homework 13 - PH 132 SPRING 2005 HOMEWORK 13 Assigned W 50...

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Unformatted text preview: PH 132 SPRING 2005 HOMEWORK # 13 Assigned: 05/11/05 W 50 SHEETS 22-141 22442 IUD SHEETS 22-144 200 SHEETS NIP-I‘D ‘ {a} At what frequency would a 6.0 mH inductor and a 10 pF capacitor have the same reactance? (b) What would the reactancc be? (c) Show that this frequency would be the natural frequency of an oscillating circuit with Lhc same L and C. ssm LC own—t L . C 5M, 9Hv77d£9 BAG—£4“ 7:021:87 3532. CAP. Mb .zwb. Hiking, 4.1111810" _3 L: 75.0w!) H c, : EGOX/D—GF Q = aflowo‘é’c N,— Am’ ZWMTEM TIME: N. sToHSD 3») CA? 2. am. $70743 3"" 5”};- ,2. MB: :L: E WHAEN THE CA? :29 FULL?” LMRéeb'. 2:6? {:0 Q: I! LE} amter 7272—: CA? :9 Fuwy bxscmmezb‘. 50'- 2:0 1:2": , ___'2 MB: ELL, me. CUR 50 SHEETS 22-142 ‘IUO SHEETS 21-144 200 SHEETS 22-14] } ~\ / C“ RMPHU 33~23 the switch is kept in posi— tion a for a long time. it is then thrown to position b. (a) Calcu— late the frequency of the resulting oscillating current‘ (b) What is the amplitude of the current 05- » cillations? (sitar: _ 9/7/6970 a/ w; pmug AM “73/ A CJMJZQNG GA ACJT‘D , E] ’“M 7M5 - - BE Chi/+2955 '3 the circuit shown in Fig. WHILE 7/725", 9W/7'C-7'1‘ 41;; “r .5 WHEN 7772:” scuxrm 11‘s I»: "Pew/770A} 5 mg HAVE AN 6. am»? amaze? osqmnoug Kai-02¢? 7w:— am Ma 70 A P07“. bIF/‘T 0/“ V fl 317 D V (fwd: we 77%: APR/5‘1) EMF“). «.9 " ‘ _ -—,,L£ My, mMJZcpz-j ON THE CAR LUN'L BE“: . -.. CLAQJZE‘MT‘ DUI LL IN "7H5 LC GILL/l :H'E 04¢, It CLOF’LDIMG tony-.— wo wcwflfl _- HEW (=2 50 SHEETS 22-142 100 SHEETE 22-144 200 SHEETS 22—1 41 (£2) ilw ‘. in an oscillating LC circuit with C = 6-4.0 (of. the current as a function oftime is given by i = t is in seconds, i in amperes, and the phase constant in radians. (a) How soon after t = 0 will the current reach in; maximum value? What are (b) the inductance L and apt-«7’AZJNG Tfljfi _.__...,,._ ._ ‘- C ;-, 4,11 OX /0 (1.60) sin£2500t + 0.680}, where (c) the total energy? FDR. 77+; GIVEN: Lg. (LI/1Com“. Id“ 3 0'50) ALL (2500'!— + 0.6805 7‘0 71H! (75M. v.56 '. we“: % THAT" 33 w =- 29003;— Oiégo Mb __~ m 925/“ ,2; W —-/—«/ 4' (Ax/Hz T .- .fi-m MK. Magmrmbé. MON-Ea -— ' fiym c3”. .Lw ‘5 . . E. F EU”) = no we.sz waé‘ro) In an oscillating san'es RLC circuit. find the time required for the maximum energy prescm in the capacitor during an oscillation to fall to half its initial value. Assume q = Q at r = 0. Gem {z 50 SHEETS 22-142 IOO SHEH’S 22-144 200 SHEETS 22-14] r‘ 0 K — ~- - —- "* Bov5a<M§$w+§i /H;_N. 2&8 : Q [union “W; 7*. E I 95" r: O /7‘£/P—€; . NR 3 I: N[- I»? i Elsa“? 19:7“kach 9C) crud; l. V: i. at u 2 In 0 in mm 1-!— mm mu: :1 mm 00 on —~c~I Her Q‘i‘ p... r # NOV! Ht" 22-1111 “\ | I'U'II‘ n) __ ,x t ""0784 '. In A i [some/t iA/temthj amt.- s.ch omit L . . An ac generator has emf ‘6 = a, sin(wdt - #4), where ‘ém = 30.0 V and nod = 350 radfs. The current produced in a con- ! nected circuit is 5(3) = I5tn(wdt‘ - 37:14). where} = 620 mA. = (a) At what time after t = 0 does the generator emf first reach a maximum? (b) At what time after: = 0 does the current first reach a maximum? (c) The circuit contains a single element other than [ the generator. Is it a capacitor, an inductor;-or a resistor? Justify _ your answer. (d) What is the value of the capacitance, ihductehoe. or resistance, as the case may be? ssm J?) ffér'fléugfi " 3;) I : (920M: c2 90% 505 to} 1%! W. m“ 216) 'Fbr‘ #6? max. of. (if) C) (afar/935 :‘nde or restsa‘ar in 7%; t’t'rcuh‘? r39 CJr Z. , or" 2 a) E: gMS’h/‘Qé’—fl/q) The mm‘mum (“rims "Eric'h‘m 065m; when “1%): i colt ‘fi’Z/=§r2n7rjn:o,¢2,3)... We frsi MMI‘MHM aromas when 11:0: 53 4 91524“; i . 717:3 happens when _ 3 e - 3E ' its. 7&4? 55] ' Ants. i b) tflVfSNMgi '" 5W4) (7%“) {‘5 Wham when 0.325 ‘Eq‘r: 311121477) WON'er T/le 1915+ mminam 1'5 41’ 17:0: _JT oat-‘3' -17“ —-" 2 5:5msfr’t/cg'f ’T’F‘f) I 7716 Stewart Pfifflfib’i Ci) t'sfih’ (ohm an akme’m‘ is a”? L. .5 [C '- (it 79435 ewe-6:? et: fl_fl\- 40¢}; * W305“) it- {765* ISrhfagf - 3"qu : I53” 636 ,_ 27L!)_ 73%] Egret/$0475}? CarrW rb cm: rah/wa Eda Kim/mm? Avis. Sec 7W: 33239. 5’23 “5:39 Micfihotig loop rule -‘ f“ 9f 50- ”” 5" 35 5m swat ‘77“) "K sot/age - ’T/q) it sat 4&0) UL: I" XL = I/wde) (6/, 33-9? dim/t7- 33~¥§ “o. 522) a. 5m Iii/0°] : 30. o v /tgm-3,4)(3srtg ) : i J33 H'flm a)“ 50 SHEETS 22442 100 SHEETS 22-144 ‘200 SHESTS 2244i AMPAD .. (:1) Find Z. d), and 1 for the situation of Sample Problem 33-? with the capacitor removed from the circuit, ail other parameters remaining unchanged. ([3) Draw to scale a phasor diagram like that of Fig. 33~l Id for this new situation, {pm—,4 TM ox? ZEMDUEZB wEMVd A“) A; KL aka-I": 5, R m L: V VF- IxLz-H: 3,4 M gag'bvaTWE m 75;, “HT 35’ i § E 1‘ I J U . “707'. VOL—That? E m 5)» ELEHCMT: X nglhk 1"“:32V i g l r ! ! I I l 22:3 - \ 3:» 50 SHEETS 22-142 IOO SHEETS 22-144 200 SHEETS 2244] @ (3) Find Z, d). and I for the situalion of Sample Problem 33-7 with C = 70.0 p.13. Ihc omer parameters remaining unchanged. (1’) Draw a phasor diagram like that of Fig. 33—11:! for this new situation and compm the two diagrams closely. ssm mm A; ma own—1 K L. cayfi‘u'rwa: MAC? ._ 1 _ I __ XL " : l 3: I s t —— QC 217%. IMPEDEMCE’. Z = J? + (x; xx = New: ——-—-—--—' A A“ LUM‘XEM‘T MP5.) TUbE '. 210% SL _ ~36. @4826 VOL-T 6-5- ? To ZZMH EKMUT gm [Ag/“11>”? ZBY M” bmflUEva: C x; {3% 50 SHEETS 22‘! 42 100 SHEETS 22-44!” _ ’ 22-1‘4 200 SHEETS J l l Sen’es RLC amt? . In an RLC Circuit, can the amplitudc of the voltage across an inductor be greater than the amplitude of the generator emf ? Con- sider an RLC circuit with ‘ém = 10 V, R = 10 Q, L = 1.0 H, and R r C = 1.0 ,tLF. Find the amplitude of the voltage across the inductor at resonance. 85m itw L = K O H ' a) dam \Q >5," .? It" We do parf b) fish-We will knawu‘fieamwi‘a 62.5. l9) \{ é’rfiafidflce 1‘ I @féjomna x X4 6’ ($014,955, l wlwzm war #2445" .—-... L:- XL @ rflsmcffKé‘, = Luna 14/50J m‘ mot/25mm) 51L 3 Q (XL: XC Z PL VL: IXL: 5) l4 @ mandate (Ste .8237-3’26 P 50 54/?sz 1 (See F575): R J lit/03V 53> gm 2/0 U 50J cdflslj UL can big/wafi 5% . Ans. ms is possible, because, WW5 mic} z:qu- Onlfl app/ks 7b {hmmfleaus Vex/0e15, it :0 c - /. 0/; ='/-0></0'é’F ..)(é) _ . ..._.—.—._fi._..u..m......-.............._..-.... _. a“ _____..fi.._.-...-__l_..__~_.__,__..___i,_._ _ An RLC circuit such as {hat of Fig. 33—? has R = 5.00 D, ' . 2 = _ {I I ' :C : 2010 #1:, L = 1.00 H. and em = 30.0 V. (a) At what angular New ' R OOLQ .) C .35.un1005'0 ,6 .; ' frequency cud will the current amplitude have its maximum value. ;- ._. ‘i as in the resonance curves ofFig. 33—13?(b] Whatis this maximum A 00 H '1 gm 30‘ O U value? (6) AL what two angular frequencies cud] and (90.2 will the current amplimde'be half this maximum value? I'd) W113: is the ‘ f. (—1! fractional half—width [= (Lad; — mdgjll'w] of the resonance curve for ‘E; ‘ (/09 b this circuit? I n .55.? i - c a) and w 6r I 0’! dz 2 d) [Mu-Mia] 7W5 f5 an expressmn '6! carrwanypflude- If is manhum when X“; = )(c l I ' or 40/. 2M7": - 7716 Katmai '98 am 60., 3m I f (y) I _. to; WT- *l%fiaaolggzl.0w—@ 221/ Wfi 4x5. lo) : ‘Efl (See 43509:.) I I: Jim—d= Qfla/QE? - 502VC-Plll5’l3rtql SR (Willy soda) " KUJZLZ” uég +wDJ‘CZ __2'_.. WA 12" %L*322 {’WJLCZHO l we; 72,2 * ("5 +5?)de *’ "“ :‘O 771:3 I541 guadmfi'c layman/Er J43. we“) b = *(ELe3R‘) J =5: | SE, N M? 4,, Do PU ‘0 '+ ($3 (13 K) N (N I‘ll—(‘5‘ _______,__-._._._H_i_. .. ‘Zlqgid: o. OL/ ANS, 224% M’ 228 “3' 60(de Hug)“: mhmmim OOH dc TUH wkuwIm 00— Ne TNN mkwu—Am on paltfim \iur I. \ __ Dd... SE... L? “'1: —b 50 SHEETS 22442 100 SHEETS 22444 200 SHEETS 22-141 as}; \ . An ac generator with ‘ém = 220 V and operating at 400 Ht. causes oscillations in a series RLC circuit having R = 220 Q, L = 150 mH, and C x 24.0 paF. Find (a) the capacitive reactance XC. ' (b) the impedance Z, and (c) the current amplitude i, A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of (d) XC, (e) Z, and (f) I increase, decrease. or remain the same. @é&?CITiU£—'REA QMCE i [a ZM?£DAN¢E '. Z:- \‘ Rz-e (XL—XX; r 7:931. z, CA?AC-ITDR—9 Le gg”/gg: ___ : #5 +__ Wfitw C236? C C. Niece: 0" H g... i “ 00;; _ I CAPACITIUE ._ .fi . : 2x 9:; 7H2? ,ZEAQTAMCE wflgfia C‘ Ame, .u—._ M?£Z> ANéé bicfig/xges : r e» 50 SHEETS 100 SHEETS 22-144 200 SHEETS 12141 22-!42 c ‘ oscillators have been used in circuits connected to loud- speakers to create some of the sounds of electronic music. What inductance must be used wiLh a 6.? uF capacitor to produce a frequency of 10 kHz. which is near the middle of the audible range of frequencies? szk A“? LC. 012C123?" .’ ————.—_._____h_______ AHG. Fifi?- an quuarzom IS: 'r i i . | 1' i , SO SHEETS 22-14] xi pm) Q: 22 I42 100 SHEETS 22-144 200 SHEETS .__/ -_'J_ fig A coil of inductance 88 mH and unknown resistance and a . 4 p.13 capacitor are connected in series With an alternating emf of frequency 930 Hz. If the phase constant between the applied VOIIage and the current is 75°, what is the resistance of the coil? i_ E i | I I 50 SHEETS 22-142 100 SHEETS 22444 200 SHEETS 22441 ..\ Ki \Inmx. A .n) I = Power In HC Cr'rcuffi \ if 5—3.5 j . .1. __ ._.. . ....J_-.‘ _\.._.. 51 )What direct currem will produce me same amount of thermal ergy, in a particular resistor. as an alternating current that has a maximum value of 2.60 A? saw. @va = max flc Carrw f: thd5 éCSO Ec—‘a‘: (W is a/fist’fmkd-h’wmd tram”) 2.0M . -_.._._..._.._....__.. m.__._‘._.. c 5 * ‘ 1Q ' - 43?. A truce-phase generator G produces electrical power that is - “ mI—u —w_ _ - I" transmitted by "ream of three wires as shown in Fig. 33-27. The C2! VI ‘- ’5] S tn . electric potentials (relative to a common reference level) of _ VZ-fism (03¢ #200 if” these wires are Vl = A sin refit, V2 = A simde - 120°}, and i’ _ _ V3 = A sinuod: — 240°}. Some types of heavy industrial equip- _ f . Vs-flsmégt ‘2???) ment (for exampie, motors) have three terminals and are designed to be connecred (finally to these three wires. To use a more con- I ventional two-terminal device {for example, a lightbnlb]. one connects it to any two of the three “ores. Show that the potential _ difference between any two of the wires (2.] oscillates sinusoidaliy * with angular frequency and and (b) has an ampiitude of A43. ‘ M: M-Vlavz-‘VSN/Flé We QSMWBM Marian; math reg/any no; ) WK? Mfr/{Wald 15A In In in I- t- l- 3 e 3 = 1 1 2 2‘; “tree-wire transmission line ‘" S 2 FIGURE 33-27 Problem 43. I0- (‘1 a V 1‘ 1‘ o'q r'u p‘: H H H J“-. / SI \ (is 1' ‘1: .- '. Itrull' bum Med ‘%5 {if/725W: 8:313’1155’125 = ZSM(§£)QZS(@ Edit) + b) {we can do Mtge 7‘0de . Wow 1‘ 145:?) qt — fisrhfltyé~120°>= Zflsrn(m*(“f"m)ms (UH—L “ifflm? 1; 2 2H sin (00’) £05 2”?“ “’3” ‘ I36 W..... flmpfi'fitdl -‘ USP: 8*de fimcfifir w/‘qumfl Lug EU2“V3 2 245;}; [wdf - IZO‘)“/451h{uut ‘ZW )3 Z/JFS {In (60°)603(Mafi '79.) ' 32‘? game/row visa wom- m) MS VI ‘Vg : 453V: welt *Fisfn {mat *29/0') ‘ 245:3“? [300595 (M515 " 0") -_.___..——l r 2‘} g Cos/cod - Mo“) = {BF} Cosfiudt 420°) W6 COMM £0 ' ' I a do as W W 33w“ twat, [gm/u; m W twee; A owl/fit: y—uz mm ts smwgaumwy l a"!!! some rant-f ’6} bit-1.6, anal L4 “J5. U, is wn'Um as Hammat "45) 543W fig and arbitrator for this (“are (p.130? "n3 potato 50 SHEETS “‘2-131'2 135' SHEETS 224411 200 SHE‘EIS 1'34“ . 21:3} ' Int-Eu. " . 111?. An electric motor has an effective resistance of 32.0 0 and an indnczive macmncc of 45.0 0 when working under load. The rms voltage across the alternating source is 420 V. Calcuiale the nus CUITGHI . 132044..— (3201529393? my (KC =0 ">110 (kit/dab?!) ...
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This note was uploaded on 11/04/2009 for the course PHYSICS PH13100 taught by Professor Dr.wick during the Spring '09 term at Clarkson University .

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homework 13 - PH 132 SPRING 2005 HOMEWORK 13 Assigned W 50...

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