GATE 2009 Electrical Engineering Question Paper

Transcription

1 GATE 9 Elctrical Enginring Qustion Papr Q. No. Carry On Mark Each. Th prssur coil of a dynamomtr typ wattmtr is highly inductiv highly rsistiv purly rsistiv purly inductiv. Th masurmnt systm shown in th figur uss thr sub-systms in cascad whos gains ar spcifid as G, G and. Th rlativ small rrors associatd with ach rspctiv subsystm G, G 3 G and G 3 ar, and 3. Th rror associatd with th output is: Input G G G3 Output Th following circuit has a sourc voltag V s as shown in th graph. Th currnt through th circuit is also shown. a b V s R k Vs(volts) Currnt (ma) Tim (ms) Tim (ms) Th lmnt connctd btwn a and b could b a b a b a b a b Pag of 5

2 4. Th two inputs of a CRO ar fd with two stationary priodic signals. In th X-Y mod, th scrn shows a figur which changs from llips to circl and back to llips with its major axis changing orintation slowly and rpatdly. Th following infrnc can b mad from this. Th signals ar not sinusoidal Th amplituds of th signals ar vry clos but not qual Th signals ar sinusoidal with thir frquncis vry clos but not qual Thr is a constant but small phas diffrnc btwn th signals 5. Th incrasing ordr of spd of data accss for th following dvics is (i) Cach Mmory (ii) CDROM (iii) Dynamic RAM (iv) Procssor Rgistrs (v) Magntic Tap v, ii, iii, iv, i v, ii, iii, i, iv ii, i, iii, iv, v v, ii, i, iii, iv 6. A fild xcitation of A in a crtain altrnator rsults in an armatur currnt of 4A in short circuit and a trminal voltag of V on opn circuit. Th magnitud of th intrnal voltag drop within th machin at a load currnt of A is V V V V 7. Th currnt through th k rsistanc in th circuit shown is k C k A k B k D k 6V ma ma ma 6mA 8. Out of th following plant catgoris (i) Nuclar (ii) Run-of-rivr (iii) Pump Storag (iv) Disl Th bas load powr plants ar (i) and (ii) (ii) and (iii) (i), (ii) and (iv) (i), (iii) & (iv) 9. For a fixd valu of complx powr flow in a transmission lin having a snding nd voltag V, th ral powr loss will b proportional to V V /V /V. How many W/V incandscnt lamps connctd in sris would consum th sam total powr as a singl W/V incandscnt lamp? not possibl 4 3 Pag of 5

3 . A Linar Tim Invariant systm with an impuls rspons h(t) producs output y(t) whn input x(t) is applid. Whn th input x (t ) is applid to a systm with impuls rspons h(t ), th output will b y (t) y ((t )) y(t ) y (t ). Th natur of fdback in th opamp circuit shown is Currnt - Currnt fdback Voltag - Voltag fdback Currnt - Voltag fdback K +6V 6V K V out Voltag - Currnt fdback V in 3. Th complt st of only thos Logic Gats dsignatd as Univrsal Gats is NOT, OR and AND Gats XNOR, NOR and NAND Gat NOR and NAND Gats XOR, NOR and NAND Gats 4. Th singl phas, 5Hz, iron cor transformr in th circuit has both th vrtical arms of cross sctional ara cm and both th horizontal arms of cross sctional ara cm. If th two windings shown wr wound instad on opposit horizontal arms, th mutual inductanc will doubl rmain sam b halvd bcom on quartr 5. A 3-phas squirrl cag induction motor supplid from a balancd 3- phas sourc drivs a mchanical load. Th torqu-spd charactristics of th motor (solid curv) and of th load (dottd curv) ar shown. Of th two quilibrium points A and B, which of th following options corrctly dscribs th stability of A and B? A is stabl B is unstabl A is unstabl B is stabl Both ar stabl Both ar unstabl Torqu B A. N N sync 6. An SCR is considrd to b a smi-controlld dvic bcaus t can b turnd OFF but not ON with a gat puls it conducts only during on half-cycl of an altrnating currnt wav it can b turnd ON but not OFF with a gat puls it can b turnd ON only during on half-cycl of an altrnating voltag wav Pag 3 of 5

4 GATE 9 Elctrical Enginring Qustion Papr 7. Th polar plot of an opn loop stabl systm is shown blow. Th closd loop systm is Always stabl = Imaginary Marginally stabl.4 Ral Unstabl with on pol on th RH s-plan Unstabl with two pols on th RH s-plan = 8. Th first two rows of Routh's tabulation of a third ordr quation ar as follows. s s 3 4. This mans thr ar 4 two roots at s j and on root in right half s-plan two roots at s j and on root in lft half s-plan two roots at s j and on root in right half s-plan two roots at s j and on root in lft half s-plan 9. Th asymptotic approximation of th log-magnitud vs frquncy plot of a systm containing only ral pols and zros is shown. Its transfr function is 4dB/dc 8dB 6dB/dc. 5.5 rad/s (s 5) s(s )(s 5) (s 5) s (s )(s 5) (s 5) s(s )( 5) 8(s 5) s (s )(s 5). Th trac and dtrminant of a matrix ar known to b - and -35 rspctivly. Its ign valus ar -3 and and - -7 and and - Pag 4 of 5

5 Q. No. 56 Carry Two Marks Each. Th following circuit has R = k, C = F R. Th input voltag is a sinusoid at 5Hz with an rms valu of V. Undr idal conditions, th currnt i s from th sourc is R ma lading by 9 k ma lading by 9 ma lading by 9 ma lagging by 9. In th figur shown, all lmnts usd ar idal. For tim t<, S rmaind closd and S opn. At t=, S is opnd and S is closd. If th voltag V c across th capacitor C at t= is zro, th voltag across th capacitor combination at t= + will b Vs=V rms, 5Hz S S i s C F + OPAMP k R 3V C F C F V V.5 V 3 V 3. Transformr and mittr followr can both b usd for impdanc matching at th output of an audio amplifir. Th basic rlationship btwn th input powr P in and output powr P out in both th cass is P in = P out for both transformr and mittr followr P in > P out for both transformr and mittr followr P in < P out for transformr and P in = P out for mittr followr P in = P out for transformr and P in < P out for mittr followr 4. Th quivalnt capacitanc of th input loop of th circuit shown is i k k input loop k 49i F F F F F 4F Pag 5 of 5

6 5. In an 885 microprocssor, th contnts of th Accumulator, aftr th following instructions ar xcutd will bcom XRA A MVIB FH SUB B H F H F H H 6. For th Y-bus matrix of a 4-bus systm givn in pr unit, th buss having shunt lmnts ar 5.5 Y BUS = j and 4 and 3 and, and 4 7. Th unit-stp rspons of a unity fdback systm with opn loop transfr function G(s) = K/ ((s + l) (s + )) is shown in th figur. Th valu of K is rspons tims(s) Th opn loop transfr function of a unity fdback systm is givn by G(s) = (.s)/s. Th gain margin of this systm is.95db 7.67dB.33dB (D 3.9dB 9. Match th itms in List-I with th itms in List-II and slct th corrct answr using th cods givn blow th lists. List I List II To Us a. improv powr factor. shunt ractor b. rduc th currnt rippls. shunt capacitor c. incras th powr flow in lin 3. sris capacitor d. rduc th Frranti ffct 4. sris ractor a b 3 c 4 d a b 4 c 3 d a 4 b 3 c d a 4 b c 3 d 3. Match th itms in List-I with th itms in List-II and slct th corrct answr using th cods givn blow th lists. List I List II Typ of transmission lin Typ of distanc rlay prfrrd a. Short Lin. Ohm Rlay b. Mdium Lin. Ractanc Rlay c. Long Lin 3. Mho Rlay a b c 3 a 3 b c a b c 3 a b 3 c Pag 6 of 5

7 3. Thr gnrators ar fding a load of MW. Th dtails of th gnrators ar Rating(MW) Efficincy (%) Rgulation (p.u.) on MVA bas Gnrator-. Gnrator- 3.4 Gnrator In th vnt of incrasd load powr dmand, which of th following will happn? All th gnrators will shar qual powr Gnrator-3 will shar mor powr compard to Gnrator- Gnrator- will shar mor powr compard to Gnrator- Gnrator- will shar mor powr compard to Gnrator-3 3. A 5MW, kv, 5Hz, 3-phas, -pol synchronous gnrator having a ratd p.f=.9, has a momnt of inrtia of kg-m. Th inrtia constant (H) will b.44s.7s 4.88s 5.4s 33. f(x,y) is a continuous function dfind ovr x, y [,] [,]. Givn th two constraints, x > y and y > x, th volum undr f(x,y) is y x y f (x, y) dxdy y xy y x y x y x x y f (x, y) dxdy y x y y x x y f (x, y) dxdy x f (x, y) dxdy 34. Assum for simplicity that N popl, all born in April (a month of 3 days), ar collctd in a room. Considr th vnt of at last two popl in th room bing born on th sam dat of th month, vn if in diffrnt yars,.g. 98 and 985. What is th smallst N so that th probability of this vnt xcds.5? A cascad of 3 Linar Tim Invariant systms is causal and unstabl. From this, w conclud that Each systm in th cascad is individually causal and unstabl At last on systm is unstabl and at last on systm is causal At last on systm is causal and all systms ar unstabl Th majority ar unstabl and th majority ar causal 36. Th Fourir Sris cofficint, of a priodic signal x(t), xprssd as jkt / T x(t) = a k k ar givn by a = j; a =.5 + j.; a = j; a =.5 j.; a = + j; a k = ; for k >. and Which of th following is tru x(t) has finit nrgy bcaus only finitly many cofficints ar non-zro x(t) has zro avrag valu bcaus it is priodic Th imaginary part of x(t) is constant Th ral part of x(t) is vn Pag 7 of 5

8 37. Th z-transform of a signal x[n] is givn by 4z 3 + 3z + 6z + z 3. It is applid to a systm, with a transfr function H (z) = 3z. Lt th output b y(n). Which of th following is tru? y(n) is non causal with finit support y(n) is causal with infinit support y(n) = ; n >3 R [Y(z)] j R[Y(z)] j ;Im[Y(z)] j Im[Y(z)] j ; z z 38. A cubic polynomial with ral cofficints can possibly hav no xtrma and no zro crossings may hav up to thr xtrma and up to zro crossings cannot hav mor than two xtrma and mor than thr zro crossings will always hav an qual numbr of xtrma and zro crossings 39. Lt x 7 =. Th itrativ stps for th solution using Nwton-Raphson's mthod is givn by 7 7 x k+ = x k x k+ = x k xk x k z z x x k+ = x k k xk+ = x k 7 x k 7 xk 4. F(x, y) = (x + xy) âx (y xy) ây. It's lin intgral ovr th straight lin from (x, y) = (, ) to (x, y) = (, ) valuats to An idal opamp circuit and its input wavform ar shown in th figurs. Th output wavform of this circuit will b 3 V 3 t t t 3 t 4 t 5 t 6 t V in k + 3V 6V k k V out 6 6 V V t 3 t 6 t t 3 t 6 t V V 3 t 6 t t t 4 3 t t 4 t 6 t Pag 8 of 5

9 4. A V, 5Hz, singl-phas induction motor has th following connction diagram and winding orintations shown. MM' is th axis of th main stator winding (M M ) and AA' is that of th auxiliary winding (A A ). Dirctions of th winding axs indicat dirction of flux whn currnts in th windings ar in th dirctions shown. Paramtrs of ach winding ar indicatd. Whn switch S is closd, th motor rotats clockwis S V 5Hz r a = L a =/H A A A M M r m =. L m =./H M M A rotats anticlockwis dos not rotat rotats momntarily and coms to a halt 43. Th circuit shows an idal diod connctd to a pur inductor and is connctd to a purly sinusoidal 5Hz voltag sourc. Undr idal conditions th currnt wavform through th inductor will look lik D + V s = sint + L = (./)H.5 currnt tim(ms) currnt tim(ms) Pag 9 of 5

10 currnt tim(ms) currnt tim(ms) 44. Th Currnt Sourc Invrtr shown in figur, is opratd by altrnatly turning on thyristor pairs (T, T ) and (T 3, T 4 ). If th load is purly rsistiv, th thortical maximum output frquncy obtainabl will b T.F T3 D + D3 D4 D A + T4.F T 5kHz 5kHz 5kHz 5kHz 45. In th choppr circuit shown, th main thyristor (T M ) is opratd at a duty ratio of.8, which is much largr th commutation intrval. If th maximum allowabl rapplid dv/dt on T M is 5 V/s, what should b th thortical minimum valu of C? Assum currnt rippl through L o to b ngligibl..f. F + V C + L D T A T M D L C 8 F F Pag of 5

11 46. Match th switch arrangmnts on th top row to th stady-stat V-I charactristics on th lowr row. Th stady stat oprating points ar shown by larg black dots (I) (II) (III) (IV) i s i s i s i s V s V s V s V s A I, B II, C III, D IV A IV, B III, C I, D II A II, B IV, C I, D III A IV, B III, C II, D I 47. For th circuit shown, find out th currnt flowing through th rsistanc. Also idntify th changs to b mad to doubl th currnt through th rsistanc V s = 4V i s = 5A (5A; Put V s = V) (A; Put V s = 8V) (5A; Put I s = A) (7A; Put I s = A) 48. Th figur shows a thr-phas dlta connctd load supplid from a 4V, 5 Hz, 3-phas balancd sourc. Th prssur coil (PC) and currnt coil (CC) of a wattmtr ar connctd to th load as shown, with th coil polaritis suitably slctd to nsur a positiv dflction. Th wattmtr rading will b a 3-Phas Balancd Supply 4Volts 5Hz Z (+j) b Z (+j) Z Z CC PC c 6 Watt 8 Watt 4 Watt 49. An avrag-rading digital multimtr rads V whn fd with a triangular wav, symmtric about th tim-axis. For th sam input an rms-rading mtr will rad. / 3 / Pag of 5

12 5. Figur shows th xtndd viw of a pol dc machin with armatur conductors. Normal brush positions ar shown by A and B, placd at th intrpolar axis. If th brushs ar now shiftd, in th dirction of rotation, to A' and B' as shown, th voltag wavform V AB will rsmbl N S B B A A rotation at spd rad/sc V AB t V AB t V AB t V AB t Pag of 5

13 Common Data Qustions: 5 & 5 A a B b C c N S S Th star-dlta transformr shown abov is xcitd on th star sid with a balancd, 4-wir, 3-phas, sinusoidal voltag supply of ratd magnitud. Th transformr is undr no load condition. 5. With both S and S opn, th cor flux wavform will b A sinusoid at fundamntal frquncy Flat toppd with third harmonic Paky with third harmonic Non of ths 5. With S closd and S opn, th currnt wavform in th dlta winding will b a sinusoid at fundamntal frquncy flat toppd with third harmonic only third harmonic non of ths Common Data Qustions: 53 & 54 Th circuit diagram shows a two winding, losslss transformr with no lakag flux, xcitd from a currnt sourc, i(t), whos wavform is also shown. Th transformr has a magntizing inductanc of 4/mH. : A i(t) S A i(t) 3 5ms ms 5ms ms 5ms 3ms t A B 53. Th pak voltag across A and B, with S opn is 4/V 8V 4/V 8/V 54. If th wavform of i(t) is changd to i(t) = sin (t) A, th pak voltag across A and B with S closd is 4V 4V 3V 6V Pag 3 of 5

14 Common Data Qustions: 55 & 56 A systm is dscribd by th following stat and output quations dx (t) = 3x (t) + x (t) + u(t) dt dx (t) = x (t) + u(t) dt y(t) = x (t) whr u t is th input and y t is th output 55. Th systm transfr function is s s 5s 6 s s 3 5s 6 s s 5 5s 6 s s 5 5s Th stat transition matrix of th abov systm is 3t t 3t t 3t t t 3t 3t 3t t t t t 3t 3t Linkd Answr Qustions: Q.57 to Q.6 Carry Two Marks Each Statmnt for Linkd Answr Qustions: 57 & 58 A C Coil Coil B D Th figur abov shows coils and, with dot markings as shown, having 4 and 6 turns rspctivly. Both coils hav a ratd currnt of 5A. Coil is xcitd with singl phas, 4V, 5Hz supply 57. Th coils ar to b connctd to obtain a singl phas, 4/V, auto transformr to driv a load of kva. Which of th options givn should b xrcisd to raliz th rquird auto transformr? Connct A and D; Common B Connct B and D; Common C Connct A and C; Common B Connct A and C; Common D 58. In th autotransformr obtaind in Qustion 57, th currnt in ach coil is Coil- is 5 A and Coil- is A Coil- is A and Coil- is 5 A Coil- is A and Coil- is 5 A Coil- is 5 A and Coil- is A Pag 4 of 5

15 Statmnt for Linkd Answr Qustions: 59 & 6 k 3V AB + A 5V + k k B 59. For th circuit givn abov, th Thvnin s rsistanc across th trminals A and B is.5k.k k.k 6. For th circuit givn abov, th Thvnin s voltag across th trminals A and B is.5v.5v V.5V Pag 5 of 5