SOLVED GATE (ELECTRICAL ENGG.) 2018 Engineering Mathematics and Technical Section

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1 SOVED GATE (EETA ENGG.) 8 Engineering Mhemics nd Technicl Secion Q. No. 5 rry One Mrk Ech. A singlephse kva, V/ V, 5 Hz rnsformer hs volge drop of 5% cross is series impednce full lod. Of his, % is due o resisnce. The percenge regulion of he rnsformer full lod wih.8 lgging power fcor is (A) 4.8 (B) 6.8 () 8.8 (D).8 mpednce 5%.5 pu Z pu esisnce %. pu pu ecnce is pu pu pu pu X Z Volge regulion full lod.8 p.f. lgging pu cosf ± X pu sinf pu 4.8% Ans. (A). n slien pole synchronous moor, he developed relucnce orque ins he mximum vlue when he lod ngle in elecricl degrees is (A) (B) 45 () 6 (D) 9 Slien pole synchronous moor power nd orque relions per phse: EV V X X b d q P sind sin( d) Ws X XX d q EV 6 V X X b d q T sind sin d p NS Xd XX d q Nm ON off The second erm is relucnce power or relucnce orque, which is direcly proporionl o sin d. Therefore relucnce orque will be mximum, when d 45. This is rue becuse sin (45 ) Þ sin 9 (Mximum) Ans. (B). A single phse fully conrolled recifier is supplying lod wih n niprllel diode s shown in he figure. All swiches nd diodes re idel. Which one of he following is rue for insnneous lod volge nd curren? (A) v ³ & i < (B) v < & i < () v ³ & i ³ (D) v < & i ³ During forwrd bis off ON i o d V i o d v [Free wheeling diode is off] e V () m sin( w ), V () m sin( w )[posiive] in m n GATE_EE_Moning Shif_8.indd 98 4:6:59 PM

2 A SOVED GATE (EETA ENGG.) 8 During reverse bis () Tric is combinion of wo ni prllel Ss i Tric: off ON V m V in () ON off o d [Free wheeling diode is off] V () V m sin(w) [posiive] MT G MT () When MT is ve nd MT is ve p p q V m V m p p p S llows curren only in one direcion node o chode ( i ). 4. Four power semiconducor devices re shown in he figure long wih heir relevn erminls. The device(s) h cn crry dc curren coninuously in he direcion shown when ged pproximely is (re) A MT A D G K Thyrisor G MT Tric G K GTO (A) Tric only (B) Tric nd MOSFET () Tric nd GTO (D) Thyrisor nd Tric S: conducs only from node o chode Tric: A G q S MOSFET () When MT is ve nd MT is ve G GTO: GTO conducs only from node o chode A G K MOSFET D D G G S S () When D is ve nd S is ve, diode is OFF D(ve) G K S(ve) GATE_EE_Moning Shif_8.indd 98 4:7: PM

3 SOVED GATE (EETA ENGG.) 8 A () When D is ve nd S is ve, diode is ON S D Ans. (A) 5. Two wmeer mehod is used for mesuremen of power in blnced hreephse lod supplied from blnced hreephse sysem. f one of he wmeers reds hlf of he oher (boh posiive), hen he power fcor of he lod is (A).5 (B).6 ().77 (D).866 n wo wmeer mehod Given W ( W W) nf ( W W) W. So we hve nf Þ f W W W W Hence cosf cos. 866 Ans. (D) 6 onsider lossy rnsmission line wih V nd V s he sending nd receiving end volges, respecively. Z nd X re he series impednce nd recnce of he line, respecively. The sedyse sbiliy limi for he rnsmission line will be (A) greer hn VV X (B) less hn VV X () equl o VV (D) equl o VV X Z For simple rnsmission line, i x eodnce V V VV Pmx () x Wih lossy rnsmission line we hve V Z VV AV P cos( b d) cos( b ) () x Z i x where enuion cons. nd b propgion cons. So wih lossy rnsmission line P VV x mx < V Ans. (B) 7. The grph of nework hs 8 nodes nd 5 independen loops. The number of brnches of he grph is (A) (B) () (D) 4 oops b (N ) Þ 5 b (8 ) Þ 5 b 7 Þ b Ans. (B) 8. n he figure, he volges re v () cos (w), v () cos (w p/8) nd v () cos (w p/6). The circui is in sinusoidl sedy se, nd << w. P, P nd P re he verge power oupus. Which one of he following semens is rue? v () P v () (A) P P P (B) P <, P >, P > () P <, P >, P < (D) P >, P <, P > Given P P v() cos( w) v() cos p w 8 v() cos p w 6 v () GATE_EE_Moning Shif_8.indd 98 4:7: PM

4 A4 SOVED GATE (EETA ENGG.) 8 So v : p 8 v : p v leds v nd v. So, v is source, v nd v re bsorbing. Hence, P >, P, P < 5 V V V Ans. () 9. Mch he rnsfer funcions of he secondorder sysems wih he nure of he sysems given below. Trnsfer funcions P: Q: : s s s 5 5s 5 Nure of sysem. Overdmped 5 s 5. riiclly dmped 5 5 8s. Undmped (A) P, Q, () P, Q, (B) P, Q, (D) P, Q, 5 We sr wih P. s 5s 5 w Now n 5 w rd/sec. n x Þx Q s s 5 w n 64. <, so underdmped 5 w 5 5 rd/sec. n x 5 Þ x, so criiclly dmped 5 5 s 8 s w n 5 ω 59. n 8 x. 5 >, so overdmped 5. 9 Ans. (). A posiive chrge of n is plced (,,.) where ll dimensions re in meres. onsider he xy plne o be conducing ground plne. Tke e 885. F/m. The Z componen of he E field (,,.) is closes o (A) V/m (B) V/m () V/m (D) V/m Given Q n plced (,,.). Also e 8.85 F/m. To clcule E Z Q E 4 pe Q E 4pe Q n P (,,.) Q n ( 6,,. ). 9 ( )(. 9 z) ( )(. z) ( E) P 4pe (.) 4pe (.) ( E ) P 6. z. 4p( ) 4p( ) z. 4p ( ) 7 z p ( ) 7 7 â 4p z 9 z z 7 Ans. (D) GATE_EE_Moning Shif_8.indd :7:6 PM

5 SOVED GATE (EETA ENGG.) 8 A5. e f be relvlued funcion of rel vrible defined s f(x) x for x ³, nd f(x) x for x <. Which one of he following semens is rue? (A) f(x) is disconinuous x. (B) f(x) is coninuous bu no differenible x. () f(x) is differenible bu is firs derivive is no coninuous x. (D) f(x) is differenible bu is firs derivive is no differenible x. Given f(x) x, x ³ nd f(x) x, x <. Firs derivive: x x f ( x) x x < From his we cn see h f ( x) is no differenible x. Since, lim fx ( ) lim fx ( ) x x, x f ( x), x < So, f(x) is differenible bu is s derivive is no differenible x. Ans. (D). The vlue of he direcionl derivive of he funcion f( x, y, z) xy yz zx he poin (,, ) in he direcion of he vecor p i j k is (A) (B).95 ().9 (D).9 Given f xy yz zx f f f f i j k x y z iy ( xz) j( xy z ) k( yz x ) f (,,) i( 4) j( 4 ) k( 4) 5i j k p i j k p 4 4 The direcionl derivive of f( z, y, z ) (,, ) in he direcion of p p is f p p ( 5 ) i j k i j k Ans. (A) z. The vlue of he inegrl dz in couner z 4 clockwise direcion round circle of rdius wih cener he poin z is (A) p i (B) pi () p i (D) pi z dz z 4 z dz ( z )( z ) z z dz ( z ) z πi f( ), where fz () z p i 4 p i p i Ans. (A) 4. n he logic circui shown in he figure, Y is given by A B D (A) Y ABD (B) Y (A B) ( D) () Y A B D (D) Y AB D Y GATE_EE_Moning Shif_8.indd :7:9 PM

6 A6 SOVED GATE (EETA ENGG.) 8 A Y B D Y Y A B AB Y D Y (AB) (D) AB D Ans. (D) 5. The opmp shown in he figure is idel. The inpu impednce v is given by iin V in (A) Z () Z V in in i in i in V n Z (B) Z (D) Z Z V o V o Y V in Z in V () V in V Subsiuing his in Eq. () we ge V Þ V Þ V Þ V Þ V Þ V in in in in Z V in Z in Z in ( ) Zin ( ) Z Z in Ans. (B) 6. A coninuousime inpu signl x() is n eigenfuncion of n T sysem, if he oupu is (A) kx(), where k is n eigenvlue (B) ke j w x(), where k is n eigenvlue nd e j w is complex exponenil signl () x()e j w, where e j w is complex exponenil signl (D) kh(w), where k is n eigenvlue nd H(w) is frequency response of he sysem For eigenfuncion of T sysem, oupu is consn ime of inpu. x () Hs () y () Here, x() which is coninuous ime inpu signl, is n eigenfuncion. So here H(s) should be consn. Therefore y() kx() For exmple, if inpu x e, hen y() ke where k H(s) s. Ans. (A) 7. onsider nonsingulr squre mrix A. f rce (A) 4 nd rce (A ) 5, he deerminn of he mrix A is (up o deciml plce). A is mrix Tr(A) 4 Þ l l 4 GATE_EE_Moning Shif_8.indd :7: PM

7 SOVED GATE (EETA ENGG.) 8 A7 Tr(A ) 5 Þ l l 5 Þ ( l l ) l l ll Þ 6 5 l l Þ l l Þ l l A 55. Ans. (5.5) 8. e f be relvlued funcion of rel vrible defined s f(x) x [x], where [x] denoes he lrges ineger less hn or equl o x. The vlue of 5. fxdx ( ) is (up o deciml plces) fxdx ( ) ( x [ x]) dx ( x [ x]) dx ( xdx ) [ xdx ] [ xdx ] x dx dx 5. (. 5) ( 5. ) (. 5) [( )] Ans. (.5) 9. n he wopor nework shown, he h prmeer V where, h, when V in ohms is. (up o deciml plces). V W W W V V W W W V V h V, V W W W V W V.5 V.5 Þ V.5 Þ V h. 5 Ans. (.5). The series impednce mrix of shor hreephse rnsmission line in phse coordines is Z Z Z s m m Zm Zs Zm. f he posiive sequence imped Zm Zm Zs nce is ( j ) W, nd he zero sequence is (4 j ) W hen he imginry pr of Z m (in W) is (up o deciml plces). GATE_EE_Moning Shif_8.indd :7: PM

8 A8 SOVED GATE (EETA ENGG.) 8 e Z ( j )W nd Z (4 j )W. We know h Z Z s Z m () Z Z s Z m () Subrcing Eq. () from Eq. () we ge Z Z Z m Z Z Þ Z m 4 j j j ( j7) The imginry pr of Z m is 7.. Ans. (7.). The posiive, negive nd zero sequence impednces of 5 MVA, hreephse, 5.5 kv, srgrounded, 5 Hz generor re j. pu, j.5 pu nd j. pu, respecively, on he mchine ring bse. The mchine is unloded nd working he red erminl volge. f he grounding impednce of he generor is j. pu, hen he mgniude of ful curren for bphse o ground ful (in ka) is (up o deciml plces). For G ful f Pu bse VTh z z z z. 5.. (. ) pu P V n f f bse Pu ka A Ans. (7.5). A bus dmince mrix for n elecric power sysem hs 8 nonzero elemens. The minimum number of brnches (rnsmission lines nd rnsformers) in his sysem re (up o deciml plces). Given bus mrix. N. 6 Tol roo buses Given number of nonzero elemens 8 Number of zero elemens Sprsiy (s) Tol numberofelemens Number of rnsmission lines nd rnsformers is N ( x) N (. 99) 5 Ans. (5). The wveform of he curren drwn by semiconverer from sinusoidl A volge source is shown in he figure. f A, he rms vlue of fundmenl componen of he curren is A (up o deciml plces). Volge nd curren i () V m sin(w) 8 p p V m sin(w) p Fourier series represenion on i () is 4 n n i () cos α α sin n n ω π n 5,, MS vlue of nh hrmonic is 4 n n n n cos cos p p MS vlue of fundmenl is ( rms ).cos p s cos 7. 9 A p w q w Ans. (7.9 A) 4. A seprely excied dc moor hs n rmure resisnce.5 W. The field exciion is kep consn. A n rmure volge of V, he moor produces orque of 5 Nm zero speed. Neglecing ll mechnicl losses, he nolod speed GATE_EE_Moning Shif_8.indd :7:5 PM

9 SOVED GATE (EETA ENGG.) 8 A9 of he moor (in rdin/s) for n rmure volge of 5 V is (up o deciml plces). Given, seprely iniied dc moor. Field exciion is consn. Produces orque of 5 Nm. V.5 W A zero speed, N, E b. e E b V Þ (.5) Þ A 5. 6 T N E 6 fznp b p pn 6 A ZP T A ZP f Nm k p where k f p A 5 Now T 5 Nm, A, k 5. When moor runs on nolod given ll mechnicl losses negleced, nolod curren is negligible nd he volge drop nolod cn be negligible. Therefore Now ZP k f p A Þ ZP f p( k) A N Þ Eb p( k) 6 Þ E b Þ w E kb E b V 5 V ZNP Eb f 6A k w (w: Nolod speed in rd/sec.) 5 Þ w 5. 6 rd/sec Ans. (5) 5. onsider uniy feedbck sysem wih forwrd rnsfer funcion given by Gs () ( s )( s ) The sedyse error in he oupu of he sysem for unisep inpu is (up o deciml plces). Uni sep inpu, kp lim G() s s For uni sep inpu, e ss k p Þ e ss 66. unis Q. No. 655 rry Two Mrks Ech Ans. (.66) 6. A rnsformer wih oroidl core of permebiliy m is shown in he figure. Assuming uniform flux densiy cross he circulr core crosssecion of rdius r <<, nd neglecing ny lekge flux, he bes esime for he men rdius is r i S i P sin w v P V cos w N P (A) mvr N p w N S (B) mr N P N S w V () mvr N P w (D) mr N P w V The inducnce of primry is Np / S, where S is relucnce of mgneic ph. l p S ma mp [ r ] mr Np Np mr mr Np r X w w m v S GATE_EE_Moning Shif_8.indd :7:8 PM

10 A SOVED GATE (EETA ENGG.) 8 V Np r X. w.. m r Np m.... w V Ans. (D) 7. A Ampere moving iron mmeer hs n inernl resisnce of 5 mw nd inducnce of. mh. A shun coil is conneced o exend is rnge o Ampere for ll opering frequencies. The ime consn in milliseconds nd resisnce in mw of he shun coil respecively re (A), 5.55 (B), ().8,.55 (D)., M mmeer 8. The posiive, negive nd zero sequence impednces of hree phse generor re Z, Z nd Z, respecively. For lineoline ful wih ful impednce Z f, he ful curren is f k f, where f is he ful curren wih zero ful impednce. The relion beween Z f nd k is Z Z k (A) Zf ( )( ) k Z Z k (B) Zf ( )( ) k Z Z k () Zf ( ) k Z Z k (D) Zf ( ) k For ful: m m se : Wihou Z f Z Z sn sn is given h m 5 mω Shun coil E g ~ m. mh Exising rnge mpere equired rnge mpere equired Sclingfcor(m) Exising The required vlue shun coil resisnce is given by se : Wih Z f f Z E g Z m 5 sn 555. mω m To mke he meer independen of frequency, he ime consn of boh prllel brnch should be sme i.e. sn m sn m. sn. m.sec 5 sn m.sec sn 555. ma. Ans. (A) Z E g ~ f Eg Z Z Z f Z f Z GATE_EE_Moning Shif_8.indd 98 4:7: PM

11 SOVED GATE (EETA ENGG.) 8 A Given, f k f. So E E g g Z Z Z Z Z k f Þ Z Z k(z Z Z f ) Z Z k Þ Zf ( )( ) k Ans. (A) 9. onsider he wo bus power sysem nework wih given lods s shown in he figure. All he vlues shown in he figure re in per uni. The recive power supplied by generor G nd G re Q G nd Q G respecively. The per uni vlues of Q G, Q G, nd line recive power loss (Q loss ) respecively re.ðd j..ð G jq G 5 j5 Q loss j G 5 jq G (A) 5.,.68,.68 (B) 6.4,.,.4 () 6.4,.4,.68 (D) 5.,.4,.4 A G lod demnd is pu, G supplies only 5. emining is supplied by G hrough rnsmission line. P Q Q S S VSV sind Þ 5 sind sin d 5. X. Þ d VS VSV X X cos d cos 4. pu.. VSV V cos d X X. The peruni power oupu of slienpole generor which is conneced o n infinie bus, is given by he expression, P.4 sin d.5 sin d, where d is he lod ngle. Newonphson mehod is used o clcule he vlue of d for P.8 pu. f he iniil guess is, hen is vlue (in degree) he end of he firs ierion is (A) 5 (B) 8.48 () 8.74 (D). P(d).4 sin d.5 sin d.8.4 sin d.5 sin d.8 d P ( d ) ( P( d )) dd.4 cos d. cos d Given d. By using Newonphson mehod for single vrible f( d) P( d) d d d f ( d ) P ( d ) 4. sin 5. sin 6. 8 Þ d 4. cos. cos 6 Þ d.9 rd.6 Þ d 8.74 Ans. (). A D volge source is conneced o series circui by urning on he swich S ime s shown in he figure. Assume i(), v(). Which one of he following circulr loci represens he plo of i() versus v()? i() S H 5 V F v() cos 4. pu.. Q loss Q S Q 4. (. 4) 68. pu (A) i() (,5) v() (B) i() (5, ) v() A G : Q G Q lod Q S pu i() i() A G : Q G Q lod (Q ) (.4).4 pu Ans. () () (, 5) v() (D) (5, ) v() GATE_EE_Moning Shif_8.indd 98 4:7: PM

12 A SOVED GATE (EETA ENGG.) 8 ( s ) V() s s () s s Þ () s V() s s 5s Þ () s 5 V() s ss ( ) s Þ () s 5 s i() 5 sin i() v () id sin d c c 5 Þ v() 5 5 cos 5 i () v () p/ 5 5 p v() Ans. (B). The equivlen impednce Z eq for he infinie ldder circui shown in he figure is j9 W j9 W (A) j W () j W Z eq 9j nfinie ldder circui Z eq Z 9j Z (B) j W (D) W eq eq 5j j 4j 4j Þ Z 9jz 6 Þ Z j Z eq Ans. (A). onsider sysem governed by he following equions dx() x() x() d dx() x() x() d The iniil condiions re such h x () < x () <. e x lim x () nd f x lim x ().Which one of he following is rue? f (A) x () x < x < (B) x < x < f f f f x < (D) x x f f Differeniing () w.r. ` f f dx() x() x() () d dx() x() x() () d Z eq j5 W j5 W j W j W dx() dx() dx() d d d dx() x() x() ( from( )) d x dx() x d dx() () () ( from( )) d GATE_EE_Moning Shif_8.indd 98 4:7:7 PM

13 SOVED GATE (EETA ENGG.) 8 A dx () dx () d d D D DD ( ) D, Soluion, x () e x lim x () f Similrly, differenly () w.r.. ` using () nd () we ge dx () dx() d d \ soluion, x() e x lim x () f xf x f < Ans. () 4. The number of roos of he polynomil s 7 s 6 7s 5 4s 4 s 7s 5s, in he open lef hlf of he complex plne is (A) (B) 4 () 5 (D) 6 The chrcerisic equion is s 7 s 6 7s 5 4s 4 s 7s 5s s s s s s 96 s 4 s 7 s Auxiliry equion is A(s) 8s 4 48s Differeniing his w.r.. s we ge d ds As s 96 s Tol number of poles 7 Two sign chnges bove uxiliry equion poles in HS Two sign chnges below uxiliry equion implies h ou of 4 symmeric roos bou origin, wo poles re in HS nd wo poles re in HS. Therefore poles in HS nd 4 poles in HS. Ans. (A) z 5. f is circle z 4 nd fz () ( z z ), hen fzdz () is (A) (B) () (D) 4 f(z) z dz ( z z ) z ( z ) ( z ) dz 4 d es. fz lim z z dz z z () ( )! ( z ) ( z ) zz ( ) z ( z ) lim z 4 ( z ) zz ( ) z lim z ( z ) 4 4 d es. fz lim z z dz z z () ( )! ( z ) ( z ) ( z ) z z ( z ) lim z 4 ( z ) zz ( ) z lim z ( z ) By residue heorem, pi (4 4) Ans. (B) GATE_EE_Moning Shif_8.indd 98 4:7: PM

14 A4 SOVED GATE (EETA ENGG.) 8 6. Which one of he following semens is rue bou he digil circui shown in he figure So F A Ans. (B) f N D Q D Q D Q f OUT (A) cn be used for dividing he inpu frequency by. (B) cn be used for dividing he inpu frequency by 5. () cn be used for dividing he inpu frequency by 7. (D) cnno be relibly used s frequency divider due o disjoin inernl cycles. D Q Q Q Q Q 5cycles; Divide by5 8. onsider he wo coninuousime signls defined below:, x(), oherwise, x(), oherwise These signls re smpled wih smpling period of T.5 seconds o obin discreeime signls x [n] nd x [n], respecively. Which one of he following semens is rue? (A) The energy of x [n] is greer hn he energy of x [n]. (B) The energy of x [n] is greer hn he energy of x [n]. () x [n] nd x [n] hve equl energies. (D) Neiher x [n] nor x [n] is finieenergy signl., x(), x () oherwise So, frequency will be divided by 5. Ans. (B) 7. Digil inpu signls A, B, wih A s he MSB nd s he SB re used o relize he Boolen funcion F m m m m 5 m 7, where m i denoes he i h minerm. n ddiion, F hs don cre for m. The simplified expression for F is given by (A) A B A (B) A () A (D) A B A, x(), oherwise x () Given F m m m m 5 m 7 nd m don cre B B B B A X A A f A x[ n],. 75,. 5,. 5,,. 5,., 5. 75, x[ n] 5,., ,.,,.,.,., GATE_EE_Moning Shif_8.indd :7: PM

15 SOVED GATE (EETA ENGG.) 8 A5 We cn see clerly, x [ n] hs greer energy hn x [ n ] Energy in x [ n] (. 75) (.) 5 (. 5) Energy in x [ n] (. 75) (. 5) (.) 5 Ans. (A) 9. The signl energy of he coninuousime signl x() [( )u( )] [( )u( )] [( )u( )] [( 4)u( 4)] is (A) / (B) 7/ () / (D) 5/ x() r( ) r( ) r( ) r( 4) x() ( ) 4 Ex () x() d ( ) d d ( 4) { } d 5 4 Ans. (D) 4. The Fourier rnsform of coninuousime signl x() is given by x( w ) ( jw), < w < where j nd w denoes frequency. Then he vlue of ln x() is (up o deciml plce). (ln denoes he logrihm o bse e) X( w) ( jw) nverse Fourier Xs () ( s ) A, we hve x () e u () Þ x() e u () { ln x ()} ln ln e e ln (x()) ln () Ans. () 4. n he circui shown in he figure, he bipolr juncion rnsisor (BJT) hs curren gin b. The bseemier volge drop is consn, V BE.7 V. The vlue of he Thevenin equivlen resisnce Th (in W) s shown in he figure is (up o deciml plces). 5 V W kw.7 V D model: Applying KV inpu loop, we hve kw Th e kω kω kω kω b r e 97. ma kω. 99 k 9. k VT 5 mv Ω. ma e b re r p.7 kw kw.7 V E kw The c model for he common bse circui is B r p kw kw E kw bi open Th b b GATE_EE_Moning Shif_8.indd :7:5 PM

16 A6 SOVED GATE (EETA ENGG.) 8 kw/b Th B r p b.7 W kw Vb kω. 7 Ω Ω Th kw.7 W kw. kw... 9 kω 9 Ω.. Ans. (9 Ω) 4. As shown in he figure, is he rc from he poin (, ) o he poin (, ) on he circle x y 9. The vlue of he inegrl ( y yxdx ) ( xy x ) dy is (up o deciml plces). y (, ) (, ) V b Given x y 9. Since he rc is from he poin (, ) o he poin (, ), we hve x cos q nd y sin q. dx sin q d q nd dy cos q d q q vries from o p/. So ( y xydx ) ( xy x ) dy π / ( 9sin q 8sinq cos q)( sin q dq ) ( 8 sinq cosq 9cos q )( cos q) dq x b π / ( 7 sin q 54 sin q cosq 54 sinq cos q 7 cos q) dq Ans. () 4. e f(x) x 7x 5x 6. The mximum vlue of f(x) over he inervl [, ] is (up o deciml plce). We hve f(x) x 7x 5x 6 in [, ]. Differeniing w.r.. x we ge Now A x A x.55 f ( x) 9x 4x 5 f ( x) 8x 4 f ( x) Þ x 4x 5 Þ x,.55 f () 8 4 4> minim f (. 55) 4. < mxim So Mximum {f(), f(.55), f()} Mximum {6, 7., } Ans. () 44. e A nd B A A 4A 5, where is he idenify mrix. The deerminn of B is (up o deciml plce). We hve A A l l Þ l l By yleyhmilon heorem A A 4A 4 Þ A A 4A 5 Þ B (ccording o he quesion) B Ans. () GATE_EE_Moning Shif_8.indd :7:9 PM

17 SOVED GATE (EETA ENGG.) 8 A7 45. The cpcince of n irfilled prllelple cpcior is 6 pf. When dielecric slb whose hickness is hlf he disnce beween he ples, is plced on one of he ples covering i enirely, he cpcince becomes 86 pf. Neglecing he fringing effecs, he relive permiiviy of he dielecric is (upo deciml plces). We hve n second cse: e A 6 pf d.4 y() (sec) Given K GsHs () () ( s ) ( s ) For closed loop sysem e s () s () GsHs () () GsHs () () s (){ GsHs () ()} s () GsHs () () pcince, d A e e A ( 6 pf) pf d/ d ee ra nd ( 6) er d pf er pf Now, er pf 86 pf ( er ) (given) e Þ r 86 ( er) Þ 86 er e 86 Þ e r 4 r 5. Ans. (.5) 46. The uni sep response y() of uniy feedbck sysem wih open loop rnsfer funcion K GsHs () () is shown in he figure. ( s ) ( s ) The vlue of K is (upo deciml plces). sk () / X s () ( s ) ( s ) K X sk () s () {( s ) ( s ) k} Given, s (). So s K s () s[( s )( s ) K] Now given h im s() s 8.. So s K 8 K. Þ K 8 Ans. (8) 47. A hreephse lod is conneced o hreephse blnced supply s shown in he figure. f V n V, V bn V nd V cn 4 V (ngles re considered posiive in he niclockwise direcion), he vlue of for zero curren in he neurl wire is W (upo deciml plces). GATE_EE_Moning Shif_8.indd :7:4 PM

18 A8 SOVED GATE (EETA ENGG.) 8 n c b For N we hve From he given volges Y B j j Y B () VN VYN jx j VBN 4 5 jx j Subsiuing hese in Eq. () we ge 5 Þ 5.77 W Ans. (5.77) 48. The volge cross he circui in he figure, nd he curren hrough i, re given by he following expressions: v() 5 cos (w 6 ) V i() 5 X cos (w) A where w p rdin/s. f he verge power delivered o he circui is zero, hen he vlue of X (in Ampere) is (up o deciml plces). i() v() Elecricl ircui Given h v() 5 cos (w 6 ) i() 5 X cos (w ) P vg Þ 5 5 [( )( X)cos( 6 )] Þ 5 [( )( X)cos( 6 )] Þ X Ans. () 49. A phse conrolled single phse recifier, supplied by n A source, feeds power o n E lod s shown in he figure. The recifier oupu volge V m hs n verge vlue given by V ( cos ), p where V m 8 p vols nd is he firing ngle. f he power delivered o he lossless bery is 6 W, in degree is (up o deciml plces). Vm sin(w) V W mh 8 V Bery Power delivered o lossless bery E 6 W 8 6 A From given f recifier, V E Vm [ cos ] E p 8p [ cos ] 8. p 4[ cos ] cos cos 9 Ans. (9 ) 5. The figure shows wo buck converers conneced in prllel. The common inpu dc volge for he converers hs vlue of V. The converers hve inducors of idenicl vlue. The lod resisnce if W. The cpcior volge hs negligible ripple. Boh converers opere in he coninuous conducion mode. The swiching frequency is khz, nd he swich conrol signls re s shown. The circui operes in he sedy se. Assuming h he converers shre he lod eqully, he GATE_EE_Moning Shif_8.indd :7:46 PM

19 SOVED GATE (EETA ENGG.) 8 A9 verge vlue of i s, he curren of swich S (in Ampere), is (up o deciml plces). V S S i S S S Swich conrol signls.5 ms ms W S nd S re complimenry. od is lwys conneced o source. Therefore V V s V () V A P in P V s s V Þ s A [from Eq. ()] Þ s s 5 A Ans. (5) 5. A phse 9 kva, kv/ kv( /Y), 5 Hz rnsformer hs primry (high volge side) resisnce per phse of. W nd secondry (low volge side) resisnce per phse of. W. ron loss of he rnsformer is kw. The full lod % efficiency of he rnsformer opered uniy power fcor is (up o deciml plces). ph ; / Hv 9 A / eq. 9 (. ) 48. Ω u loss( f) eq W 4. 4 kw ore loss kw 9 % h 97. 6% Ans. (97.6) 5. A V D series moor, when opering from red volge while driving cerin lod, drws A curren nd runs r.p.m. The ol series resisnce is W. The mgneic circui is ssumed o be liner. A he sme supply volge, he lod orque is incresed by 44%. The speed of he moor in r.p.m. (rounded o he neres ineger) is. se From circui digrm, we hve A E b V ( se ) () 9 V N rpm V od orque incresed by 44% ( T ). So T T 44. T T A sme volge, For series moor, So 44 A E V ( ) b se () 88 V b N E f ( f ) N Eb N Eb N 88 9 Þ N rpm 85 rpm Ans. (85) GATE_EE_Moning Shif_8.indd :7:49 PM

20 A SOVED GATE (EETA ENGG.) 8 5. A dc o dc converer shown in he figure is chrging bery bnk, B whose volge is consn 5 V. B is noher bery bnk whose volge is consn 5 V. The vlue of he inducor, is 5 mh nd he idel swich, S is opered wih swiching frequency of 5 khz wih duy rio of.4. Once he circui hs ined sedy se nd ssuming he diode D o be idel, he power rnsferred from B o B (in W) is (up o deciml plces). 5 mh D i 5 V B S B 5 V mx Given V in 5 V, V 5 V ou V Vin D 5 5 D D. 666 Bu given duy cycle.4 \ The boos converer is opering in disconinuous mode. 5 b 5 b 6. b 4. V di s d on A ( ) mx (vg) mx min min 6 T mx ( b ) 8. [ 6. ] T 6 4. A Power rnsferred from B o B V in (vg) 5.4 W Ans. () 54. The equivlen circui of single phse inducion moor is shown in he figure, where he prmeers re Xl Xl Ω, X 4 Ω M nd s is he slip. A nolod, he moor speed cn be pproximed o be he synchronous speed. The nolod lgging power fcor of he moor is (up o deciml plces). jx l j X M s j X l VÐ DT BT T T m sec f on DT 8msec. j X M ( s) j X l V b D V s b GATE_EE_Moning Shif_8.indd 98 4:7:5 PM

21 SOVED GATE (EETA ENGG.) 8 A urren drwn by moor is W j W V Z q {\q impednce ngle will be p.f. ngle} j W j W () j ( ) j Therefore, nolod lgging p.f. of moor is (cos q) cos (8.9).6 lgging power fcor Ans. (.6) 55. The volge v() cross he erminls nd b s shown in he figure, is sinusoidl volge hving frequency w rdin/s. When he inducor curren i() is in phse wih he volge v(), he mgniude of he impednce Z (in W) seen beween he erminls nd b is (up o deciml plces). i() V() On nolod, N; N s slip, Z µf W W j W b j W i() j W On nolod, N; N s slip, W j6 W Simplifying he bove circui ino simple circui, we hve VÐ jx Z eq jx ZÐq j j Zeq ( 6)( ) [ j] ( j6) Ω V() b Z µf v() is in phse wih i() (only resisive) y jw z wj W Now w (\ w nd mf). So z j z jw j z 5( j) j z 5 5j j () For only resisive z 5 Þ.5 So using Eq. () z 5. Ans. (5) GATE_EE_Moning Shif_8.indd 98 4:7:54 PM

22 GATE_EE_Moning Shif_8.indd 98 4:7:54 PM