46S Set Sate ass Problems Section 9. ‘94 sinusoidal current is given by the expression 12508 800 + 3687) mA. ad fi et (Fn mn Sth) gin dep anda he sae ee eye Sera eich = na) eal pone ae sich i 10008 (at + 8) ver 92 Ina singe graph, sketch » sso for = 90°, 45", 0", 45", and 90 2) State whether the voltage function is shifting to the right of left as becomes more negative the direction of shift if changes fom 193, Consider the sinusoidal voltage 1) = 28 cos 400 + 607) V. 4) Wnatintemoxinum ample fe voluge? 0) Wat she reneny nb? 2) athe Gowen ina pecan? 5 wtih pe agin depres? 1) Whats pein millones? 2 natn time err ~ Ott» = OV? $) The sia ction sit 6s wo te tin ein th What she expreion ioe fs 1) Wt he minim mambo of illseconds , ‘that the function must be shifted to the left if the Sirenion xv) 25st V7 94 A soll yolge ito as» (40/3) mand nant ate et os Vs the maxima ond tie vlogs 9 2) hatte guns fina prscod? 1) wt isthe xpreson fore? 95: AL = 5 ma sini crete known be Sogn see econ ons 2 eset astimowntat te circ MA 2) ‘atthe nen of inher? 8) ws expen fo? $46 Tuer ve othe ssl og soppid io Te vcince ae of» Home Scand 3 Sea he matinum ale fh aes ibe ott? 194 Find the rms val ofthe half-wave rected sna soidal voltage shown in ig. P97. gr 78.2 vat ve vasa ote? 98 Show that [Ovacsttor +o Section 92 99 ‘The voltage applied tothe circuit shown in Figg tr = 0187500 (4008 ~ 60") V. The circuit “ce is 400 and the initial curent inthe 75 inductor i200 8) Find) fort = 0. 1) Wiite the expressions for the transient eady state components of 1). ©) Find the mamercal value of after the sve ‘been closed for 750s. &) What are the maximum amplitude, fre (in sadian per second), and phase angle steady-state current? ) By how many degrees are the volage steady state curren ou of phase? 1) Verity that Eg.99s the solution of Eg 9 ‘an be dane by substituting Eq. 9:9 int hand side of Eq. 98 and then noting ‘sas the right-hand sie for al values ‘Att = 0, Bq. 99 should reduce tthe vale ofthe current 1) Because the transient component time elapses and because our solution {sy the eiflerential equation for all the steady-state component, by isl satisfy the differential equation ‘Observation by showing that the s ‘component of £4.99 satisfies Ea. 98. Sections 93-94 9:11 Use the concept ofthe phasor to Towing sinusoidal functions into 8 si reine expression: 8) y = Weon(00e — 160") + 15 csi 1) y = 90 in(Soe — 207) +6 con ©) y= $0.c03(S000 ~ 60") + 25 sia(S000 +110") 75 eos(5000~ 30°), 4) y= Neos (ot + 30") + 10sin a + 1Doos(ar + 1507), 942 A 400 He sinwsoial voltage with & maximum Amplitude of 100 V at = 0's applied across the terminals of an inductor. The maximum amplitade ofthe steady-state curent inthe inductor i 20 A. 8) What the frequency ofthe inductor eurrent? the phase angle ofthe voltage zero, wha is the phase angle ofthe current? ©) Whatis the inductive reetance ofthe inductor? 4) What is the inductee of the inductor in nilhenrys? ©) What isthe impedance of the inductor? ‘A 80 kz sinusoidal volige as 2ero phase angle and 2 maximum amplitude of 25 mV. When this ‘voltage is applied across the terminals ofa tor, the resulting steady-rate current has a mati mum amplitude of 28.2 yA. 18) What isthe frequeney ofthe current in radians per second? b) What isthe phase angle ofthe curr? ©) What isthe capacitive reactance ofthe capacitor? ©) What is the capacitance of the cap rcroarad? ©) What she impedance of the capacitor? ‘The expresions for the steady-state voltage and current at the temminas of the circuit seen in Fig PAG are 30008 (500088 + 78°)V, = 6sin So0et + 123°) A 8) Whats the impedance seen by the source? ) By how many microseconds isthe current out of phase withthe wltage? Fue P36 PSand96 25 01 restr, a 50 mH inductor, and a 32 uF tor ae connected series Te serie connected Fetlem 347 ements are energized by a snuoidal voltage source ‘whose vltage 25 cos (S000 — 6V. 8) Draw te frequency-domain equivalent circuit. b) Reference the current in the lection of the voltage rise across the source, and find the pha ©) Find the steady-state expression for i. 946 A 2501 resistor and 9 mE inductor are con ‘ov nected in parallel. This parallel combination ao ‘7 iq parallel withthe series combination of «30 0 fesstor and a 10 uF capacitor. These thee parallel branches are driven by a sinusoidal current source whose current i 125 in250e + 6) 8) Draw the frequency-domain equivalent circuit. »b) Reference the voltage across he current source 8 rein the direction ofthe source current, tnd find the phasor voltage. ©) Find the steady-state expression fr () SAT Three tranches having impedances of 3 + /4 0, 16~ /120, and ~ 6.0, respectively, are connected in pale. What are the equivalent (a) admitance, (@) condctance, and (6) susceptance ofthe paral connection in millsemens? (8) Hr the. parallel branches are exited from a sinusoidal current source where = Seas. A, what is the masini ampli Te of the current inthe purely captive branch? 9.18 a) Show that 2 given frequency ay the circus in Fg. P18(a) and (b) will have the sme imped ance between the terminals abit oP = RL Bile We wl We wilt b ) Find the values of resistance and inductance that winen connected in series will have the same impedance at 4kradls a that of a Skil resistor conaected in paallel with 1.5 H inductor, pre 38 Ri a 5 ° o 9219 a) Show that at a given frequency the cre in Fig P919(a) and () will have the same imped. ance between the terminals abit268 Simul date Aas tine The $wo circuits will have the same Powe P22 {Impedance f they have the sare admittance.) peat ae en +) Find the values of resistance and inductance that ‘onen connected in parallel will have the same Impedance at 1 krads as an 810 resistor con- netied in series with a 4H inductor 1920) Show that ata given Fequency othe cieits in Fis P920(a) and () will have the same imped lance between the terminals if 923 Find the admitance Yq in the circuit seen Fig P923. Express Yq is both polar and rein Tat tor, Give the vate of Yn milisiemens a ins yd te aio ek tnd ence as es a Noonerted in ert wl have he Cay Safe al Same impedance at 404Krad/s as that of 8 6a joa ae eee Tf beh SO a capacitor. eect |e cr be + 925) Using component values from Apo combine at Teast one resistor, ind apactor in series Wo cteale an imp S00 HOO Oat a frequency of 10.000 by At what frequency does the crit fom fave an impedance that is purely ress (ing The two crests will have the same (ifedance if they have the same admittance) by Find the values of resistance and capacitance whem conncted in paral} will give the me impedance t 50 kradls as that of a 10) ‘Saor connected in eres with a capacitance of wor 926 a) Using component valves fom Apps combine at Teast one resistor and oe Sn" parallel to create an imp Wo + 200 ata frequency of SO rad Use the results of Probiem 9.19) 1) Using component values from APh ombine atleast one resistor and one in parallel" to. create an 40 ~ 720.0 ata frequency of $000 Use the result of Problem 921.) 932 Find the impedance Zyy in the circuit seen in Fig P22. Express Zayin both polar and rectangular form sar 1 7 8) Using component values from Appendix Hind a single capacitor or 8 network of capacitors that when combined in parallel with the RL ce cuit from Problem 9.26(, gives an equivalent, impedance that is prey restive at frequency tsi ale d - 'b) Using component values from Appendix Hy ind single inductor or a. network of inductors that, when combined in aralel with the RC ce exit om Problem $26(0), gives an equivalent impedance that is purely essive a a frequency of 500 rads Find the steady-state expression for i) inthe circuit Fig PO2Bit v, = 80 eos2000¢ V. gre 8.28 lnor Soom i 9.24 a) For the circuit shown in Fig, P9.24, find the zoe Bt ch cst i 29 pening ni ck LT Revenant: ‘tna eae nn — 6 ° oe fee a + 421-9) Sona tapen rn cin I SVT SNS Sa oo eat jon fom + The stein Fig. P30 is operating in the sinwoidal steady sat. Bindi if 000) ‘5 n 4000 V. ] 200 Fs Pratlens 340 931 a) Fortho circuit shown in Fig P93) ind he stendy- Et, sate enpreson fore ig = 25 co 30,0 mA By how many microsezonds does ead i? ower. Oj fee bee : 932 Find fy and Z inthe circuit shown in Fig, 9.2 i Vy=2520°Vand], 5250" A 19.38 Find the value of Zin the circuit sen in Fig. P33 i Vpn 100 SOV, ty = 304 OAL and Y= Los j20¥. Flguer2.33 ma maja om 1000250 Sensi stent ae Aas etane 351 4.38 ‘The iit shown in Fig P9238 is operating in the fiers Pirro 94s Use Tins steady sate Find the vale off mgs : Une sae anomatns 0 dhe Tea : — a auvalent crt with respect othe tera i= Hsin (ot + 21877) mA, Fale c forthe cit shown nig 948, tg = A0con(at— 15 «De i ae awe Ps fe 7935 _-| —_| ~j000 Se 9.39 ‘The frequensy othe sinusoidal voltage source € ; 22 Re cheat in Fig 9.39 fs ajstd antl is veo © he os pase with * 942, Find Z,, for the circuit shown in Fig P9.42. 2ojarma ( 250.0 mo a 1) Whats the vale of in aians po second? Piguet poe 7 b) It 1, = 1Scosut V (where o Is the fequeme four inal), whats the steady-state expreS 9.36 ‘The phasor current Ty in the circuit shown in it at Fig P9365 25/0" mA. SO) Find Hy Handy Figure 79.39 1b) Iw = 1500 rads, write expressions for 0, 10 Ld) and 0) pe ey] 240.0 9.46 Find the Norton equivalent circuit with respect to the teminals 2 forthe crit shown in ig PAG Figure 9.8 owe riat ne a a ese | > omit [ison “weak on “aa pov ‘sh tc hi i rn we source voltage in the circuit in Fi in Fig, P93 is developing a voltage equal to a _| cas Tess AP he ln Sinn, © TS = 947 The devieinFe PT isrepsetesi tee ri 2 ee Eyes res tap saan ne atta acre teeter teins ing an inpedancs of 290) comected co te ‘operating inthe steady state 1b) For he values of Z found in (a), find he Sate expressions fo ©) Bd the Therein impedans with eps © epee rake th 80+ S.A Venn easel inductor having an impedance of /200 connected Rice ie ros the device, the vale f Vy 8 (40 = 40) V. Find the Thevenin volte Vy and the Thévein impedance Ze. 9.37 Te frequency of the sinusoidal voltage source ia 2A hc eatin Fig, POST is adjusted wo he current SSS fei phase with 8) Find the frequency in ert 1 Find the sendy een fo (te 7 frequency ound) ey = SDCORO - ne ‘Figure P9.67 jen i $444 The cit shown in Fe. P41 is ope o . Js saree transformations to fin the Norton ‘ibe — a Gnosedal steady sate. The capacitor & 7 SoS. ha he caren jn phase with the sven et wih epet ote ternal Find the Norton equiva is poset cnet wits ramet fo tn equivalent with respect to term show in Fig Ps anal bin the cro of ig P98, dan 5) Tetequney fae ore voagsin tee ge 228 © fig 38 wae ul phe wi eae Some FP What the vale of win adn er second? 2) Spey he copes mas 1) thay = ensue mA (were wt he equensy a bea ere whe egiisy yin the dentate expression ee tovihe ale fond in). cormv() aePrtens 353 352 snc Sey Sate As 956 Use the node voltage method 1 fd the eadystste Section 9.9 91 od the Tenn equivalent cca withreectto MNFRS? sent n of tect shown in Fig. P28 2 se exreion fri in the ds " ea — inthe cet seen in Fig 7956 if . creo fi et wen Fe PS 94 Us th thet mad fd te pao Fgue P2.48 alg earl ¢ ary. curren inthe ctcit in Fig PSS, = 10! 0 aH itga00 Lamitend a ae . a 3 $9.64 Us he mehcrveatmetod to fn the seat + ee state expression for e(?) in the circuit in Fig. PDS ary ov, Q) -n07:v. 962. Use the mes-curent method to nd the branch sas Find the Tévenin impedance sen looking nt te Peano apey opr ert ae Bans Tu ofthe exc n Big P23 ithe fe me ain (Guencyof operation (25/2) KH Fue r.62 ‘950 Find the Norton equivalent circuit with respect fo {he terminals a forthe erat shown ia Fig, 9.50 ane when V, = 520° V. as ar, 25a eee i eM . Fig. Poti equals cons ¥ be_—____+—— ‘Use the node-voltage method to find V, and I, in. rege tO) wo 4 the cee sen in ig P39, Gad 4, F so ‘952 Find Zin the circuit shown in ig, P22 when the ‘ret operating ata feauency of 100 rads 1004,354 Sil set Sate A Sestons9.5-99 sStsn Fig P65 if = 120eos 100,000 V, wer. io °F soa Himes “© ; So Fig P66 fly ~ cos 280" MA. 19467 For the cneit in Fig POST. Suppose 1 = 2eose20001 ~ 36387") V 1 cos s000" + 1625") V Fig 67 1004 oe I ect 9.68 For the cic in Fig P63, suppose ‘y= 1eos 16000" V y= 20.08 40001 V. ‘9465 Use the concept of voltage division to find the ee sendy-state expression for 14() in the ict in 8) What circuit analysis techni . fd the steady state expression fori) 1b) Fd the steed state expression fori) ye mut be used te 9469 The sinusoidal voltage soure inthe ctclt shown Fue P68 9466 Use the concept of current division t find the ms Steady-state expression for iy in the elrcit in a) What circuit analysis technique must be sed 10 find the steady-state expression for #0 1) Find the steady-state expression foro. Fie P96? is generating the thy = 2beos S00 V. Hf the opamp i desl Wh the steady state expresion for 14)? moa 1205 iF expr inthe cit seen in elaea wha vanabl capaci. The Sed un teen lag ad te voting by 135 2) inthe alc of Cin iota 2) ate te stand at expr o hush we found in “The op amp in the cicutin Fg P971 ise 4) Find the steady-state expression fF 10 1) How lage ean the amplitude of», be before . amplifier saturates? Fwer9.71 oe [sta T $ oes n= Reon 000 9.72 The op amp inthe dest seen ia Fig PTE fu Find the steady-state expression for sme = Deas 1. voltage 973 The operational amplifier in the creut shown in fos Fig. P73 is ideal. The voltage of the ideal sau 5 sojdal source ito, = 30cos 10 V. 8) How small can C, be before the steady-state ‘output voltage no longer has a pure sinusoidal ‘waveform? 1b) For the value of C, found in (3), write the g steady-state expression for 1000 “The value of kin the circuit in Fg 9.14 adjustod 0 that Zs purely resistive when = 4 kad Find Ze For the circuit in Fig POS, find the Thévenin ‘uivatent with respest tothe terminals Potlems 355 gre 3.75 oo so so sae Views) 5 —+a 9376 a) Find the steady-state expresions for the cr ress rents jg andi, im the crclt in Fig. P976 when st py = eos Sr V, 1) Find the coefficient of coupling. ©) Find the energy stored inthe magnetically cou- pled coils at = 625q us and = 1280 ps aoe $100 tt “ ‘wan} — froomn ; aon 9.77 The sinusoidal voltage sousce in the circuit seen in prs Fig P97 is operating at a frequency of 200 kal "SS" The coefficient of coupling i adjusted until the peak amplitude of is maximum 2) What she vale otk? b) What_ is the peak amplitude of 4, if 1, = S6Dcos(2 x 104) V2? Fie 99.77 9.78 A series combination of 4 60 0 resistor and a SO ml inductors connected toa sindsoidal voltage source by a linear tansformer The source is ope ating at a frequency of 400 rad/s. At this frequency, the internal impedance of the source. is (iO + 12.75) {Theme voltage atthe terminals ot {he source is 75 V when tis ot loaded. The param- ters ofthe linear transformer are R, = 8340, 1000, 1, = 280 mH, and 18) What isthe value of the impedance reflected into the primary? 1) What ithe value ofthe impedance seen fom the terminal ofthe practical source?356 Smid sey State ti Section 9.11 9:79 At st glance, induetive load could make Tatutvely,we know sis iy terminals a in bythe expression 1) Show that if the polarity ol the oils is reversed, be bythe expression es: tf the cus is reversed that — 2. = 200/880. se may appear from E969 tha an mete estanssenlooking She primary ternal (2%) look caste Tate we : possible. Show thiat Xp tan never be negative if Xsan inductive reactance 2) how ht he impedance sen ooking it the ae the cet in Fg PSD i given ‘983 Show by wsing a phasor diagram what happens 1 22? nc magnitude and phase angle ofthe voltage 0 SKS the eet in Fig, PSS a Ris varied from zero Infinity The amplitude and. phase angle of the ure voltage ae eld constants R vais terminal of either one (984 "The parameters in the ccuit shown in Fie 9.35 3) cae tephra 3) canon scant pari with hein So Satan the econ ae eae its nimn Wh 1 cance! What lo oan the va ofthe apc ect Eee mapas ofa el ‘efthatahesane ne makes 5.1») Show that be impedance ee ooking into he o ‘terminals a,b in the circuit in Fig, P9.81 is given Wy) = Vil = 20. 1) Show that if the polarity terminal of either one Iv) = vu = 240 ‘985 2) For the circuit shove in Fig. P95, com ‘Construct & phasor diagram showing the SSonship between V,, Vj and the load Repeat pars (2) and (given tat ‘Stage femnins Constant 8280 20° Ys ° ome of 50 apace. ree fcros the lon terminals tenn \s a F fe ‘982 Find the impedance Zin the cieitin ig POA Sections 9.9.2 986 You may have the opportunity as an enginering graduate to sere as an expert witness in lawsuits involving ether personal injury o property damage. ‘As an example of the type of peablem on hich you ‘may be asked to give an opinion, consider the fllon- Ing even. A the end of dayof fieldwork, farmer ‘eur ois farmstead, checks his hog confinement Dulin, and finds to his dismay that the hogs are ead, The problem is uaced to a blown fise that fused 8 240 fan motor to stop The los of vat ‘on ed to the suffocation ofthe livestock. The inter rupted fuse is located in the matin switch that connects the fammstad to the electrical scr [Before the insurance company sets the cai, i wants to know ifthe electric cicut supplying the farmstead functioned propety. The lawyers for the inrance company ae pued because the farmers ‘ie, who was inthe house onthe day he aeident onvaescng from minoe suger, was able to watch ‘TV during the afternoon. Furthermore, when she ‘went tothe kitchen to start preparing the evening ‘mea the electric clock indented the correct ime. The lawgershave hired you to explain (1) why the electric clock nthe kitchen and the elevision set inthe ving oom continued to operat after the fe inthe main soitch blew and @) why the second fuse in the main Switch didn’ bow after the fan motor stalled. ter tom crcult prior to the interruption of fe A you are able to construct the eircut model shown in Fig. P986. The impedances ofthe line conductors and the neural conducta are assumed negligible. 8) Calculate the branch currents Hy Ts, I, Hs Hs tnd I prior fo the insertion of se. b) Calelate the branch current afte the iterrup- tion of fuse A Assume the stalled fan motor behaves as short eeu ©) Explain why the lock and television set were notafeced by the momentary shor cite hat imterrpted fase A. 4) Assume the fan motor is eatipped witha ther- ‘mal cutout designed to iaterupt the motor P36 wie A (100) Folens 357 circuit ifthe motor current becomes excessive, ‘Would you expect the thermal cutout to oper ate? Explain, ©) Explain why fase B is not interrupted when the fan motor stalls 987 3) Caleulte the branch currents I)~Iy inthe Gir suse cuitin Fig. 958 ) Find the primary current 9388 Suppose the 40 resistance inthe dsibution ci 25095 cul in Fig 9.58 replaced by 200 resistance, 2) Recaleulate the branch current in the 20 resistor. I 'b) Recalculate the primary current. ©) On the bass of your answers, is it dsiable to have the resistance of the two 120°V loads be equal? 989 A residential wting circuit is shown in Fig. P99. In “S584 this model, the resistor Ry fused to model a 250 V "= appliance (sich av an electric range), and the resis- tors Ry and Rare used to model 125 V appliances (Gach a lamp, toaster, and iron). The branches camying Ty and Iy ate modeling what electricians {fort as the hot conductors in the circa the branch carrying I, is modeling the neutral conde: tor. Our purpose in analyzing the circuit iso show the importance of the neutral conductor inthe st- ‘sfctory operation ofthe cieat You ae to choose ‘the method for analyzing the eet 8) Show that Ips 2er0if Ry = Ro 1) Show that V, = Voit Ry = Re ©) Open the neural branch andcaleulate Vand Vs TR, = 400, R; = 400 0, and Ry = 8.0. 4) Close the neutral branch and repeat (0 ©) On the basis of your calculations, explain why the neutral conductor is never fed in such & ‘manper that it coud open while the hot conde tors ate energized Fer. oF alta ea sary “4 ar ev} || Fase B ODA 990 a) Find the primary current I for (e) and (d) in Problem 99, b) Do your answers make sense in terms of known ‘iret behavior?