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GATE: 1996EE:Electrical Engineering

Dum tio n : T h re e Hour s Maximum Marks: 150SECfION-A(MARKS = 100)

EE.l. In each of the subquestions (1.1 to 1.48), four/five alternatives, A, B,C, and D(E) are providedof which one is correct. Indicate in you answerbook the correct answer by writing the alphabetcorresponding to the answer against thesubquestion. (48)< 1= 48)

1.1. The unit-impulse response of a unit-feedbackcontrol system is given byc(t) = - te-' +2 e-', (t < : : 0)the open loop transfer function is equal to

5+1 28 + 1(a ) (s + 2)2 (b ) ~8 + 1 5+1(e ) (s + 1)2 (d ) -o-s-

1.2. Consider the unit-step response of a unity-feedback control system whose open-loop

1transfer functions is G(s) = ---. Thes(s + 1)

1.3.

maximum overshoot is equal to(a ) 0.143 (b) 0.153(e ) 0.163 (d) 0.173For a feedback control system of type 2, the steadystate error for a ramp input is(a) infinite (b ) constant(e ) zero (d ) indeterminate

1.4. The closed-loop transfer function of a controlC(s) 1 .system is given by -- = --. For the inputR(S) 1+ s

ret) = sin t, the steady state value of c(t) isequal to

1.5. A periodic rectangular signal, xU) has the waveform shown in Figure.Frcquencv ol the fifthharmonic of its spectrum is

.(t)

(a ) 40 Hz(e ) 250 Hz

(b ) 200 Hz(d ) 1250 Hz

1,6. In the circuit shown in Figure.Xds an elementwhich always absorbs power. During a particularoperations, it sets up a current of 1amp in thedirection shown and absorbs a power Px' It ispossible tha tX can absorb the same power Px foranother current i,the value of this current is(a) (3 - J 1 4 ) amps

~(b ) (3 + Jl4) amps(e ) 5 amps(d ) none of these

1.7. A water boiler at home is switched on to the a.c.mains supplying power at 230 V /50 Hz. Thefrequency of instantaneous power consumed bythe boiler is(a ) 0 Hz(e ) 100 Hz

(b ) 50 Hz(d ) 150 Hz

1.S. Inthe seriesRCcircuit shown in Figure the voltageacross C starts increasing the d.c. source isswitched on. The rate of increase of voltage acrossC at the instant just after the switch is closed(i.e., at t =0 "),will be(a ) zero c1 G :Ja) .fi cos t (b ) 1 (b ) infinity1 J z sin (1 -~) (e ) RC(c ) . J 2 sin t (d ) (d ) l/RC

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1.9. The v-I characteristic as Seen from the temunat-pair (A, B) of the network of Figure. is shown inFigure. If an inductance of value 6 mH isconnected across the terminal-pair (A, B), the timeconstant of the system will be

(n ) 31J se c(b ) 12 se c(e l 32 se c(d ) unknown, unless the actual network is

specified1.10. Inside a hollow conducting sphere(n ) electric field is zero(b ) electric field is an non-zero constant(t') electric field changes with the magnitude of

the charge given to the conductor(d ) electric field changes with distance from the

cen Ire of the sphere1.11. If v,w, q stand for voltage, energy and charge,

then v can be expressed asdq dw(4 ) v=- (br. v = dqdwdw dq( e l dv= dq (d) dlJ= dw

1.12. The energy stored in the magneuc field of solenoid30 cm long and 3 em diameter wound with 1000turns of wire ca rryin g a cu r rent of 10 A is(a) 0.Q15 joule (b ) 0.15 joule( e l O.Sjoule (d ) US jou Ie

1.13. The function of oil ina transformer is(a l to provide insulation and cooling(b ) to provide protection against lightning( e l to provide protection against short circuit(d ) to provide lubrication

1.14. Auto-transformer is used in transrnissiodistribution nand(II) when operator is not available(b ) when iron losses are to be reduced(el ~hen efficiency considerations can b.ignored(d) when the transfonnation ratio is small1.1S. Keeping in view the requirement of paralleloperation. which of the 3-phase connectionsgiven betow are possible?(tI) delta-delta to delta-star( 1 ) ) delta-delta to star-delta(e ) star-star to delta-delta(d) delta-star to star-delta

1.16. A 4 pole generator with 16 coil has a two layerlap winding. The pole pitch is(a ) 32 (1 1 ) 16(e ) 8 (d) 4

1.17. A 4 pole dynamo with wave wound armaturehas 51 slots containing 20 conductors in eachslot. The induced emf is 35 7 volts and the speedis 8500 rpm.The flux per pole will be(a ) 3.5mWb (b ) 1.2mWb(e l 1.4mWb (d) 21mWb

1.18. A cylindrical rotor synchronous motor isswitched on the supply with its field windingsshorted on themselves. It will(a ) not start(b ) start but not run at synchronous speed(.) star Ias an induction motor and then run as

synchronous motor(d) start and run as a synchronous motor

1.19. In Figure. the characteristic that corresponds tothe variation of synchronous reactance of asynchronous motor with field current is(a ) curvel m

I:~~._...,2-!

(b ) curve II ,-".t::~ .( e l curve 1 IJ(d) curve IV

1.20. During hunting of sy.1cl1ronous motor(tI) negative phase sequence currents are

generated( I harmonics are developed in the armature

circuit(e ) damper bar develops torque(d ) field excitation increases

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1.21. Unbalanced supply voltage given to a 3.phasedelta-connected ind uction motor will cause '(n) zero sequence currents( / 7 ) less healing of the rotor(e ) negative sequence component current(d) a IIof these

1.22. When the supply voltage to an induction motoris reduced by 10%, the maximum torque willdecrease by approximately(a ) 5% (b) 10%(e ) 20% (d) 40%

1.23. An induction motor having full load torque of 60Nm when delta-connected develops a startingtorque of 120 Nm. For thesame supply voltage. ifthe motor is changed to srar-coonecuon, thestarting torque developed will be(a ) 40 Nm ( / 7 ) 60 Nm(el 90 Nm (d) 120 Nm

1.24. The torque speed characteristic of a repulsionmotor resembles which of the following de motorcha racteris tic ?(a ) Separatelyexcited{l1l Shunt( e ) Series (d) Compound

1.25. Which type of motor is most suitable for computerprinter drive?(a) Reluctance motor(b ) Hysteresis motor( e l Shaded pole motor(d ) Stepper motor

1.26. Incase of a split phase motor, the phase shillbetween currents in the two windings is around(a ) 30 degrees ( 1 1 ) 70 degrees( e l 90 degrees (d ) 120 degrees

1.27. In an induction motor, if the air gap is increased(a ) speed will reduce( 1 1 ) efiiciency will improve( e l power factor will be lowered(d) breakdown torque will reduce

1.28. Which semiconductor power device out of thefollowing is not a current triggered device?(d ) Thyristor ( / 7 ) C.T.O.(e ) Triac (d) MOSi-"Ef

1.l9. The Triac can be used only in(a ) inverter( I I ) rectifier

(e ) mulliquadrant chopper(d) cyclocorwerter

1.30. Which of the following does not cause permanentd~mage of an SCR ?(n) High current(h ) High rate df riSj!of.currentM High temperature rise( o f ) High rate of rise of voltage

1.31. In a lh yristor de chopper. which type ofcommutation results in best performance?(~) voltage commutation(b) current commutationM load communication(d) supply commutation

1.32. In a 3-phase controlled bridge rectifier, with anincrease of overlap angle, the output de voltage(a ) decreases(b ) increasesk) does not change(d) depends upon load inductance

1.33. During a disturbance on a synchronous machine,the rotor sw ings from A to Bbefore finally settlingdown to a steady state at point C on the powerangle curve. The speed of the machine duringoscillation is synchronous at point(s)(n ) A and B (b) A and C') BandC (d ) onlyatC

1.34. II the reference bus is changed in two load flowruns with same system data and power obtainedfor reference bus taken as specified P and Q inthe laIte r run(0 ) the system losses will be unchanged but

complex bus voltages will change( 1 1 ) the system losses will change but complex

bus voltages remain unchanged(e ) the system losses as well as complex busvoltage will change

(d ) the system losses as well as complex busvoltage will be unchanged

1.35. Resistance switching is normally employed in(0) a l\ breakers(b ) bulk oil breakers( e l minimum oil breakers(d) air blast circuit breakers

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1.36. Which material is used in controlling chainreaction in a nuclear reactor ?( I I ) Thorium (b ) Heavy water(e ) Boron (d) Beryllium

1.37. For a 500 Hz frequency excitation, a SOkm longpower line will b e modelled as(n ) short line(b ) medium line( e l long line(d) data insufficient for decision

1.38. For an unbalanced fault. with paths for zerosequence currents, at the point of fault( I I ) the nega tlve and zero sequence voltages are

minimum(b ) the negative and zero sequence voltages are

maximum(e ) the negative sequence voltage is minimum

and zero sequence voltage is maximum(tf) the nega live sequence voltage is maxi mum

and zero sequence voltage isminimum1.39. If the fault current is 2000 A, the relay setting is

50% and CT ratio is 400.5, the plug settingmultiplier will be(a ) 25 A (b ) 15 A(e ) 50 A (d) J O A

1.40. An advantage of a permanent magnet movingcoil instrument is that it is(a) free from friction error(b) has high (torque /weighr of the moving parts)

ratio(e ) has low (torque/weight of the moving parts)

ratio(d) can be used on both a.c , and d.c.

1.41. The moving coil in a dynamometer wattmeter isconnected(I I) in series with the fixed coil(b ) across the supply(e ) in series with the load(d) across the load

1.42. For a given frequency, the deflecting torque 01 aninduction ammeter is directly proportional to(a ) current- (b ) clIrrento(e ) Jcurrent (d) current

1,43. The scale of a voltmeter is uniform. Its type is( I I ) moving iron(b ) induction

(e ) moving coil permanent magnet(d) moving coil dynamometerThe ~~pletio~ region Or space charge regiOn O rtranstnon reglon 111 a semiconductor p-n junctid~ehu ~(II) electrons and holes(b) positive ions and electrons( e l positive ions and negative ions(d) negative ions and holes(e l no ions, electrons or holes

1.45. A non-inverting Op-Amp amplifier is shown inFigure. The output voltage V0 is

1.44.

(n ) (3/2) sin (100 t) (b ) 3 sin (100 I)( e l 2 sin (100 I) (d ) None of these

1.46. In the transistor amplifier shown infigure., th eratio of small signal voltage gain, when th e emitterresistor R,. is bypassed by the capacitor C,. towhen it is not bypassed, (assuming simplifiedapproximate h-parameter model for transistor, is

(n ) (b ) hJ,'(1 + ilfr) R,(d) 1+ _ ...........-

h"(e )

1.47. Let the magnitude of the gain in the invertingOP-Amp amplifier circuit shown in be x withswitch S1 open. When the switch S1 is closed,the magnitude of gain becomes(a) x/2

~(b ) -x " -. . . . . . .(e ) 2x 1(d) - 2 .t

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l.48. ~le Boolean expression forthe output of .circutt shown in Figure. is the log!c

:~c~

(a ) y= AS +AB+ C(b ) Y= AB +AB+ C(e ) Y = A B + A B +C(d ) Y = A B + A B + c

E E . 2 . The ques~on consists of 6 parts. Each part isaccompanied by four answers of which one iscorrect. Indicate the correct answer by writingthe alphabet A, B,C,or D. (6 x 2 = 12)

2.1. For the system shown in Figure, with a dampingratio (.of 0.7 and an undamped natural frequencyffi~ of 4 Tad/sec, the values of Kand a are

(a ) K = 4 , a = 0.35 (b ) K = 8 , a = 0.455(e ) K = 16, a = 0.225 (d) K = 64, a = 0.9

2.2. Th e unit impulse response of a system is given ascrt) =-4 ....+6e-21.Thestepresponseof the samesystem for t '"0 is equal to(a) - 3e -21 - 4e -I + 1 (b ) - 3e -21 + 4e -I - 1( e l - 3e -21- 4e -I - 1 (d ) 3e -21 + 4e -/ -1

2.3. A coil (which can be modeled as a series RLcircuit) has been designed for high-Qperforrnanceat a rated voltage and a specified frequency. Jf thefrequency of operation is doubled, and the coil isoperated at the same rated voltage, then the Q -factor and the active power P consumed by thecoil will be affected as follows(a ) P is doubled, Q is halved(b ) P is halved, Q is doubled(c ) P remains constant, Q is doubled(d) P decreased 4 times Q is doubled

2.4. Out of the following factors Ior a de h'_ . u mac me,(,) lnterpoleIii) A.rmature resistance(iii) Armature(iv) Reduction in field currentthe factors that are responsible fOT decrease -the terminal voltage 01 a shunt generator are m(a) r.nand IV (b ) I I, I II and V(e ) II, I V and V (d) It I V and VFor equilateral spacing of conductors 01 anuntransposed 3-phase line, we have(a ) balanced receiving end vollage and no

communication interference(b) unbalanced receiving end voltage and no

communication interference(e ) balanced receiving end voltage and

communication interference(d) unbalanced receiving end voltage and

communication interference

2.5.

2.6. The voltage series feedback in a feedbackamplifier leads to(a ) increase in band width, while the voltage

gain becomes less sensitive to varia lions incomponents and device characteristics

(b ) decrease in overall gain, while the inputresistance decreases

(e ) increase in distortion, while the outputresistance decreases(d) decrease ininput resistance, while the outputresistance increases

EE.3. This question contains five parts. In each part(3.1 to 3.5), three items are given on the left sideand more than three on the fight. For each itemon the lelt, match a suitable answer from the listgiven on the right. (5 ~ 3 = 1 5 )The performance of a general two-port networkN shown in the Figure. can be described in termsof its z-pararneters of h-pararneters as indicatedbelow

3.1.

[ V I ] = [ Z I I Z I 2 ] [ I I ]V2 Z21 Zn 1 '1[ 7 : ] = [ ~ : : : : ] [ ~ JIf the two-port is further characterized byadditional constraints, a few conditions have tobe satisfied by the parameters of the network. Foreach of the constraints specified in Table A .choose the appropriate condition to besatisiltxl,from amongst those listed in Table B.

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Table A Table B(n) Reciprocity at (P) I'll "22 -1'12 "21 = 1

the ports(b ) Passivity at the (Q) Z,2 = -Z21

ports(e l Eledrical (R) h'2 =1121

symmetJyatth e ports

3.1.

(l) absence of negativeresistors inside the2-porl

(U) energy input to thenetwork from theports is non-nega Iivefor all conditions atthe ports

Out of !h e several characteristics shown inFigure.identify the appropriate ones to match thefollowing for a J-phase induction motor.

\ .---~---- -\ - -~~. . . . ""II"

x-axis y-axis(I I) Load efficiency (P ) curve I(b ) Speed current (Q ) curve II(e ) Speed power factor (R) curve III

(S) curve IV(l) curve V

3.3. The per unit voltages of two synchronousmachines connected through a lossless line are0.95 L 10 and 1.0 L 0. Match the two sides inth e following

(a) Real power of (P) Positive real P O W I ! I "Machine 1(b ) Reactive power (O l Positive reactive

of Machine 1 power(e ) Power factor of (R ) Negative real P O W e r

Machine 1(5) Negative reactive

IX 'weTe n Leading power factor(U) Lagging power f a c t o r

3.4. In a 8085 microprocessor. the fOllowinginstructions may result inchange of accumulatorcontents and change in status flags. Ch oose thecorrect match for each instruction.

ConlenbiofACC Cyflag ACOag(I I) ANAr (P) unchanged maybySETunchanged(0) XRA r (Q ) unchanged SET SET(e l eMP r (R) unchanged SET RESET

(S ) may change RESET RESET(T ) may change RESET SET

3.5 . In an O S Cilloscop e, the input to th e horizontalplates is a 10 0 Hz voltage signaL The Lissajouspa ttems (A), (B) and (C) wi l l be generated whendifferent frequency voltage signals are applied tovertical plates. Match each Lissajous pattern tothe corresponding f r equency fy.(n) (P )J y '" 5 0

(Q) fy = 66.66(F)fy = 12 5(S)jy = 150(1)fy=200(U )fy = 300

(h )

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ANSWERS1.1 (/I) 1 .1 ( /1 ) 1.3 (e) 1.4 (d) I.S(d) 1.6(d) 1.7 (c) 1.8(n) 1.9(n) 1.10 (n)1.11 (II) 1.12 (/I) 1.13 (n) 1.14 (d) 1.IS{c) 1.16 (d) 1.17(11) 1.18 (II) 1.19 (b) 1.20 (e l1.11(r) 1.22 (c ) 1.23 en) 1.24 (c ) 1.2S(d) 1.26 (a) 1.27{,) 1.28 (d) 1.29 (c) 1.30(~)1.31 (a ) 1.32 (a ) 1.33(,) 1.34(11) 1.35 (d) 1.36 (b ) 1.37 (c) 1.38(11) 1.39 (d) 1.40 (b)1.41 ( l r ) 1.42(11) 1.43 (b) 1.44 (e l 1.45(11) 1.46() lA7(,,) 1.48 (/I)

EXPLANATIONSEE. l . C(t) : - te-I+ 2rl,.1.

(t < ': 0)1 2 2 .s + 1C(s} - --+--2--- - (8 + 1)2 s + 12 (s+)2

C{s) ~1 + G(s) ,28+

C(s) ... '" (s+)2 26 +1G( s ) 1- C(s) 28+1 T1---(8+1)21.2. C(s) ___g&_R(s) 1+ G(s) ,

G(s) 8 (8 + 1)- - - = 1 '" 82 + 8 + 1I-G(s) 1+--8 (8 + 1)

0 0 , , = 2'_~R 1-.,2)141 ~ (1/1)M '" e ~,-~- " ep= e ",[3 '" 0,163C(jw) __ 1_

R(jw) - 1+ ) 0 >C(s)1.4. R(s) = 1 + 5

Fromr{t) sint, w '" 1, i C(jW) 1 J. . . .R(jw) "P" . f 21 1= - tan-II = - 4 '

.. 55 value of cO )

1.S. The Periodic time = 4 ms = 4 x 10-3 S(;.. . Fundamental frequency

103

= - =25OHz4. . Frequency of the 5th harmonic= 250 >