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SECTION -A 1. This question consists of TWENTY-FIVE sub-questions (1.1 - 1.25) of ONE mark

each. For each of these sub-questions, four possib I e alternatives (A ,B, C and D) are given, out of which 0 N L Y 0 NE is correct. Indicate the correct answer by darkening the app rap ri ate bubble against the question number on the I eft hand side of the Objective Response Sheet (ORS). You may use the answer ok

1.1

1.2

provided for any rough work, if needed.

A current 1m pulse, 55( t), 1 s forced through across the capac1 tor 1s g1 ven by

(a) 5t (b) 5u(t)-C (c)

(a)

(b)

(b)

capac1 tor C.

branches. The number of

(d) N - 2B -1

of unit am pi i tude are fed in to channel 1 and channel 2 respect1 vely of an ascii I oscop e. Assum mg that the val tage scale, time seale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-V mode? (a) A drcle of unit radius (b) An ellipse (c) A parabola

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1. 5 Given a vector field F, the divergence theorem states that

1.6

1.7

1.8

If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction oto is operated from a 400 V, 75Hz supply, the torque that the motor co whi I e drawing rated current from the supply? (a) reduces (b) in creases (c) remains the same

A de series motor fed from rated supply val tage is overloaded and its magnetic circuit is saturated. The torq ue-spee characteristic of this motor wi II approximately represented by which~ of Fig.l. 7? . (a) Curve A (b) Curve B

(d) CurveD ...L_C Torque

A 1 kVA, 23ovaJt.'.ll~ phase, 50 Hz transformer having negligible winding resistance and a 1n ductance is operating under saturation, whi I e 2 50 V, 50 Hz sin usa al s s connected to the high voltage winding. A resistive load is conn ecte o th.& low val tage winding which draws rated current. Which one of the fol qu~nti ties wi II not be si nu soi d al?

(a)

du ced across the I ow val tage wmdm g

the source

(b) 400 v (d) 800 v

in V,

400:200:200

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1.10

1.11

1.12

The frequency of the clock signal ap pi i ed to the rising edge triggered D flip-flop shown in Fig.1.10 is 10 kHz. The frequency of the signal available at Q is Q

Ilil_ ( ) =--f>CU<

(a) 10kHz (b) 2.5 kHz

FFO

(c) 20kHz (d) 5kHz

(a) Vm 50Jr

Vm (b) so..r../2

(c) 3. V bo!f positive and negative half cycles (d) 4 h positive and negative half cycles

(d) 2Vm

50Jr

(a) 3.3 v in tht:;}c.v half cycle and 1.4 v in the negative half cycle (b)~4 v in the~ half cycle and 5 v in the negative half cycle

1.1~ne-to-line input voltage to the 3 R a , 50 Hz, ac circuit shown in .. 1.13 is 100 V rm s. Assuming that

the phase sequence is R VB, the wattmeters wou I d read. (a) W1 = 886 wand W2 = 886 w (b) W1 = SOD wand W2 = SOD w (c) W1 = 0 Wand W2 = 1000 W (d) W1 = 250 Wand W2 = 750 W

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1.14

1.15

1.16

1.17

The I ogi c circuit used to generate the microprocessor to ad dress a peripheral resp and to addresses in the range.

active low chip select (CS) by an 8085 is shown in Fig.1.14. The peripheral will

(a) EOOO-EFFF Au---f-----.., (b) 00 DE -FFFE At---j (c) 1000-FFFF Au---l CSS;

Au --~L--~"" (d) 0001-FFF1

Con s1d er a I ong, two-wl re line com posed of solid round con ductor~a s of both conductors 1s 0.25 em and the distance between the1r cente 1s 1 . If th1s distance 1s doubled, then the inductance per un1t length Q (a) doubles (b) halves (c) increases but does not double (d) d ecren~ t do s not halve

Consider a power system with three identical geG~e : ansmission losses are negligible. One generator (G1) has a spe go rnor which maintains its speed constant at the rated value, while~ t erators (G2 and G3) have governors with a droop of 5%. If the Ia e system is increased, then in steady state. ~ (a) generation of G2 and G3 is i (:r ed ually while generation of G1 is

unchanged. (b) eas d while G3 is

(c) (d)

A long wire c~ed fa smooth round conductor runs above and parallel to the ground ( be a I arge conducting pI ane). A high val tage exists between the c , and the ground. The maximum electric stress occurs at (a) the u er sur ace of the conductor (b) th sit face of the conductor

TZ2RI = 0. 3s, TZ2R2 = 0. 6s (c) TZ2RI = 0.3s, TZ2R2 = 0.3s (d) TZ2RI = 0.1s, TZ2R2 = 0.3s Zonel (Rl)

Zone2 (R2) Zonel (R2); ~~ - . DID i PID ol R2 i

7.-..-. ... ? {01~

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1.19. Let s(t) be the step response of a linear system with zero initial conditions; then the response of this system to an input u(t) is

' (a) Js(t-r)u(r)dr 0

' (d) J s(t-r)2 u(r)dr 0

1.20.

1 0 0 1.21. The determinant of them atrix 100 1 0

100 200 100 200

(a) 100 (b) 200 (d) 300

1. 2 2. The state tr ansi ti on matrix for t X= AX with initial state X(O) is

1.23.

~

(a) (si-Ar1 (b) eA' (d) Laplace mverse of (~ 0)]

(c) Laplace mverse of [(si-Ar1 ]

ac source. As _ t t the de output current of the rect1 fi er 1 s constant, the I owest freq uen ar om c component 1n the ac source line current 1 s (a) 100 . (b) 150Hz (c) 250Hz (d) 300Hz

(a) 200v 7r

lOOV f-- ,-- ,--

lOOV ....

(b) 100V 7r

~

1-1 I I I ../3 2Jo/3 4r/3 5../3 2~

(c) 200 V

e

(d) 100 v

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1.25

2.

2.1

2.2.

A step down chopper is operated in the con ti nu ous conduction mode in steady state with a constant duty ratio D . If v 0 is the m agn i tude of the d c output val tage and if v. is the magnitude of the de input voltage, the ratio Vo is given by

v.

(a) D (b) 1 - D ( ) 1 (d) D c 1-D 1-D.

Th1s question cons1sts of TWENTY-FIVE sub-questions (2 .1 - 2.25) ofT m s

are g1 ven, out of wh 1 ch 0 N L Y 0 NE 1 s correct. I nd 1cate the cor ,ct a wer by darkening the appropriate bubble against the question nume ft hand side of the Objective Response Sheet (ORS). You may u the nswer book provided for any rough work, if needed.

A two port network, shown in Fig.2.1 is described by ~wtg equations It = YuEt + Y1~2 ~

c Z~.=30L40

6.81 ~F

2.3. A first order, low pass filter is given with R = 50 nand C = 5 ~F. What is the frequency at which the gain of the voltage transfer function of the fi Iter is 0. 25? (a) 4.92 kHz (b) 0.49 kHz (c) 2.46 kHz (d) 24.6 kHz

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2.4. A series R-L-C circuit has R = 500., power frequency of the circuit is (a) 30.55 kHz (b) 3.055 kHz

L = 100 ~H and C = 1 ~F. the lower half

(c) 51.92 kHz (d) 1.92 kHz

2.5. A 200 V, 2000 rpm, lOA, separately excited de motor has an armature resistance of 20.. Rated de voltage is ap pi i ed to both the armature and field winding motor. If the armature drawn SA from the source, the torque develope

2.6.

2.7.

2.8.

motor is (a) 4.30 Nm (b) 4.77 Nm (c) 0.45 Nm a The rotor of a three phase, s kw, 400V, so Hz, slip nng mduce s wound for 6 poles wh II e 1 ts stator 1 s wound for 4 poles. The approx 1m e a~r age no I oad steady state speed when th 1s motor 1 s connected to 400 V, 50 ply 1 s (a) 1500 rpm (b) 500 rpm (c) 0 rpm(>. + (d) 1000 rpm The flux per pole in a synchronous motor with t...J"':!~~~ ON and the stator disconnected fi'om the supply is faun d to ~e '~~~b. hen the stator is connected to the rated supply with the fiel ex unchanged, the flux per pole in the machine is found to be 20 ~ e e motor is running on no load. Assuming no I oad losses to be zero, th o I u rrent down by the motor from thesupply ~ (a) I ags the supp I y val tage (b) I eads the supply val tag e (c) is in phase with the suppl Ita (d) is zero

'" " ' '"'" '~~'"'~ .... , ,, '""'' d=" '"'"" '" "''' Assuming that the ca i~oO':'m pi etel y discharged prior to applying the pulse, the peak value oft or voltage is lkn (a) 11 V ~ ... < 5.5 V o------J'Nif'---,----, (c) 6.32 v '(.;

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2.10. For the circuit shown in Fig .2 .10, the Boolean expression for the output Y in terms of inputs P, Q, R and S is

p ----r:::i__}-~----r--\ f--------[:::0

Q y

(a) P+Q+R+S (b) P + Q + R + CJ (d) (P + ,.: ~

2.11. In the drcuit shown in Fig .2.11, it is found ttt:":.h~ ac voltage (v) and current i are in phase. The coupling co0t~ = ~'where M is the

'Ill..!~ mutual inductance between the two c~T , lue of K and the dot polarity of the coil P-Q are . K (a) K = 0.25anddotatP ~ ~

p (b) K = 0. 5 and dot at P F---vv\1'--(c) K = 0.25 and dot at Yli_ zn lOn jan jan

~ ~ ~ (d) K = 0.5 and dot at Q

'" """'" ~\:'" "''"

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2.14.

2.15.

2.16.

A power system consists of 2 areas (Area 1 and Area 2) connected by a single tie line (Fig.2.14). It is required to carry out a load flow study on this system. While entering the network data, the tie-line data (connectivity and parameters) is inadvertently left out. If the load flow program is run with this incomplete data (a) The I oad-fl ow wi II con verge ani y if the slack bus is sped fi ed in Area 1 (b) The load-flow will converge only if the slack bus is spedfied in Area~ (c) The load-flow will converge if the slack bus is spedfied in either A 1

Area 2 (d) The I oad-fl ow wi II not converge if only one slack bus is specifi e~

A transmission line has a total series reactance of 0.2 aR~ power compensation is ap pi i ed at the midpoint of the I i ne and it is ntr ed such that the midpoint voltage of the transmission line is always m ainta " t 0.98 pu. If val tage at both ends of the I in e are m ai ntai ned at 1rZJth" the steady state power transfer I i mit of the tr an sm i ssi on I i ne is (a) 9.8 pu (b) 4.9 pu (c) r r: (d) 5 pu A generator is connected to a transfor~~eds another transformer through a short feeder (see Fig .2 .16 )~ ro qu ence impedance values are expressed in pu on a common base ar 1cated in Fig.2.16. the Thevenin equ iv alent zero sequence i m pedan t nt B is

Xa=0.03

."0~ (a) 0. + .6 + (b) 0.75 + j0.22 (c) 0.75 + j0.25

The system is con troll able but un stab I e (b) The system is un con trollab I e but un stab I e (c) The system is con troll able but stab I e (d) The system is un con trollab I e but stab I e

(d) 1.5 + j0.25

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2.18. A unity feedback system has an open loop transfer function, G (s) = ~. The root s

locus plot is (a)

(c)

jw (b) jw

(d)

2.19. The transfer function of the system u as

2.20.

input andy as output is (s+ 2)

(a) ( 2 ) S +S (b) 2s (d) ( 2 ) S +S

o] X, with u as unit impulse and with

(c) 2 e4' (d) 4 e4t

+ 0 1 0 0 0 es of the system represented by X =

0 0 l]x. 1 0 0 0 0

(b) 1, 1, 1, 1 (c) 0, 0, 0, -1 (d)1,0,0,0

the chop per circuit shown the de

T c

of D at the boundary of con ti nu ous and

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2.23.

(a)D=l-v. v.

(b) v,

(c) vH; s 2Jr (d) v.

7r

+

(b) D = 2L RT

0

(c) D=l- 2L RT

v, Vza

(d) D = RT L

e

2.24. In the cirruit shown in Fig.2.24, ~ the switch is closed at time t = 0. The steady state value of~th" voltage Vc is

ln

2.25.

(a) 0 v + lOV

(c) 5 V (b) 10 v flj (d)W 0~

400 w 800 w

ph~e diode b ridge recti tier shown in figure 2. 25, the load resi star is e Source VOltage is v=200 sin(oot), where oo=21t X 50 radians per

wer dissipated in the load resi star R is

R

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SECTION- B This section consists of TWE N TV questions of FIVE marks each. ANY FIFTEEN out of them have to be answered. If more than fifteen questions are attempted, score off answers that are not to be eva I u a ted. Otherwise on I y the first fifteen u nscored answers wi II be considered.

3. The m agnatic vector potential in a region is defined by A= e-Y sin I#N!z

Determine the ex pression for (a) dens1ty 1 exerted on the

4.

conductor.

A constant current source in 10 A to a circuit shown in Fig.P4. the swi , w h is initially closed for a sufficiently ion~ , s denly opened. Obtain the di fferen ti al eq t1 rn i ng the behaviour of the inductor cu rren l nee obtain the com pI ete time response0 ductor current. What is the energy stored , on g time after the switch is opened?

I + lOA

R s

10n SH

5. An ~e~etork 1s fed by two ac sources, as shown F1g.PS. G1ven that Z1 = ( ~2~ (1 + J) 0, X ZL (1 + JO)O.. z

the Thevenm + z, l ' + lent CirCUit Vt=JOL4 so ~ z, I, ~ Vz=30L-4S

en 1n val tage and impedance) across terminals x and y, and determine the current I L Y through the load ZL

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6. In the resistor network shown in Fig .P6, all resi star values are Hl.. A current of 1A passes from terminal a to terminal b, as shown in the figure. C a leu I ate the voltage between terminals a and b. [Hint: You may exploit the symmetry of the

7.

8.

circuit].

R=ln

o---'---lVV\1'--" lA ~

A 2 30V, 2 50 rpm . 100 A separately excited de motor has an a re resistance of 0. 50.. the motor 1 s connected to 23 ov de supply an~ed de vo tage is applied to the field w1ndmg. It IS dnvmg a load whose torque p htl-actenst1c IS g1ven by TL = 500 - lOoo, where oo IS the rotational spe~ ss 1n rad/sec and TL IS the load torque 1n Nm. Fmd the steady state sp at the motor w1ll dnve the I oad and the armature current drawn by fi'o the source. Neglect the rotat1 anal I asses of the mach me. ~

A smgle phase 6300 kVA, 50 Hz,~;~v d1stnbut1on transformer 1s connected between two 50 Hz m s, A and B as shown 1n F1g.PB. the transformer has 12 and 9 9 s e I ow and h1 g h val tag e wmdm gs respectively. The mag neti zing a ce of the transformer referred to the high voltage side is 500 O.~T ag reactance of the high and low voltage windings are 1. on and 1 r ecti vel y. Neglect the winding resistance and core losses of the tra r. e Thevenin voltage of system A is 3300V while that of system B is 0 . t art circuit reactance of systems A and B are 0. 5 n and 0. 0 10 0. respect! o power is transferred between A and B, so that the two system v~ in phase, find the magnetizing ampere turns of the transformer. '(../

+ A B

400V 50Hz

A 440 v, 50 Hz, 6 pole and 960 rpm star connected mduct1on machine has the foil owm g per phase parameters referred to the stator:

Rs = 0.60. R, = 0.30. Xs = 10. The m agn eti zing reactance is very high and is neg I ected. The machine is connected to the 440V, 50 Hz supply and a certain mechanical load is coupled to it. It is found that the magnitude of the stator current is equal to the rated current of the machine but the machine is running at a speed higher than its rated speed. Find the speed at which the machine is running. AI so find the torque rioHol nnori hH tho 1"1"'1 :.rhino

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10.

11.

12.

A 415 v, 2 pole, 3 phase, 50 Hz, star connected, non-salient pole synchronous motor has synchronous reactance of 2 0. per phase and neg I i gi b le stator resistance. At a particular field excitation, it draws 20 A at unity power factor from a 415 V, 3 phase, 50 Hz supply. The mechanical load on the motor is now increased ti II the stator current is equal to 5 OA. The field excitation remains unchanged. Determine: (a) the per phase open circuit voltage Eo ~ (b) the developed power for the new operating con di ti on and carr o in g

power factor.

For the circuit shown in Fig .Pll, IE= 1m A, ~ = 99 and VsE = Ou.o ine (a) the current through R1 and Rc. (b) the output voltage v. (l) (c) the value ofRF 15V

R,

R,= 17kn

=

Determine (~)for the RC network shown in Fig.P12(a).

Vo

(a) (b)

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13. The ripple counter shown in Fig. P 13 is made up negative edge triggered J-E flips flops. The signal I eve Is at J and K inputs of all the flip-flops are maintained at I ogi c 1. Assume that all outputs are cleared just prior to ap pi yi ng the clock signal.

14.

(a) Create a tab I e of Q o. Qt. Q2 and A in the form at given bel ow for 10 successive

(b) (c)

input cydes of the clock CLK 1. D eterm in e the module number of the counter. Modify the circuit of Fig .P 13 to create a mod ul o-6 components used in the figure.

CLKl Q, Format for (a):

J Qo J CLKl CLK

CLR

A

A long lossles~0 1.:, lioo h" ooi

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15. Two transposed 3 phase I in es run parallel to each other as shown in Fig .P 15. the equation describing the val tage drop in both I in es is given bel ow .

16.

.6.Val 0.15 0.05 0.05 0.04 0.04 0.04 Ial

.6.Vbl 0 .OS 0.15 0.05 0.04 0.04 0.04 Ibt

.6.Vc1 0 .OS 0.05 0.15 0.04 0.04 0.04 Ic1 =j

.o.v.2 0.04 0.04 0.04 0.15 0.05 0.05 I.2

.6.Vb2 0.04 0.04 0.04 0.05 0.15 0.05 Ib2 0.04 0.04 0.04 0.05 0.05 0.15

compute Z Olb Zotz, Zo22 in the foil owing equations r ~ 6Vot = Zou lot+ Zotzl02 ~

r ad/sec. All q uan t1 t1 es are ex press The genera tor is initially run ni

Hmt: Use the ee;

~-d2y dy du by --+2-+10y =5--3u. dt2 dt dt

0.0 pu, oos = 21t x 50

the maximum value of li\nint so

with y as output and u as input, is described

For the above system find an mput u(t), with zero initial condition, that produces the same output as with no input and with the initial con di ti ons.

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18.

19.

20.

Obtain a state variable representation of the system governed by the differential

equation d2~ + dy- 2y = u (t) e-1, with the choice of state variables as dt dt

x1 = y, x2 = (d;- y) e'. Also find x2(t), given that u(t) is a unit step function and X2 (0) = 0.

G(s) _ 2(s+a) - s(s+2)(s+10) ~

Sketch the root locus as tx vanes from 0 to oo, Fmd the le nd real ax1s intercept of the asymptotes, breakaway p omts and the 1m ag1 ax 1 s crossm g points, if any.

s

~i lOOV

21. u sht wn in Fig.P21, the source I is a de current source. The switch S ~~~~':~ith a time period T and a duty ratio D. You may assume that the ' c C has a finite value which is I arge enough so that the val tage. V c has ~~iib I e ri pp I e. Cal cui ate the following under steady state conditions, in terms ., andR.

The val tage V o with the polarity shown in Figure P21. The average output val tag e V0, with the polarity shown.

c +

r s v.

I

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22. The semiconductor switch S in the circuit of Fig. P22 is operated at a frequency of 20 kHz and a duty ratio D = 0.5. The circuit operates in the steady state. Cal cui ate the power-transferred form the de val tage source v 1 to the de val tage source V2 .

+

v. +lOOV

lOO~H

Vz +300V