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106-20002-MT2

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

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

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