106-20002-MT2 - 3 7 PROBLEM (I) (25 points) A capacitor...

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Unformatted text preview: 3 7 PROBLEM (I) (25 points) A capacitor with capacitance C1 = SDFF is charged to a C- potential difi'erence oidflfl V. disconnected from the ] charging source, and then connected in parallel to an uncharged capacitor with capacitance C; = 10 pF, as shown in the figure. (a) Find the final charges on die capacitors. {12 pro.) ‘11; = CWIL" my mm): am: an“; =0 Cflb‘iSlrUm'I-i {if Glam; ‘; anti-qt;- : Q's +fiaf 'T‘M. ' r' ' 1ch 15'- and. Bo enclccqari'lor [AMMI fifimfirfiif‘igyfl x: which Edam fli‘lnl cluufle GM “(Ayn-1M. Than, F -'_ ‘Jlfzzf=v; .._) M=Mfiq1fafifiif=%fitf.squ 3 " _ %qf:ih MC. _ “IV—1r" . (b) Find the cncrgy lost when the connection is made (13 pta.) o Ur”. ‘ Uri. + :5. '-‘- L-‘i-IVIE = %‘(3fi)’-FHWW)L=2-HJ " '5 I --5 e a _ ‘1'; “l1; _ (hm r.) [ham :1 U} Ulii‘uq — fill-Ci + 1:1. - CoyF + 2a)“? '— ‘S'L = ~ ~ =13 — 03-1-3233 dBBJ-i-c‘fifi J Emm “Iii ‘ 0-6 I -! ?K|‘O C f- L i' t c. J— qlf 1—1 Ncagri Uf = i" 5-1“? “ 1. “HQ-3‘? 2 (9+nglj-; (5‘4ny 3””. Phys ME Second We”: Page 335 April 23. 2001 3 8 PROBLEM (2) (’25 points) A parallel plate ca itor of plate separation d‘ is half filled with =| a dielectric alah dielectric constant it {2 5} as shown in the I figure. W, it is charged tea potential _ difierenee Vand then disconnected from the charging source. The capacitance of the capacitor in the absence of the slab is C. Give your answers in terms of C. V, and d. (a) What is the capacitance when the slab is present? (5 pts.) it 1" I l - l1 = _.l L— _'--=-‘-‘- +L- '" ---""i”-'- EEJM’; "‘ .pf «1+1 - +1 1 c“ Cpl CL ZKL 1‘. Cl. C}. CH :fE(—'E+l)=3iz(—Efil) Curly-é- “ _z.rcc. 41.15 a came. ; =2neé-sz'tc C“ an "—g—l'.‘ . c. cant-4&5 .21.,11- 1:. “1.5.? {b} What is the magnitude of the electric field in the slab? {6 pts.) L an. a»; fickd-rie am Wan—plain at was“ C.) E -.- {'1 (The. W I r E: E 2’ 5a“ v 'wqifc' =._."_'._'. V a. V ‘m- ‘=--—'"‘ E1: :11.- ' d. etc, etc. meta 3- ;‘Efid 3‘” m=§1wL~Find 9‘1. m U‘ r -_- ml." std Essa“ n. %“n a. M“ E = la". d [W1 U ' 3 if! ‘ 4—“. -¢ (c) How much electmstatie potential energy is stored in the air gap behveen the slab and the upper plate? {6 pts.) L11: '? (The. grammar. re Hard at in sanqu I t. 1 al I._ 1' _ =§_C_E- JAIN-.2 “faith =E‘H‘Ei] “We “ma-co" a I“ 1 C I :__*___ 'L_ new" =2. w. J1 ' "_'_) u; (d) How.' much work is required to pull the slab completelyr out of the plates? (3 pts.) ,5. W-fi $::-I'I W : war-la. = dU:{é-UL w “i =L u‘:.'.. 2. 1-25 .5!- +1 film-Ht L} 2:: ZL(3UJ - in”: [ailiqu (i) new“! if) UL t .5. Q1 1;“: J5 (£35)u‘=%cul --_‘1__ ~ ' 1 '3- LL}- "*1 “Lam” s 5 a 1 Vi ‘ ‘5- .' ‘fir:-'§:'v W-icv" Phys lMSeeondMMtcrm Pascfli Mazes: - 3 9 PROBLEM (3) (25 points) In the 'vtm circuit, the potential difiercnc: across th: 1- resistor is 9 V. in) Find the equivalant resistant: between points a and b. (7 pts.) HI. m an. m .- u h mfl h m. iii-h. a _ (swam) =j‘l_1_ 9“. 5141-13-1 32. R. (:2) At what rate is the thurmal energy produced in the 24—52 resistor? {‘7 pts.) Lcoffch‘uc.):u-tstLJL')-(i1+15}(5fl)+t*[1‘t-’L}=a *EEVH‘OU+£1(LHJL}=0 I” Lt: p = 5.1 um) : (u. mth -—> if (d) 1What power is supplied by the. battery? ('1' pm.) 3M"ns and c: i..il+u‘.L= i,+£3+i.t c $A+M+H in“ L“f{‘°ha"”l\=-i.'{tltJL‘Jnt.{tJL)+g-_=g 'fi‘U—B'LV'I'E =0 3. E=Iuv a) Pt=£t=tlhfi]{lflu)-l Mlflfimflflflm Pwfl'fi ApriflflJflfli a a: G PROBLEM (4) (25 points) The switch Sin the given circuit is initially left open for a long time and then it is closed. {1 M9 = 105 Q) [a] Find the current through each resistor at the instant the switch 3 is closed. (7 pts.) "filer. capacitor is. undwatd htfitft Mwi'l'ch S is. closed. '5ch , It acts. we a chaff ciws'it at M classes 11w. wiich 5 Lee-1552.4 l; e ‘1th EMJL I I i r I I 1 - ' -. lit-l c:e,+c =3”- -3 =-- =- W ’ . *- ' *r " i“ H {In} Find the maximum charge that will appear on the capacitor during charging. (1 pts.) Lou/t3 fluf‘hd‘ 5 w C'lfitmégmmcihr is filth! We Md has “luster-insect darne- Nc sci-"mat fie-wt- flare-.ng m act-IL resists-revue «New, ssemwaaw “mmanwchmfl. w HML’tSHJL i VL': 1- it. use) = («spam are.) E; L V (c) Suppose the switch has been closed sufficiently long for the capacitor to become filly charged. The switch is now opened again at time I = {1. Find the initial current [that is. at t = D] in the discharge circuit.(5 pts.) ' WWW arouH'cl-t lid WI.) “flu. afidw<fillwduya¢d1fiu¥hw WM “’i‘wrwsk that. BMJLAMd turn. sews-ers- - 1'. = i- (M {asst came an mm} cum) 1‘s SMJL a tut . _ irrLU EMJL + L ‘ _ I. : tars-r ’ 6”“ We” a” ‘R' ~ {:1} Find the time that it takes for the charge on the capacitor to fall to one-half of its initial value (thfltifigfltr=fl}+{6 P'ts.) I Th1. cw o... ‘i'lu. credence“ W5. / _thfi .thfii’fi t “mam: -|-o t! 1;; . m e «a E Fr: - ac . . 6'1 it] = “im 8 Tent: «H. mm! iaymsiii WW; NM R E son't thi. .73 .‘qga-s'i-‘ML have RL- (‘iMlXWfiFli 705 FI I Phys 196 Second Midterm Page 6'6 April 28. 2001 ...
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This note was uploaded on 04/09/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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106-20002-MT2 - 3 7 PROBLEM (I) (25 points) A capacitor...

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