f meal, i can supply charges fr curren wihu significanly changing is elecrical penial. 5. Waer flws immeiaely frm he spu because here is alreay waer in he spu when yu urn n he fauce. Since waer is (essenially) incmpressible, a push n he waer frm sme isan lcain (a he valve r pump) causes all he waer mve alms immeiaely, pushing he waer u f he spu. n a baery, a similar phenmenn exiss in ha he wires are full f charges (free elecrns). The vlage push frm he baery pushes all he elecrns alng he wire alms immeiaely, an he firs nes a he her en f he wire are he beginnings f he elecric curren. 6. esisance is given by he relainship. f he rai f resisiviy area is he same fr bh he cpper wire an he aluminum wire, hen he resisances will be he same. Thus if r, he resisances will be he same. Cu Cu l l l Cu l Cu ls, resisance changes wih emperaure. By having he w wires a ifferen emperaures, i migh be pssible have heir resisance he same. 7. We assume ha he vlage is he same in bh cases. Then if he resisance increases, he pwer elivere he heaer will ecrease accring. f he pwer ecreases, he heaing prcess will slw wn.. esisance is given by he relainship. Thus, minimize he resisance, yu shul have a small lengh an a large crss-secinal area. ikewise, maximize he resisance, yu shul have a large lengh an a small crss-secinal area. (a) Fr he leas resisance, cnnec he wires he faces ha have imensins f a by a, which maximizes he area (6a ) an minimizes he lengh (a). 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 7

2 Chaper Elecric Currens (b) Fr he greaes resisance, cnnec he wires he faces ha have imensins f a by a, which minimizes he area (a ) an minimizes he lengh (a). 9. T say ha inicaes a ecrease in pwer as resisance increases implies ha he vlage is cnsan. T say ha inicaes an increase in pwer as resisance increases implies ha he curren is cnsan. Only ne f hse can be rue fr any given siuain. f he resisance changes an he vlage is cnsan, hen he curren mus als change. ikewise, if he resisance changes an he curren is cnsan, hen he vlage mus als change.. When a ligh bulb burns u, is filamen burns in w. Since he filamen is par f he cnucing pah fr he elecriciy flwing hrugh he bulb, nce he filamen is brken, curren can n lnger flw hrugh he bulb, an s i n lnger gives ff any ligh.. When a ligh bulb is firs urne n, i will be cl an he filamen will have a lwer resisance han when i is h. This lwer resisance means ha here will be mre curren hrugh he bulb while i is cl. This mmenary high curren will make he filamen quie h. f he emperaure is high, he filamen will vaprize, an he curren will n lnger be able flw in he bulb.. ssuming ha bh ligh bulbs have he same vlage, hen since, he higher pwer bulb will raw he ms curren. ikewise assuming ha bh ligh bulbs have he same vlage, since, he higher pwer bulb will have he lwer resisance. S he W bulb will raw he ms curren, an he 75 W bulb will have he higher resisance.. Transmissin lines have resisance, an herefre will change sme elecrical energy hermal energy (hea) as he elecrical energy is ransmie. We assume ha he resisance f he ransmissin lines is cnsan. Then he ls pwer is given by, where is he curren carrie by he ransmissin lines. The ransmie pwer is given by rans vlage acrss he ransmissin lines. Fr a given value f rans lwer he curren has be. s he curren is ecrease, a lwer amun f pwer ls. 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he ls ls, where is he, he higher he vlage is, he is als ecrease, an s here is. The 5- fuse is blwing because he circui is carrying mre han 5 f curren. The circui is prbably esigne nly carry 5, an s here migh be a shr r sme her malfuncin causing he curren excee 5. eplacing he 5- fuse wih a 5- fuse will allw mre curren flw an hus make he wires carrying he curren ge her. fire migh resul, r amage cerain kins f elecrical equipmen. The blwn fuse is a warning ha smehing is wrng wih he circui. 5. nly Hz, he meal filamen in he wire will g n an ff imes per secn. ( has a maximum magniue f curren a he maximum curren in each irecin.) The meal filamen has ime cl wn an ge im uring he lw curren pars f he cycle, an yur eye can eec his. 5 r 6 Hz, he filamen never cls enugh im significanly. 6. There are several facrs which can be cnsiere. s he vlage reverses wih each cycle f C, he penial energy f he elecrns is raise again. Thus wih each pass hrugh he ligh, he elecrns lse heir penial energy, an hen ge i back again. Secnly, he heaing f he filamen (which causes he ligh) es n epen n he irecin f he curren, bu nly ha a curren exiss, s he ligh ccurs as he elecrns mve in bh irecins. ls, a 6 Hz, he curren peaks

3 Giancli hysics: rinciples wih pplicains, 6 h Eiin imes per secn. The small amun f ime while he magniue f he curren is small is n lng enugh fr he h meal filamen cl wn, s i says li he enire cycle. Finally, he human eye sees anyhing mre rapi han abu Hz as cninuus, even if i is n. S even if he ligh was g im uring par f he cycle, ur eyes wul n eec i. 7. When he aser is firs urne n, he Nichrme wire is a rm emperaure. The wire sars hea up alms immeiaely. Since he resisance increases wih emperaure, he resisance will be increasing as he wire heas. ssuming he vlage supplie is cnsan, hen he curren will be ecreasing as he resisance increases.. Curren is NOT use up in a resisr. The same curren flws in he resisr as flws u f he resisr. f ha were n he case, here wul be eiher an increase r ecrease in he charge f he resisr, bu he resisr acually says neural, inicaing equal flw in an u. Wha es ge use up is penial energy. The charges ha cme u f a resisr have lwer penial energy han he charges ha g in he resisr. The amun f energy ecrease per uni ime is given by. 9. (a) Wih he baeries cnnece in series, he vlage acrss he bulb is higher, an s mre curren will flw. Tha will make he bulb glw brigher. (b) Wih he baeries cnnece in parallel, each baery wul nly have prvie half he al curren ligh he bulb, meaning ha he evice cul be n lnger befre he baeries ran wn, as cmpare a single baery. ls, if ne baery shul fail, he her baery can sill prvie he curren ligh he bulb. Sluins rblems. Use he efiniin f curren, Eq. -. Q.C elecrn.. elecrns s 9 s.6 C. Use he efiniin f curren, Eq. -. Q 5 Q h 6s h. C. Use he efiniin f curren, Eq. -. Q 9 ins.6 C in 6.5 s 5.5. Use Eq. -a fr resisance Use Eq. -b fr he vlage earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 9

4 Chaper Elecric Currens 6. (a) Use Eq. -a fr resisance (b) Use he efiniin f curren, Eq. -. Q Q 7.5 5min 6s min 6. C 7. (a) Use Eq. -b fin he curren (b) Use he efiniin f curren, Eq. -. Q Q 5 5 min 6s min 7.5 C. Fin he curren frm he vlage an resisance, an hen fin he number f elecrns frm he curren C elecrn 6s elecrns min 9 s.6 C min 9. Fin he penial ifference frm he resisance an he curren..5 m. m (a) f he vlage rps by 5%, an he resisance says he same, hen by Eq. -b,, he curren will als rp by 5%. final iniial (b) f he resisance rps by 5% (he same as being muliplie by.5), an he vlage says he same, hen by Eq. -b, he curren mus be ivie by iniial final (a) Use Eq. -a fin he resisance..6 (b) n amun f charge Q lses a penial energy f Q as i passes hrugh he resisr. The amun f charge is fun frm Eq. -. E Q.6 6s J 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 5

5 Giancli hysics: rinciples wih pplicains, 6 h Eiin. Use Eq. - fin he iameer, wih he area as r.. m 5.6 m..7 m. Use Eq. - calculae he resisance, wih he area as r..5m.6 m..5 m. Use Eq. - calculae he resisances, wih he area as. l l l l l l Cu Cu Cu Cu Cu l Cu Cu.65 m. m.5mm.6 m. m. mm 5. Use Eq. - express he resisances, wih he area as. W Cu W Cu W Cu r, an s. r, an s 5.6 m W.5mm W Cu Cu.6 m The iameer f he ungsen shul be.6 mm..6mm 6. Since he resisance is irecly prprinal he lengh, he lengh f he lng piece mus be. imes he lengh f he shr piece.. 5..,. shr lng shr shr shr shr lng Make he cu a % f he lengh f he wire..,...,.. shr lng shr lng 7. Use Eq. - muliplie by s ha i expresses resisance insea f resisiviy. T T.5 T T.5 T T C S raise he emperaure by C C a final emperaure f C. 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 5

6 Chaper Elecric Currens. Use Eq. - fr he resisiviy. T T T T Cu Cu Cu W T C 5.6 m 6. C 6 C.6 C W.6 m Cu Cu 9. Use Eq. - muliplie by s ha i expresses resisances insea f resisiviy. T T T T C 79 C C.6 C. Calculae he vlage rp by cmbining Ohm s aw (Eq. -b) wih he expressin fr resisance, Eq m 6 m.5.6 m. n each case calculae he resisance by using Eq. - fr resisance. (a) (b) (c) x y z yz xz xy x y z 5. m. m.75.. m. m 5. m. m. m. m 5. m. m. m. m The wires have he same resisance an he same resisiviy. lng shr shr shr lng lng shr lng shr shr. The riginal resisance is, an he high emperaure resisance is, where he w vlages are he same. The w resisances are relae by Eq. -, muliplie by s ha i expresses resisance insea f resisiviy. T T T T T T.. C 5. C.9 C.6 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 5

7 Giancli hysics: rinciples wih pplicains, 6 h Eiin. (a) Calculae each resisance separaely using Eq. -, an hen a he resisances geher fin he al resisance..6 Cu Cu m 5. m Cu. m l l m 5. m l. m.67 al Cu l (b) The curren hrugh he wire is he vlage ivie by he al resisance al (c) Fr each segmen f wire, Ohm s aw is rue. Bh wires have he curren fun in (b) abve. Cu l Cu l Nice ha he al vlage is 5 m. 5. The al resisance is be 7 hms a all emperaures. Wrie each resisance in erms f al Eq. - (wih T C ), muliplie by express resisance insea f resisiviy. T T T T al C C N N C C C N N N T C N C C N N Fr he abve be rue, he erms wih a emperaure epenence mus cancel, an he erms wihu a emperaure epenence mus a. Thus we have w equains in w unknwns. T C C N N N al C N C C N C C N C C N C N C al N C N al. C 7. C.5 C N al C 6 6. Use Eq. -6b fin he resisance frm he vlage an he pwer. W 7. Use Eq. -5 fin he pwer frm he vlage an he curren W 7 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 5

8 Chaper Elecric Currens. Use Eq. -6b fin he vlage frm he pwer an he resisance. 7.5 W 6 9. Use Eq. -6b fin he resisance, an Eq. -5 fin he curren. (a) (b) 75W W.65.6 W.7 W (a) Use Eq. -5 fin he curren. W.96 5 (b) Use Eq. -6b fin he resisance. 5 W 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 5. (a) Since says ha he resisance is inversely prprinal he pwer fr a cnsan vlage, we preic ha he 5 W seing has he higher resisance. (b) (c) 5 W 5 W 7. The pwer (an hus he brighness) f he bulb is prprinal he square f he vlage, accring Eq. -6a,. Since he resisance is assume be cnsan, if he vlage is cu in half frm, he pwer will be reuce by a facr f. Thus he bulb will appear nly abu / as brigh in he Unie Saes as in Eurpe.. T fin he kwh f energy, muliply he kilwas f pwer cnsumpin by he number f hurs in perain. kw h Energy in kw in h 55 W 5 min.75 kwh. kwh W 6min T fin he cs f he energy use in a mnh, muliply imes ays per week f usage, imes weeks per mnh, imes he cs per kwh.

9 Giancli hysics: rinciples wih pplicains, 6 h Eiin kwh week 9.cens Cs.75 cens mnh week mnh kwh. T fin he cs f he energy, muliply he kilwas f pwer cnsumpin by he number f hurs in perain imes he cs per kwh. kw h $.95 Cs 5 W 65ay $ W ay kwh 5. (a) Calculae he resisance frm Eq. -a, an he pwer frm Eq W. W.5 (b) f fur D-cells are use, he vlage will be uble 6.. ssuming ha he resisance f he bulb says he same (by ignring heaing effecs in he filamen), he pwer ha he bulb wul nee issipae is given by Eq. -6b,. ubling f he vlage means he pwer is increase by a facr f. This shul n be rie because he bulb is prbably n rae fr such a high waage. The filamen in he bulb wul prbably burn u, an he glass bulb migh even exple if he filamen burns vilenly. 6. The h raing is he amun f charge ha he baery can eliver. The penial energy f he charge is he charge imes he vlage. 6s 6 E Q 5 h.7 J h 7. Each bulb will raw an amun f curren fun frm Eq. -5. bulb The number f bulbs raw 5 is he al curren ivie by he curren per bulb. 5 al n n n bulbs al bulb W. Fin he pwer issipae in he cr by Eq. -6a, using Eq. - fr he resisance..7 m 5..6 m 6 W.9 m 9. Fin he curren use eliver he pwer in each case, an hen fin he pwer issipae in he resisance a he given curren. = issipae 5 6. W issipae. W,. 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 55

10 Chaper Elecric Currens 5 6. W issipae. 6W ifference W 6W 7.5 W 5, 5. The waer emperaure rises by absrbing he hea energy ha he elecrmagne issipaes. Express bh energies in erms f pwer, which is energy per uni ime. Q mc T hea waer elecric hea waer m c T J kg C 7.5C This is abu ml per secn.. kg s.kg s. (a) By cnservain f energy an he efficiency claim, 6% f he elecrical pwer issipae by he heaer mus be he rae a which energy is absrbe by he waer. Q mc T hea waer.6.6 emie by absrbe elecrmagne by waer. kg 6 J kg 95 C 5 C mc T.6.6 s (b) Use Ohm s aw fin he resisance f he heaer...7. Use Ohm s law an he relainship beween peak an rms values. rms. peak rms..7. Fin he peak curren frm Ohm s law, an hen fin he rms curren frm he relainship beween peak an rms values. peak peak rms peak (a) When everyhing elecrical is urne ff, n curren will be flwing in he huse, even hugh a vlage is being supplie. Since fr a given vlage, he mre resisance, he lwer he curren, a zer curren crrespns an infinie resisance. (b) ssuming ha he vlage is, use Eq. -6a calculae he resisance. = W 5. The pwer an curren can be use fin he peak vlage, an hen he rms vlage can be fun frm he peak vlage. peak 5 W.9 rms rms rms rms 5. peak 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 56

11 Giancli hysics: rinciples wih pplicains, 6 h Eiin 6. Use he average pwer an rms vlage calculae he peak vlage an peak curren. (a) (b) peak rms peak rms rms rms peak rms W (a) We assume ha he. hp is he average pwer, s he maximum pwer is wice ha, r 6. hp, as seen in Figure W 6. hp 76 W.5 W hp (b) Use he average pwer an he rms vlage fin he peak curren. peak rms rms rms peak rms 76 W. (a) The average pwer use can be fun frm he resisance an he rms vlage by Eq. -9c. rms 69 W.7 W (b) The maximum pwer is wice he average pwer, an he minimum pwer is. max 69 W. W W min 9. We fllw exacly he erivain in Example -, which resuls in an expressin fr he rif velciy. m v ne N mle N e D e D m mle kg kg m.6 C.65 m 5. (a) Use Ohm s aw fin he resisance (b) Fin he resisiviy frm Eq m r 5. m (c) Fin he number f elecrns per uni vlume frm Eq. -. nev n ev e r v C. m.7 m s 5. m s.6 m. e m 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 57

12 Chaper Elecric Currens 5. We are given a charge ensiy an a spee (like he rif spee) fr bh ypes f ins. Frm ha we can use Eq. - eermine he curren per uni area. Bh currens are in he same irecin in erms f cnveninal curren psiive charge mving nrh has he same effec as negaive charge mving suh an s hey can be ae. nev nev He nev.6 m, Nrh O 9 6. ins m.6 C in. m s ins m.6 C in 7. m s 5. The magniue f he elecric fiel is he vlage change per uni meer. E x 7. m 6 7. m 5. The spee is he change in psiin per uni ime. x 7. m. m v 5 m s.6s.5 s Tw measuremens are neee because here may be a ime elay frm he simulain f he nerve he generain f he acin penial. 5. The energy require ransmi ne pulse is equivalen he energy sre by charging he axn capaciance full vlage. n Example -5, he capaciance is esimae a. F, an he penial ifference is abu.. E C.5 F. 5 J The pwer is he energy per uni ime, fr, neurns ransmiing pulses each per secn. E 5 J neurn. neurns 5 5 W.s 55. The pwer is he wrk ne per uni ime. The wrk ne mve a charge hrugh a penial ifference is he charge imes he penial ifference. The charge ensiy mus be muliplie by he surface area f he cell (he surface area f an pen ube, lengh imes circumference) fin he acual charge mve. W Q Q 7 ml ins 9 C m m. m s ml in 9 5. W 56. C s 6s. h 6 C h 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 5

13 Giancli hysics: rinciples wih pplicains, 6 h Eiin 57. Use Eq. -5 calculae he curren. 76 W The energy supplie by he baery is he energy cnsume by he lighs. E E Q supplie Q cnsume 95 h 6s h h 69s.9 h h 9 W 6s 59. Use Eq. -6 express he resisance in erms f he pwer, an Eq. - express he resisance in erms f he wire gemery. r 9.7 m 5. m 5 W.9 m 6. Frm Eq. -a, if, hen G G.7.S. 6. T eliver MW f pwer a requires a curren f pwer issipae in he resisrs using he curren an he resisance.,.6 m r 7.7 W 7 Cs wer ime rae per kwh.7 W h $7 $, per hur per meer 7 W, kw $. W kwh. Calculae he. m 5. m 6. (a) Calculae he al kwh use per ay, an hen muliply by he number f ays an he cs per kwh.. kw. h.kw 6. h. kw. h. kwh. kwh $.5 Cs. kwh $. per mnh kwh 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 59

14 Chaper Elecric Currens (b) The energy require by he husehl is 5% f he energy ha nees be supplie by he pwer plan. Husehl Energy.5 cal mass cal energy per mass cal mass Husehl Energy. kwh 65 W 6s kw.5 cal energy per mass kcal 6 J.5 7 kg kcal h 79 kg kg f cal 6. The lengh f he new wire is half he lengh f he riginal wire, an he crss-secinal area f he new wire is wice ha f he riginal wire. Use Eq. -. The new resisance is ne-furh f he riginal resisance. 6. (a) Use Eq. -6 relae he pwer he vlage fr a cnsan resisance r a 9.5% ecrease (b) The lwer pwer upu means ha he resisr is generaing less hea, an s he resisr s emperaure wul be lwer. The lwer emperaure resuls in a lwer value f he resisance, which wul increase he pwer upu a he lwer vlages. Thus he ecrease wul be smewha smaller han he value given in he firs par f he prblem. 65. ssume ha we have a meer f wire, carrying 5 f curren, an issipaing. W f hea. The pwer issipae is, an he resisance is. r.6 m. m 5. m. W 66. (a) The angular frequency is ra s. ra s f. Hz (b) The maximum curren is... max rms.7 (c) Fr a resisr,.. sin sin 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 6

15 Giancli hysics: rinciples wih pplicains, 6 h Eiin 67. (a) The pwer elivere he inerir is 65% f he pwer rawn frm he surce. 95 W inerir.65 6 W 5 W inerir surce surce (b) The curren rawn is curren frm he surce, an s he surce pwer is use calculae he curren. 6 W surce surce surce. surce 6. The vlume f wire is unchange by he sreching. The vlume is equal he lengh f he wire imes is crss-secinal area, an s since he lengh was increase by a facr f, he area was ecrease by a facr f. Use Eq The lng, hick cnucr is labele as cnucr number, an he shr, hin cnucr is labele as number. The pwer ransfrme by a resisr is given by Eq. -6, same vlage applie. iameer iameer : :,an bh have he 7. The heaer mus hea m f air per hur frm 5 C C, an als replace he hea being ls a a rae f 5 kcal/h. Use Eq. - calculae he energy neee hea he air. The ensiy f air is fun in Table -. Q m Q mc T c T m kg kcal kcal h m kg C h.9.7 5C kcal kcal kcal 6 J h wer require W 5 W h h h kcal 6 s 7. (a) Use Eq W (b) Only 75% f he hea frm he ven is use hea he waer..75 Hea absrbe by waer mc T ven mc T ven kg. 6 J kg C 5C W 5.s 6 s 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 6

16 Chaper Elecric Currens (c) cens kwh h. kw 5.s.7 cens 6 s 7. (a) The hrsepwer require is he pwer issipae by he fricinal frce, since we are neglecing he energy use fr accelerain. Fv m s hp N 5 km hr W. hp.6 km hr 76 W 5 (b) The charge available by each baery is Q 95 h 95C s 6s. C, an s he al charge available is imes ha. The penial energy f ha charge is he charge imes he vlage. Tha energy mus be elivere (baeries ischarge) in a cerain amun f ime pruce he W necessary. The spee f he car imes he ischarge ime is he range f he car beween recharges. E Q Q v Q Q Q v v v Fv F 5. C N km 7. The mass f he wire is he ensiy f cpper imes he vlume f he wire, an he resisance f he wire is given by Eq. -. We represen he mass ensiy by an he resisiviy by. m m m m m m. kg.5.9 kg m.6 m.79 m. m.6 m.79 m.5.5 m 7. Use Eq. -6. (a) W (b) W W 75. Mel he prns as mving in a cninuus beam f crss-secinal area. Then by Eq. -, N nev. The variable n is he number f prns per uni vlume, s n, where N is he l number f prns in he beam an l is he circumference f he ring. The rif velciy in his case is he spee f ligh. N N nev ev ev l l 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 6

17 Giancli hysics: rinciples wih pplicains, 6 h Eiin N l ev 6 m 9.6 C. m s. prns 76. (a) The pwer is given by. (b) The pwer issipae is given by (c) 6W 6 W r 7 W.6 m 5 m.5 m, an he resisance is..6 m 5 m 7.W.6 m.96 W W () The savings is ue he pwer ifference. kw h $. Savings 7. W.96 W W kwh $.795 / mnh cens per mnh 77. The resisance can be calculae frm he pwer an vlage, an hen he iameer f he wire can be calculae frm he resisance. m. m 95 W. m 7. Use Eq. -6 fr he pwer in each case, assuming he resisance is cnsan % increase (a) The curren can be fun frm Eq. -5. W. W. B B B (b) The resisance can be fun frm Eq. -6. B B 6.6 W W B (c) The charge is he curren imes he ime. Q Q. 6s C Q B B. 6s,C 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 6

18 Chaper Elecric Currens () The energy is he pwer imes he ime, an he pwer is he same fr bh bulbs. E E E B 5 W 6s. J (e) Bulb B requires a larger curren, an s shul have larger iameer cnnecing wires avi verheaing he cnnecing wires.. The curren in he wire can be fun by. (a) 5 W r.6 m 5. m.59 m. W (b) 5 W.6 m 5. m. m.w. Eq. - can be use. The area be use is he crss-secinal area f he pipe. r r usie insie.6 m. m.5 m.5 m.. The vlume f wire lume lengh crss-secinal area remains cnsan as he wire is sreche frm he riginal lengh f he final lengh f. Thus he crss-secinal area changes frm. Use Eq. - fr he resisance an -6 fr he pwer issipae. The pwer is reuce by a facr f.. The resisance f he filamen when he flashligh is n is wih a cmbinain f Eqs. - an - fin he emperaure. T T T T. 6. C 6 6 C C.5 C.5. Tha can be use 5 earsn Eucain, nc., Upper Sale iver, NJ. ll righs reserve. This maerial is prece uner all cpyrigh laws as hey currenly exis. N prin f his maerial may be repruce, in any frm r by any means, wihu permissin in wriing frm he 6