GATE- EE. (Electrical Engg) Previous Year: Fully Solved Papers ( ) (Total- 6 Tests)

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1 GATE- EE (Electrical Engg) Previous Year: Fully Solved Papers (-4) (Total- 6 Tests)

2 GATE- EE 4 Paper-

3 Q. No. 5 Carry One Mark Each. Which of the following options is the closest in meaning to the phrase underlined in the sentence below? It is fascinating to see life forms cope with varied environmental conditions. (A) Adopt to (B) Adapt to (C) Adept in (D) Accept with Answer: (B). Choose the most appropriate word from the options given below to complete the following sentence. He could not understand the judges awarding her the first prize, because he thought that her performance was quite. (A) Superb (B) Medium (C) Mediocre (D) Exhilarating Answer: (C) 3. In a press meet on the recent scam, the minister said, The buck stops here. What did the minister convey by the statement? (A) He wants all the money (B) He will return the money (C) He will assume final responsibility (D) He will resist all enquiries Answer: (C) 4. If ( z / z) 98, compute( z / z ) Exp: 96 Expanding z.z. 98 z 96 z z z 5. The roots of Answer: (D) Exp: ax bx c are real and positive a, b and c are real. Then has (A) No roots (B) real roots (C) 3 real roots (D) 4 real roots ax bxc for roots to be real & ve b -4ac> This will have real positive roots. ax b x c This can be written as; ax bx c Discri min ant b 4ac > ax bx c ( b) 4ac b 4ac Is also > This will have real roots This will have 4 real roots. ax b x c

4 Q. No. 6 Carry One Mark Each 6. The Palghat Gap (or Palakkad Gap), a region about 3 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures. Answer: (B) What can be inferred from this passage? (A) The Palghat gap is caused by high rainfall and high temperatures in southern Tamil Nadu and Kerala (B) The regions in Tamil Nadu and Kerala that are near the Palghat Gap are low lying (C) The low terrain of the Palghat Gap has a significant impact on weather patterns in neighbouring parts of Tamil Nadu and Kerala (D) Higher summer temperatures result in higher rainfall near the Palghat Gap area 7. Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy. Answer: (B) On which of the following assumptions does the statement above rely? (A) Strategies are now available for eliminating psychiatric illnesses (B) Certain psychiatric illnesses have a genetic basis (C) All human diseases can be traced back to genes and how they are expressed (D) In the future, genetics will become the only relevant field for identifying psychiatric illnesses 8. Round trip tickets to a tourist destination are eligible for a discount of on the total fare. In addition, groups of 4 or more get a discount of 5 on the total fare. If the one way single person fare is Rs, a group of 5 tourists purchasing round trip tickets will be charged Rs Answer: 85 Exp: One way force Two way fare per person 5 persons/- Total discount applicable55 5 Discount amount 5 Amount to be paid-585

5 9. In a survey, 3 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter? Own vehicle Answer: 48 Exp: Total respondents3 Those who don t have scooter Men women Men Women Car 4 34 Scooter 3 Both 6 46 Do not own vehicle 5. When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? Answer: 6

6 Q. No. 5 Carry One Mark Each. Given a system of equations: Answer: (B) Exp: x y z b 5x y 3z b Which of the following is true regarding its solutions? (A) The system has a unique solution for any given b and b (B) The system will have infinitely many solutions for any given b and b (C) Whether or not a solution exists depends on the given b and b (D) The system would have no solution for any values of b and b [ A / B] b 5 3 b R R 5R 9 7 b 5b rank ( A / B) b rank A < number of unknowns, for all values of b and b The equations have infinitely many solutions, for any given b and b x. Let f ( x) x e. The maximum value of the function in the interval Answer: Exp: (A) e (B) e (C) (A) M ax imum value is f e ' x '' f x e x x and f x < at x e (D), is e 3. The solution for the differential equation dx x ( ) and, is dt t (A) t t (B) d x (C) sin3t cos3t (D) cos3t t 3 dt 9x with initial conditions sin 3t cos3t 3 3

7 Answer: Exp: (C) A.E : m 9 m ± 3i t Solution is x a cos3t bsin3t... dx and 3a sin3t 3bcos3t... dt dx U sin g x ( ) and, and gives dt a and 3b b 3 x cos3t sin 3t 3 X s 4. Let 3s 5 s s be the Laplace Transform of a signal x(t). Then, x ( ) (A) (B) 3 (C) 5 (D) Answer: (B) Exp: s. 3s 5 x lim u sin g initial value therorem s [ ] s s 5 s 3 s lim 3 s s s s is 5. Let S be the set of points in the complex plane corresponding to the unit circle. (That is, * * f (z) z z where z denotes the complex conjugate of Answer: Exp: f ( Z) S { z : z }. Consider the function z. The f (z) maps S to which one of the following in the complex plane (A) Unit circle (B) Horizontal axis line segment from origin to (, ) (C) The point (, ) (D) The entire horizontal axis (C) Z.Z* where Z* is conjugate of Z Z i. f Z maps S to the point, in the complex plane

8 6. The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is A 8A V 8V 5V Answer: 33 watts. Exp: A 8A V 8V A 5V By KCL, current through 5V source is A. When current entering in to ve terminal of a battery means, it is absorbing the power. When current entering in to ve terminal, means, delivering the power. V source is absorbing the power i.e. () () watts. 8V source is delivering the power i.e. (8) (8) 64 watts 5V source is delivering the power i.e. () (5) 3 watts The total power absorbed by the circuit elements ie - (643) 33 watts. 7. C is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity r, the expression for the modified capacitance is ( a ) ( b) C (A) ( ) (B) r C C (C) r r (D) C r

9 Answer: Exp: (A) Co. Ad ε A ε d Aε C C C C d Aε Aε C d d Aε Aεrε d d Aε C ( εr ) d C ε C r 8. A combination of F µ capacitor with an initial voltage v V in series with a Ω resistor is connected to a ma ideal dc current source by operating both switches at t s as shown. Which of the following graphs shown in the options approximates the voltage v s across the current source over the next few seconds? c V C t V S t V S V S (A) t (B) t V S V S (C) t (D) t

10 Answer: (C) Exp: Under steady state, ϑ c v ma 3 ϑ s µ F Ω When switch is opened: I ϑ s µ F s Ω By using Laplace transform approach, ( ) VS S S SC S S ϑ s V ( S) S S 3 V ( t) S S t S 4 V t t 9. x(t) is nonzero only for Tx < t < T ' x, and similarly, y(t) is nonzero only for Ty < t < T' y. Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE? Answer: (A) z(t) can be nonzero over an unbounded interval (B) z(t) is nonzero for t < Tx Ty (C) z(t) is zero outside of Tx Ty < t < T' x T' y (D) z(t) is nonzero for t > T' x T' y (C) Exp: Given that z( t) is x ( t) y( t) Range of z(t) is [sum of lower limits of x( t) and y( t ) to sum of upper limit of x(t) and y(t)]. Tx Ty < t < Tx Ty

11 . For a periodic square wave, which one of the following statements is TRUE? (A) The Fourier series coefficients do not exist (B) The Fourier series coefficients exist but the reconstruction converges at no point (C) The Fourier series coefficients exist and the reconstruction converges at most points. (D) The Fourier series coefficients exist and the reconstruction converges at every point Answer: Exp: (C) For a periodic square wave, fourier series coefficients value decreases as the k increases. At some value of k coefficient becomes zero, thus no conveyance otherwise it converges at most points.. An 8 pole, 3 phase, 5 Hz induction motor is operating at a speed of 7 rpm. The frequency of the rotor current of the motor in Hz is Answer: 3.33Hz Exp: Given, P 8, F 5Hz, N7 rpm 4 Frequency of Rotor current s.f Ns N 75 7 S.67 fr (.67) Hz N 75 s. For a specified input voltage and frequency, if the equivalent radius of the core of a transformer is reduced by half, the factor by which the number of turns in the primary should change to maintain the same no load current is (A) /4 (B) / (C) (D) 4 Answer: Exp: (C) If the equivalent Radius of the core of a transformer is reduced by half then the reluctance of the core becomes double. 4 to maintain same no-load current the primary turns should be double. Then flux remains same. 3. A star connected 4V, 5Hz, 4 pole synchronous machine gave the following open circuit and short circuit test results: Open circuit test: Voc 4V (rms, line to line) at field current, If.3A Short circuit test: Isc A (rms, phase) at field current, If.5A The value of per phase synchronous impedance in Ω at rated voltage is Answer: 5.6 Ω / ph Exp: Given, O.C. test: OC S.C test: sc V 4V L L I.3A I A phase, I.5A 4 Per phase synchronous impedance, Z s? Voc ` We know, Zs I I issame sc.3 Isc at If.3A 5.33A.5 4 Z 3 s Ω / ph 5.33 f f f

12 4. The undesirable property of an electrical insulating material is (A) High dielectric strength (B) High relative permittivity (C) High thermal conductivity (D) High insulation resistivity Answer: (B) 5. Three phase to ground fault takes place at locations F and F in the system shown in the figure EA δ IF A IF F F B EB V F V F Answer: If the fault takes place at location F, then the voltage and the current at bus A are VF and I F respectively. If the fault takes place at location F, then the voltage and the current at bus A are V and I respectively. The correct statement about voltages and currents during faults at F F F and F is (A) VF leads IF and VF leads I F (B) VF leads IF and VF lags I F (C) VF lags IF and VF leads I F (D) VF lags IF and VF lags I F (C) Exp: When fault takes place at F A B F F Current is feeding into the BUS A. It is like a generator delivering power to Bus (A) When fault takes place at F, F point is like load, taking power from generator. 6. A bus system and corresponding zero sequence network are shown in the figure. Bus T T Bus X Gn X Mn ( a) XG XT XL XT XM 3X Gn 3X Mn ( b)

13 The transformers T and T are connected as (A) and (B) and (C) Answer: (B) Exp: and (D) and XOTI Transformer zerosequence network Transformer zerosequence network 7. In the formation of Routh Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of Answer: (B) Exp: (A) Only one root at the origin (C) Only positive real roots (B) Imaginary roots (D) Only negative real roots If all elements of a row have zero values. Which leads to auxiliary equation formation and roots of auxiliary equations gives imaginary roots. 8. The root locus of a unity feedback system is shown in the figure jω K K σ The closed loop transfer function of the system is (A) (C) K ( )( ) C s R s s s K C s R s s s K (B) (D) K C s R s s s K K C s R s s s K

14 Answer: (C) Exp: k C s R s s s k will give the root locus given the diagram. 9. Power consumed by a balanced 3 phase, 3 wire load is measured by the two wattmeter method. The first wattmeter reads twice that of the second. Then the load impedance angle in radians is π π π π (A) (B) (C) (D) Answer: C Exp: When load impedance is wattmeter. π radians. The first wattmeter reads twice that if the second 6. In an oscilloscope screen, linear sweep is applied at the (A) Vertical axis (B) Horizontal axis (C) Origin (D) Both horizontal and vertical axis Answer: (B). A cascade of three identical modulo 5 counters has an overall modulus of (A) 5 (B) 5 (C) 5 (D) 65 Answer: (C) Exp: When more than one modulus counter is cascaded then their overall modulus will be product of modulus of each individual.so, in this question overall modular of the counter In the Wien Bridge oscillator circuit shown in figure, the bridge is balanced when C R V cc V cc R 3 C R R 4 R 3 R R C (A), ω (B), ω R R R C R C R C R C R C 4 (C) 3 4 R R C R 3 R C, ω (D), ω R R C R C R C R R C R C R C 4

15 Answer: (C) Exp: When bridge is balanced, zz4 zz3 R3 R C,f R R C π R R C C 4 3. The magnitude of the mid band voltage gain of the circuit shown in figure is (assuming h fe of the transistor to be ) V cc k C V C k hfe V i k C (A) (B) (C) (D) Answer: (D) Exp: A A V V s s V s V V o s hfeib ( k) ( k) I k I h b b ie hfe k h ie k k A ( neglecting hie) VS k I3 hfc h I fc b I C V k 4. The figure shows the circuit of a rectifier fed from a 3 V (rms), 5 Hz sinusoidal voltage source. If we want to replace the current source with a resistor so that the rms value of the current supplied by the voltage source remains unchanged, the value of the resistance (in ohms) is (Assume diodes to be ideal.) 3V,5Hz A

16 Answer: Exp: Vs 3Ω 3V, 5Hz The rms volt of given Re ctifier V or or or V 3V I V or or R 3Ω s V V 3 R R I or V s A 5. Figure shows four electronic switches (i), (ii), (iii) and (iv). Which of the switches can block voltages of either polarity (applied between terminals a and b ) when the active device is in the OFF state? a a a a b ( i) b ( ii) b ( iii) b ( iv) (A) (i), (ii) and (iii) (B) (ii), (iii) and (iv) (C) (ii) and (iii) (D) (i) and (iv) Answer: (C) Exp: Switch (i) blocks the voltage in only forward direction Switch (ii) blocks the voltage in both forward and reverse directions Switch (iii) blocks voltage in both direction Switch (iv) blocks voltage in only forward direction Hence Ans. is (C) because switch (i) & (ii) only satisfy the given requirement Q. No Carry Two Marks Each 6. Let g :[, ) [, ) be a function defined by g( x) x [ x ], where[ x] Answer: / represents the integer part of x. (That is, it is the largest integer which is less than or equal to x). The value of the constant term in the Fourier series expansion of g(x) is

17 Exp: Clearly, g(x) is a periodic function with period consider, g( x) x [ x] for < x < The constant term in the fourier series expansion of g x is A a g x dx x x dx [ x] dx ( ) dx 7. A fair coin is tossed n times. The probability that the difference between the number of heads n 3 is Answer: Exp: and tails is (A) n (B) (C) n C n n 3 (B) Let X difference between the number of heads and tails. (D) n 3 Take n S { HH,HT,TH,TT} and X,,; Here, n 3 is not possible { } Take n 3 S HHH, HHT, HTH, HTT,THH,THT,TTH,TTT and X 3,,,3 Here n 3 is not possible Similarly, if a coin is tossed n times then the difference between heads and tails is n 3 is not possible required probability is 8. The line integral of function F yzi, in the counterclockwise direction, along the circle x y at z is (A) π (B) π (C) π (D) π Answer: (B) Exp: Line int egral F.dr π C C is circle x y at Z yzdx C x cos θ, y sin θ and θ to π ( sin )( sin d ) θ θ θ π π cosθ sin θ d θ θ π 9. An incandescent lamp is marked 4W, 4V. If resistance at room temperature 3 o 4.5 / C, then its ON state o ( 6 C) is Ω and temperature coefficient of resistance is filament temperature in o C is approximately Answer: 47

18 Exp: P 4W V 4V V 4 R 44Ω lamp P 4 Α 6 Ω α o 3 o t t, R, 4.5 / C o C 3 [ ] R R lamp α θ θ θ 6 θ 3. In the figure, the value of resistor R is ( 5 I / ) ohms, where I is the current in amperes. The current I is I 3V R Answer: A Exp: Given I R 5 V IR I 3 I 5 I 5 I 6 I A 8 6A. The current A is correct based on the given direction. 3. In an unbalanced three phase system, phase current a ( o ) o current Ib 4 ( 5 ) pu, zero sequence current IC o 3 9 pu. Answer: Exp: current I b in pu is I 9 pu, negative sequence The magnitude of phase (A). (B) 7.8 (C).53 (D) 3. a b c (C) I 9 p.u I 4 5 p.u I 3 9 p.u I I I I a a a a

19 sin ce I a b a a bo co a a αi 4 5 I I 4 7 a a I I I 3 9 I 9 I I 8 9 Ib α Ia I I I I b b b b p.u 3. The following four vector fields are given in Cartesian co ordinate system. The vector field which does not satisfy the property of magnetic flux density is (A) y a z a x a (B) x y z z a x a y a x y z Answer: (C) x a y a z a (D) x y z (C) Exp: For magnetic fields.b By verification (a).b ( ) (b).b (c).b x y z So C is correct y z a x z a x y a x y z 33. The function shown in the figure can be represented as (A) ( ) ( ) t T t T u t u t T u ( t T) u t T T T t T t T (B) u ( t) u( t T) u( t T) (C) ( ) ( ) t T t T u t u t T u ( t) u t T T (D) Answer: (A) ( ) ( ) t T t T u t u( t T) u t T T T t T t T T T Exp: x ( t) u ( t) u( t T) u ( t T) u ( t T) T T t

20 be the Z transform of a causal signal x[n]. Then, the values of z x and x 3 are 34. Let X( z) 3 [ ] [ ] (A) and (B) and (C) and (D) and Answer: (B) Given x z z Exp: 3 x z can be written as [ ] [ ] z z x correspond to coefficient z 3 x 3 correspond to coefficient of z 35. Let f ( t ) be a continuous time signal and let F( ω ) be its Fourier Transform defined by Define g t by ( ω ) jωt F f t e dt jut g t F u e du What is the relationship between f ( t) and g( t )? (A) g(t) would always be proportional to f(t) (B) g(t) would be proportional to f(t) if f(t) is an even function (C) g(t) would be proportional to f(t) only if f(t) is a sinusoidal function (D) g(t) would never be proportional to f(t) Answer: (B) Exp: We know the fourier transform relationship jωt F f t.e dt ( ω ) and f t F jwt e d ω ω π ω can be replaced by u f t F u e du... π jut jut Now g t F u.e du... replace t by t in jut f ( t) F( u) e du...( 3) π f ( t) g( t) π if f t f t f t is even function g t π f t

21 36. The core loss of a single phase, 3/5V, 5Hz power transformer is measured from 3 V side by feeding the primary (3V side) from a variable voltage variable frequency source while keeping the secondary open circuited. The core loss is measured to be 5 W for 3V, 5Hz input. The core loss is again measured to be 5W for 38V, 3Hz input. The hysteresis and eddy current losses of the transformer for 3V, 5Hz input are respectively, (A) 58 W and 54 W (B) 468 W and 58 W (C) 498 W and 55 W (D) 488 W and 56 W Answer: (A) Exp: Given data, 3 φ, 5Hz 5V Care loss 5W at 3V, 5 Hz Care loss 5W at 38V, 3 Hz 4 In both cases V f Hence, n e ratio is constant W A.f B.f W W i n e CORE LOSS at 5Hz 5 A 5 B 5 at 3Hz 5 A 3 B 3 A.67 B.7 W at 5 Hz W W at 5 Hz W 37. A 5kW, 3V dc shunt motor has armature circuit resistance of.4ω and field circuit resistance of 3Ω. At no load and rated voltage, the motor runs at 4 rpm and the line current drawn by the motor is 5 A. At full load, the motor draws a line current of 7A. Neglect armature reaction. The full load speed of the motor in rpm is Answer: 4 rpm. Exp: Given 5kW, 3V. dc shunt motor Armature resistance Field Resistance, R a.4ω R sh 3Ω A 5A A 7A 4A 69A 3Ω 3V 3V E b 8.4V E b.4v

22 N E φ N E φ b b E E b b ( Flux is constant ).4 N 4 4 rpm A 3 phase, 5 Hz, six pole induction motor has a rotor resistance of.ω and reactance of.9ω. Neglect the voltage drop in stator and assume that the rotor resistance is constant. Given that the full load slip is 3, the ratio of maximum torque to full load torque is (A).567 (B).7 (C).948 (D).34 Answer: (C) Exp: Given, P b, f 5Hz T max R. Ω, X.9Ω fl S 3.3 T S S?, weknow that T S S T S S T S S max m fl fl m fl (.8) (.3) max m fl fl m fl where sm.8.3 x.9 Tmax fl R. T A three phase synchronous generator is to be connected to the infinite bus. The lamps are connected as shown in the figure for the synchronization. The phase sequence of bus voltage is R Y B and that of incoming generator voltage is R ' Y' B'. R Y B R ' Y ' B' L a Infinite Bus L b Inco min g Generator L c

23 Answer: It was found that the lamps are becoming dark in the sequence La Lb Lc. It means that the phase sequence of incoming generator is (A) Opposite to infinite bus and its frequency is more than infinite bus (B) Opposite to infinite bus but its frequency is less than infinite bus (C) Same as infinite bus and its frequency is more than infinite bus (D) Same as infinite bus and its frequency is less than infinite bus (A) Exp: According to given connection of Lamp s. Tthey are becoming dark in the sequence L a - L b- L c. Hence the phase sequences are different, and also the frequency is more than infinite bus. 4. A distribution feeder of km length having resistance, but negligible reactance, is fed from both the ends by 4V, 5Hz balanced sources. Both voltage sources S and S are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure. S 4m m m m S 4V 5Hz A A A 4V 5Hz Answer: (D) Exp: The contributions of S and S in A current supplied at location P respectively, are (A) 75A and 5A (C) 5A and 75A 4m m m m source source I B A A A (B) 5A and 5A (D) A and A Let I be current supplied by source r be resistance/ length 4 4r I r I r I 3 r I 5 4 4rI ri 4r ri 6 ri r Ir r I A Current in branch- B is I 4 point p, source- supplies A current Source- supplies A current

24 4. A two bus power system shown in the figure supplies load of. j.5p.u. G Bus V o Bus δ j j.. j.5 Answer: (B) Exp: The values of V in p.u. and δ respectively are (A).95 and 6. ο (B).5 and ο (C). and -6. ο (D). and -7. ο A B j.. 9 C D I s Z I r V s V r Vs I s A B V V r s V, B. 9 C D I Vr δ, A V AV BI s r r r V A V I V δ B B. 9 ( ) s r r V 9 δ 9 I V 9 9 δ * r [ ] S P jq V I δ V 9 δ * r r r r r V 9 δ 9 V cos 9 δ jv sin 9 δ j [ ] V sin δ jv cosδ j Given [ V sin ] j[ V cos ] δ δ r S j.5 V sin δ V sin δ tan δ δ 5.44 V.5 cosδ.5 V cosδ.5 From V sin δ [ ] V sin 5.44 V.54

25 4. The fuel cost functions of two power plants are Answer: (D) Plant P : C.5Pg APg B Plant P : C.Pg 3APg B Where, Pg and Pg are the generated powers of two plants, and A and B are the constants. If the two plants optimally share MW load at incremental fuel cost of Rs/MWh, the ratio of load shared by plants P and P is (A) : 4 (B) : 3 (C) 3: (D) 4 : Exp: C Pg.5 APg B Pg Pg dc dc C.Pg 3A Pg B dpg dp dc dpg dc dpg.5pg A.Pg 3A.Pg A.3Pg. Pg. Pg 3A Pg Pg Solving, Pg 8 MW Pg MW Pg 4 Pg 43. The over current relays for the line protection and loads connected at the buses are shown in the figure A B C R A R B 3 A A A The relays are IDMT in nature having the characteristic t.4 Time Multiplier Setting Plug Setting Multiplier op. The maximum and minimum fault currents at bus B are A and 5 A respectively. Assuming the time multiplier setting and plug setting for relay R to be. and 5A respectively, the operating time of R (in seconds) is B B

26 Answer:.3 Exp: A B C R A R B 3A A A For Relay B.4 T.M.S top T.M.S.. ( P.S.M ) P.S.M 5A I I fault( max) fault( min ) A 5A Maximum load current at C A For a setting current of A, plug setting is Max fault current PSM CT ratio current setting.4 T.M.S.4. top.7.3sec.. P.S.M 44. For the given system, it is desired that the system be stable. The minimum value of α for this condition is ( s α) R( s ) C 3 ( s ) s α s α s α Answer:.68 Exp: The characteristic equation is G(s) ( s α) 3 s α s α s α 3 s s s α α For stable system α should be.68 By R- H criteria, ( α) α >. α α > α.68 &.68

27 45. The Bode magnitude plot of the transfer function G( s) below: ( )( ) K.5s as s s s ( bs) 8 36 a Note that 6dB / octave db / decade.the value of is bk I shown db 6dB / Octave 6dB / Octave db / Octave db / Octave 6dB / Octave db / Octave Answer:.75 Exp: By observing the magnitude plot, G s S S K 4 S S S S By comparing with given transfer function, a ; b. 4 4 For finding K: ω( rad / s) (M) ind B ( db/ dec) ω bg ω ( ω ) n where n is no.of poles from the given plot; K ( 8) K : i.e.k 8 a So, 4.75 bk.8 4

28 46. A system matrix is given as follows A The absolute value of the ratio of the maximum eigen value to the minimum eigen value is Answer: /3 Exp: Characteristic equation is A λ I 3 λ λ λ max λ max min i.e., 6 λ λ 6 6 λ,, 3 are the eigen values of A λ and λ 3 λ λ min The reading of the voltmeter (rms) in volts, for the circuit shown in the figure is R.5Ω jω / jω sin ( ωt) V / jω jω Answer: 4 Exp: Net z j j, acts as short circuit ( ωt) sin i( t) sin ωt.5 i( t) i sin V ( ω t) i V V j sin ωt V j sin ωt V V V jsin ωt V V m RMS 4.4 Volts sin( ωt).5ω j j V V j j

29 48. The dc current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains turns in the coil, the flux density in the air gap is. Wb / m, and the area of the coil is 8mm. The electrodynamometer ammeter has a change in mutual inductance with respect to deflection of.5 mh/deg. The spring constants of both the meters are equal. The value of current, at which the deflections of the two meters are same, is Answer: 3. Exp: Given pmmc and electro dynamometer type meters are connectsed in series. Both meters are carrying same current. And both are having same spring constants. Both are reflecting same readings. i.e. we should equate the reflecting torques. For pmmc, T def BAN.I. dm Electrodynometer, Tdef I. d θ dm BAN.I I. d θ. 8 I I.5 I Given that the op amps in the figure are ideal, the output voltage V is (A) ( V V ) (B) ( V V ) (C) ( ) V V / (D) ( V V ) V V R R R R R R R V Answer: (B) Exp: V V V R R V R I V / I R f V V V R V / R

30 V V R V... V... I I f V V R 3V V V V R V V R 3V V V V V V R R 3V V 3V V V V V V V V from & 5. Which of the following logic circuits is a realization of the function F whose Karnaugh map is shown in figure. C AB (A) A (B) A B C B C A (C) C (D) A C B B Answer: Exp: (C) AC AB C F AC BC BC

31 (A) A B A A.B.C C BC A A (B) B A BC C BC (C) A A AC C C AC BC B BC A A (D) AC C AC BC B BC Among all the options, option (C) is matching with function F AC BC 5. In the figure shown, assume the op amp to be ideal. Which of the alternatives gives the correct V ( ω) Bode plots for the transfer function? V ω V i kω V cc µ F V V cc R f

32 (A) V log V i ( ω) ( ω) 3 ω φ π / 4 3 ω π / 3 (B) V log V i ( ω) ( ω) 3 φ π / π / 4 3 ω π / 4 ω π / 3 (C) V log V i ( ω) ( ω) 3 ω φ π / π / 4 π / 4 3 ω π / 3 (D) V log V i ( ω) ( ω) 3 ω φ π / π / 4 π / 4 3 ω π / 3

33 Answer: (A) Exp: K Rf V V in µ F Act as Buffer The given circuit is LPF (Low Pass Filter) V V in SCR jω ( )( ) jω( ) jω S V V in ( db ) Actual Curve o 3 ω Slope db decade Low frequency asymptote curve Corner frequency is at ω Low frequency gain{ ω } 5. An output device is interfaced with 8 bit microprocessor 885A. The interfacing circuit is shown in figure AB 8 BDB A IO / M A A 3 A A 5 4 WR 3L 8L Decoder I I I E E E Output Device BCB

34 Answer: The interfacing circuit makes use of 3 Line to 8 Line decoder having 3 enable lines E,E,E 3. The address of the device is (A) 5 H (B) 5 H (C) A H (D) AH s (B) Exp: To enable 3L 8L decoder, three enable lines E (which is connected as an output of ANDgate) should be HIGH and E and E I 3 should be active low, it means should be active low m which is indicating that it is memory mapped I/O interfacing. So, address of the device will be in 6-bits. To select output port through decoder nd line the status of A5 ( I ) A4 ( I ) A3 ( I ) and to enable decoder through E enable line A and A should be zero.so, overall port address is and by default as a starting address other address lines ( A...A ) A5 A4 A3 A A A A9 A8 A7 A6 A5 A4 A3 A A A 5H 53. The figure shows the circuit diagram of a rectifier. The load consists of a resistance Ω and an inductance.5h connected in series. Assuming ideal thyristor and ideal diode, the thyristor firing angle (in degree) needed to obtain an average load voltage of 7V is 35sin 34t V Load Answer: α 69.3 Exp: Vo 7v; Load, R Ω ; L.5H Firing angled? The o/p volt of given converter is V V π 55 7 cosα π α 69.3 ( cos ) m α V s T D V load π π 3π V α π π 3π u( t)

35 54. Figure (i) shows the circuit diagram of a chopper. The switch S in the circuit in figure (i) is switched such that the voltage v D across the diode has the wave shape as shown in figure (ii). The capacitance C is large so that the voltage across it is constant. If switch S and the diode are ideal, the peak to peak ripple (in A) in the inductor current is S mh V V D C Load Figure ( i) V D V Figure ( ii) t ( ms) Answer:.5A Exp: Peak to peak ripple in inductor current in Vs Vo I Tm L I.5 A 3 I I V V TON.5. T on TOFF I T 55. The figure shows one period of the output voltage of an inverter. α should be chosen such o o that 6 < α < 9. If rms value of the fundamental component is 5V, then α in degree is V V V α 8 α 8 8 α 36 α 36 ωt ( deg ree) V V V Answer: 76 to 77

36 π 4 α Exp: b Vs sin θdθ sin θdθ π α 4Vs cos cos 4Vs [ ] α α π [ cos ] α π 4Vs RMS Value of V cosα π 4 5 ( cos α) π α 77.5 o

37 GATE- EE 4 Paper-

38 Q. No. 5 Carry One Mark Each. Choose the most appropriate phrase from the options given below to complete the following sentence. India is a post-colonial country because (A) it was a former British colony (B) Indian Information Technology professionals have colonized the world (C) India does not follow any colonial practices (D) India has helped other countries gain freedom Answer: (A). Who was coming to see us this evening? (A) you said (B) did you say (C) did you say that (D) had you said Answer: (B) 3. Match the columns. Column Column () eradicate (P) misrepresent () distort (Q) soak completely (3) saturate (R) use (4) utilize (S) destroy utterly (A) :S, :P, 3:Q, 4:R (B) :P, :Q, 3:R, 4:S (C) :Q, :R, 3:S, 4:P (D) :S, :P, 3:R, 4:Q Answer: (A) 4. What is the average of all multiples of from to 98? (A) 9 (B) (C) (D) Answer: (B) Exp: 9 8 : 9 [() 9 ] 9 : The value of... is (A) (B) 3.93 (C) 4. (D) 4.444

39 Answer: (C) Exp: let... y y y y y (y 4)(y 3) y 4, y 3 Q.No. 6 Carry Two Marks Each 6. The old city of Koenigsberg, which had a German majority population before World War, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the Baltic Sea on the north and the countries of Poland to the south and west and Lithuania to the east respectively. Which of the statements below can be inferred from this passage? Answer: (B) (A) Kaliningrad was historically Russian in its ethnic make up (B) Kaliningrad is a part of Russia despite it not being contiguous with the rest of Russia (C) Koenigsberg was renamed Kaliningrad, as that was its original Russian name (D) Poland and Lithuania are on the route from Kaliningrad to the rest of Russia 7. The number of people diagnosed with dengue fever (contracted from the bite of a mosquito) in north India is twice the number diagnosed last year. Municipal authorities have concluded that measures to control the mosquito population have failed in this region. Answer: (D) Which one of the following statements, if true, does not contradict this conclusion? (A) A high proportion of the affected population has returned from neighbouring countries where dengue is prevalent (B) More cases of dengue are now reported because of an increase in the Municipal Office s administrative efficiency (C) Many more cases of dengue are being diagnosed this year since the introduction of a new and effective diagnostic test (D) The number of people with malarial fever (also contracted from mosquito bites) has increased this year 8. If x is real and x x 3, then possible values of 3 x x x include (A), 4 (B), 4 (C) 4, 5 (D) 4, 5

40 Answer: (D) Exp: x x 3 (x 4)(x ) x 4, x 3 Values of x x x For x 4 Value 5 for x Value 4 Option D 4,5 9. The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 9, by what percent did the number of male students increase in 9? Ra tio of m al e to fe m al Answer: 4 Exp: m 3 f m.5 f m.5f m' 3 f m' 6f m' m m 3.5f.5f

41 . At what time between 6 a.m. and 7 a.m will the minute hand and hour hand of a clock make an angle closest to 6? (A) 6: a. m. (B) 6:7 a.m. (C) 6: 38 a.m. (D) 6:45 a.m. Answer: (A) Exp: Angle by minute s hand 6 min 36 ο 36 min 6 6 o 8min 48 o Angle 48 with number 6 Angle by hours hand 6 min 3 3 min 6 o Total Angle4859 o. 6.am ο

42 Q.No. 5 Carry One Mark Each. Which one of the following statements is true for all real symmetric matrices? (A) All the eigenvalues are real. (B) All the eigenvalues are positive (C) All the eigenvalues are distinct (D) Sum of all the eigenvalues is zero. Answer: (A) Exp: Eigen values of a real symmetric matrix are all real. Consider a dice with the property that the probability of a face with n dots showing up is proportional to n. The probability of the face with three dots showing up is. Answer: /7 Exp: P( n) k.n where n to 6 x [ ] we know P x K K required probability is P( 3) 3K 7 3. Maximum of the real valued function 3 f x x occurs at x equal to Answer: ( A) ( B) ( C) ( D) (C) Exp: f ( x) ( ) is negative, x < or x in h, 3 x 3 is positive, x > or x in, h h is positive & small f has local min ima at x and the min imum value is '' 4. All the values of the multi-valued complex function i, where i, are Answer: (B) (A) purely imaginary (C) on the unit circle. Exp: cos( kπ ) i sin ( kπ ) where k is int eger e i( kπ) i ( kπ) e All values are real and non negative (B) real and non-negative (D) equal in real and imaginary parts

43 d y dy 5. Consider the differential equation x x y. Which of the following is a solution dx dx to this differential equation for x >? (A) Answer: (C) Exp: x e (B) d y dy x x y is cauchy Euler equation dx dx d ( θ ).y where θ and z log x, x e dz x (C) /x (D) ln x z A.E : m m, Z Z C Solution is y Ce Ce Cx x is a solution x 6. Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are 38µ H and 4µ H. Their mutual inductance in µ H is Answer: 35µ H Exp: Two possible series connections are. Aiding then L equation L L M.. Opposing then L equation L L M L L M 38 H L L M 4 H From &, M 35µ H () () 7. The switch SW shown in the circuit is kept at position for a long duration. At t, the switch is moved to position Assuming V > V, the voltage VC ( t ) across capacitor is R '' SW V V C R VC t/rc t /RC ( A) vc ( t) V ( e ) V B v t V e V c t/rc t/rc ( C) vc ( t) ( V V )( e ) V D v t V V e V c

44 Answer: (D) Exp: When switching is in position ϑ R C t z V t Initial final final value VC ( t) V e t RC When switch is in position Initial value is VC ( t) V e Final value is V t RC e V R R C ϑ c VC ( t) V [ V V ] e t RC C ϑ c 8. A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is place symmetrically with respect to the plates. Volt ε ε ε Answer: Exp: If the potential difference between one of the plates and the nearest surface of dielectric interface is Volts, then the ratio ε : ε is (A) : 4 (B) : 3 (C) 3: (D) 4 : Q (C) CV C V cons tan t C V Aε C d ε ε V V ε V ε ε V V 6 ε ε ε ε ε V 3ε 3ε 5ε ε ε : ε 3: ε 3 d / d V 8V V V ε ε ε

45 9. Consider an LTI system with transfer function H`( s) s s 4 ( ) If the input to the system is cos(3t) and the steady state output is Asin( 3t α ), then the value of A is (A) /3 (B) /5 (C) 3/4 (D) 4/3 Answer: (B) Exp: Given H( s) s s 4 ( ) H( jω ) ω ω 6 cos ( ω t) ( ω) A H j ω 3 H( jω) ωω A ( ω) ( ω θ) y t H j cos t ωω ( ω) where θ H j ω. If the output of the system is 5t. Consider an LTI system with impulse response h(t) e u( t) t 5t y( t) e u( t) e u( t) then the input, x(t), is given by 3t ( A) e u( t) 3t B e u ( t ) 5t C e u ( t ) 5t D e u ( t ) Answer: (B) Exp: x ( t) 5t h ( t) e u( t) H( s) s 5 3t 5t y( t) e e u( t) Y( s) s 3 s 5 Y s H( s) X s 3t h ( t ) y ( t) ( ) ( ) ( 5 3)( s 5) Y s 5 5 s 3 X( s) H s s 3 s 5 x t e u t

46 . Assuming an ideal transformer,. The Thevenin s equivalent voltage and impedance as seen from the terminals x and y for the circuit in figure are sin ( ωt) Ω x ( A) sin ( ωt ), 4Ω ( ω ) ( C) sin ( ωt ), Ω ( ω ) Answer: A Exp: ϑ xy Voc ϑ ϑ in xy ϑ ϑ ω R xy 4 ϑ th sin ω t R th 4Ω xy oc sin t : B sin t, Ω D sin t,.5ω. A single phase, 5kVA, V/V two winding transformer is connected as an autotransformer as shown in the figure. y V V V The kva rating of the autotransformer is. Answer: 55kVA Exp: Given, V 5 kva, V 3 5 I 5 kva 5 55 kva A.TFr V I 5A V

47 3. A three-phase, 4pole, self excited induction generator is feeding power to a load at a frequency f. If the load is partially removed, the frequency becomes f. If the speed of the generator is maintained at 5 rpm in both the cases, then Answer: (C) (A) f f > 5Hz and f > f (B) f < 5Hz and f > 5Hz (C) f f < 5Hz and f > f (D) f > 5Hz and f < 5Hz Exp: Initially self excited generator supply power to a load at f. If load is partially removed then slightly speed increase, also frequency f f > f But both cases f f < 5Hz 4. A single phase induction motor draws MW power at.6 lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of motor and capacitor to.8 lagging. Assuming that the real and reactive power drawn by the motor remains same as before, the reactive power delivered by the capacitor in MVAR is. Answer: 7MVAR Exp: Given, φ Induction motor draws mw at.6pf, lag Let P mw cosφ.6 pf To improve pf, cosφ.8 Q? c del bycapacitor P cosφ S MVA 6 S S.6 4 Reactive power, Q S P 6 MVAR When capacitor is connected then cosφ P S.8 S S 6 5MVA ( Real power drawn issame) Re active power, Q S P 9MVAR But motor should draw the same reactive power. Q 6 9 7MVAR c delby capacitor

48 5. A three phase star-connected load is drawing power at a voltage of.9 pu and.8 power factor lagging. The three phase base power and base current are MVA and A respectively. The line-to line load voltage in kv is. Answer: 7- Exp: Given, mva, A V L L (kv)? We know that, S 3 V L.IL 6 3.V L.IL V V L L kV But it is drawing power at a voltage of.9 pu V Vpu V actual Base V V V V actual LL pu B kV 6. Shunt reactors are sometimes used in high voltage transmission system to (A) limit the short circuit current through the line. (B) compensate for the series reactance of the line under heavily loaded condition. (C) limit over-voltages at the load side under lightly loaded condition. (D) compensate for the voltage drop in the line under heavily loaded condition. Answer: (C) 7. The closed-loop transfer function of a system is due to unit step input is. Answer: Exp: Steady state error for Type- for unit step input is. 4 T s. ( s.4s 4) The steady state error 8. The state transition matrix for the system x x u x x is t e A e t e t ( B) t e e t e t t ( C) te t e t t e ( D) t t e te t e Answer: (C)

49 Exp: Given A B s s [ SI A] ( s ) ( s ) ( s ) [ SI A] The state transition matrix At e L SI A e At t e t t te e 9. The saw-tooth voltage wave form shown in the figure is fed to a moving iron voltmeter. Its reading would be close to V ms 4ms Answer: Exp: V m sec 4 m sec t Moving iron meter reads RMS value only RMS value of saw-tooth waveform is Meter reads volts ϑmax 3

50 . While measuring power of a three-phase balanced load by the two-wattmeter method, the readings are W and 5 W. The power factor of the load is. Answer:.8 Exp: In two-wattmeter method, The readings are W & 5 W Power factor cos φ 3 ω ω cos tan ω ω 3 5 cos tan Which of the following is an invalid state in an Binary Coded Decimal counter Answer: (D) Exp: (A) (B) (C) (D) In binary coded decimal (BCD) counter the valid states are from to 9 only in binary system to only. So, in decimal it is which is invalid state in BCD counter.. The transistor in the given circuit should always be in active region. Take VCE ( sat).v. VEE.7 V. The maximum value of R C in Ω which can be used is. Rs kω 5V RC β 5V Answer:.3Ω Exp: I B C 5.7.5mA k I.5A 5. RC.3Ω.5

51 3. A sinusoidal ac source in the figure has an rms value of V. Considering all possible values of R L, the minimum value of R S in Ω to avoid burnout of the Zener diode is. R S V ~ 5V R L / 4W Answer: 3Ω Exp: Vm V Pz Pz Vz Iz Iz 5mA V 5 RS ( min) 3Ω 5mA z 4. A step-up chopper is used to feed a load at 4 V dc from a 5 V dc source. The inductor current is continuous. If the off time of the switch is µ s, the switching frequency of the chopper is khz is. Answer: 3.5 khz Exp: V 4v, Vs 5 v, Toff µ sec, F? Given chopper in step up chopper Vs Vo D D D 4 D but T D T off ( 3 ) 6 T T 3µ sec 8 Then f 3.5 Hz 6 T 3 f 3.5kHz

52 5. In a constant V/f control of induction motor, the ratio V/f is maintained constant from to base frequency, where V is the voltage applied to the motor at fundamental frequency f. Which of the following statements relating to low frequency operation of the motor is TRUE? Answer: (B) (A) At low frequency, the stator flux increases from its rated value. (B) At low frequency, the stator flux decreases from its rated value. (C) At low frequency, the motor saturates. (D) At low frequency, the stator flux remains unchanged at its rated value. Exp: During constant V control, at low frequency, the voltage also applied to the induction motor f is low. Hence the stator flux also decreases from its rated value. Q.No Carry Two Marks Each 8 ( y/) x y 6. To evaluate the double integral dx dy y/, we make the substitution x y u and y v. The integral will reduce to Answer: (B) 4 4 ( A) ( u du ) dv ( B) ( ) 4 4 ( C) ( u du ) dv ( D) ( ) x y y Exp: u... and V... y y x u ; x u y v ; y 8 v 4 from and,x u v... 3 and y v... 4 x x u v Jacobian transformation; J y y u v y 8 4 x y dx dy ( u ) J du dv y v u 4 u du dv u du dv u du dv

53 7. Let X be a random variable with probability density function Answer:.4., for x f ( x)., for < x 4, otherwise The probability p(.5 < x < 5) is 5 Exp: P.5 < x < 5 f x dx Opposite f ( x) dx f ( x) dx f ( x) dx.5 4 Hypotenuse 4. x. x The minimum value of the function f ( x) x 3x 4x in the interval [-3. 3] is Answer: (B) Exp: (A) (B) 8 (C) 6 (D) 3 f x x x 8 x, 4 [ 3,3] ( ) ( ) Now f 3 8 ; f 3 8 and f 8 ; f 4 44 f x is min imum at x 3 and the min imum value is f Assuming the diodes to be ideal in the figure, for the output to be clipped, the input voltage v i must be outside the range k V i ~ k V V V o Answer: (B) (A) V to V (B) V to 4V (C) V to V (D) V to 4V vi Exp: When both diodes are FF, vo (Not clipped). For the clipped, vi must bt ouside the range V to 4V

54 3. The voltage across the capacitor, as sown in the figure, is expressed as v t A sin ω t θ A sin ω t θ t Ω H sint ~ VC ( t) F sin 5t The value of A and A respectively, are (A). and.98 (B). and 4. (C).5 and 3.5 (D) 5. and 6.4 Answer: (A) Exp: By using super position theorem,. ϑ ( t) C When sin t voltage source is acting, Network function H( j ) ϑ c. ϑ ( t) c jωc ω R j jωc ( t) sin t tan ( ) ( ) When sin 5t current source is acting ϑ c.j.j ϑ c j.j ϑ ( t ).sin 5t θ. c ϑ c ( t).98 sin ( 5t θ ) ( θ ) ( θ ) V t sin t.98 5t C A. By comparing with given expression, A The total power dissipated in the circuit, show in the figure, is kw. A A Ω Xc XL R ac source ~ X c V V Load The voltmeter, across the load, reads V. The value of X L is.

55 Answer: 7.34 Ω Exp: Total power dissipated in the circuit is kw. P kw I. I.R...R. R 9.96 Ω V Z I Z R X L X Z R L L X 9.96 XL 7.34 Ω 3. The magnitude of magnetic flux density ( B) at a point having normal distance d meters from µ an infinitely extended wire carrying current of l A is I (in SI units). An infinitely nd extended wire is laid along the x-axis and is carrying current of 4 A in the ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying A current in the ve y direction µ is permeability of free space Assume ˆ I, J, ˆ K ˆ to be unit vectors along x, y and z axes respectively. y I amps d µ I B πd A 4A (,, ) z Assuming right handed coordinate system, magnetic field intensity, H at coordinate (,,) will be 3 ˆ π ( A) k weber / m ( C) 3 k ˆ A / m π ( B) ( D) 4 ˆ i A / m 3π A / m

56 Answer: (C) Exp: H Hx Hy I 4 H aφ a a a πρ π π x x y z I H aφ a a a πρ π π y y x z 3 H a π π z 33. A discrete system is represented by the difference equation It has initial condition X k a a X k X k a a X k X ; X. The pole location of the system for a, are (A) ± j (B) ± j (C) ± j (D) ± j Answer: (A) Exp: from the given difference equation, a a A a a The pole locations of the system for a. Then A SI A. ( s ) S ± j 34. An input signal x ( t) 5sin ( πt) is sampled with a sampling frequency of 4 Hz and applied to the system whose transfer function is represented by N Y z z X z N z where, N represents the number of samples per cycle. The output y(n) of the system under steady state is (A) (B) (C) (D) 5

57 Answer: (C) Exp: x( t) 5sin( π t) x n Ts 5sin π n. 4 π 5sin n, N 8 4 Ω jω j Y e jωn e H e jω X e N e [ ] [ ] [ ] [ n] x n x n x n due to x jω [ ] [ ] y n H e x n r [ ] y n jω π y n H e sin n H e 4 jω jω [ ] π jω H e π Ω 4 [ ] [ ] [ ] [ ] y n y n y n y n Ω π 4 Ω 4 Thus at steadystate y[n] 35. A khz even-symmetric square wave is passed through a bandpass filter with centre frequency at 3 khz and 3 db passband of 6 khz. The filter output is (A) a highly attenuated square wave at khz (B) nearly zero. (C) a nearly perfect cosine wave at 3kHz. (D) a nearly perfect sine wave at 3kHz. Answer: (C) Exp: KHz even symmetric square wave have frequency component present KHz, 3KHz, 5KHz, 7KHz [only odd harmonics due to half wave symmetry] Since bandpass filter is contered at 3KHz, 3KHz component will pass through filter output is nearly perfect cosine wave at KHz Cosine in due to reason that signal in even signal. 36. A 5 V dc shunt machine has armature circuit resistance of.6ω and field circuit resistance of5 Ω. The machine is connected to 5 V supply mains. The motor is operated as a generator and then as a motor separately. The line current of the machine in both the cases is 5 A. The ratio of the speed as a generator to the speed as a motor is.

58 Answer:.7 Exp: Given: A 5A A 5A 48A 5A 5Ω 5V 5Ω 5V E V I R Ng? N m b a a V N g g We know that ( flux is constant ) N Motor m E E b 8. Ng.7. N m Generator E V I R b a a V 37. A three-phase slip-ring induction motor, provided with a commutator winding, is shown in the figure. The motor rotates in clockwise direction when the rotor windings are closed. 3 phase ac, fhz Pr ime mover Slip Ring Induction Motor f f r If the rotor winding is open circuited and the system is made to run at rotational speed f r with the help of prime-mover in anti-clockwise direction, then the frequency of voltage across slip rings is f and frequency of voltage across commutator brushes is f. The values of f and f respectively are (A) f f r and f (B) f - f r and f (A) f - f r and f f r (D) f - f r and f Answer: (A) Exp: Whenever the Rotor winding is open circuited and rotating in anti-clockwise direction then the ( Ns Nr ) P frequency of voltage across slip rings is f f f f r At the same time frequency of voltage across commutator brushes if f N P s f f

59 38. A -pole alternator is having 8 identical stator slots with 6 conductors in each slot. All the coils of a phase are in series. If the coils are connected to realize single-phase winding, the generated voltage is V. If the coils are reconnected to realize three-phase star-connected winding, the generated phase voltage is V. Assuming full pitch, single-layer winding, the ratio V / V is ( A) Answer: (D) Exp: Given poles, P 3 Total slots 8 4 Total no. of conductor ( B) ( C) 3 D 4 the ratio of voltage generated when the coils are connected in φ to when the coils are connected in 3 φ, Y-connection. ( V ) i.e., ( V ) φ 3φ 39. For a single phase, two winding transformer, the supply frequency and voltage are both increased by. The percentage changes in the hysteresis loss and eddy current loss, respectively, are Answer: (A) Exp: (A) and (B) - and (C) and (D) - and Given φ Transformer V and f are increased by W? e n W? Here V is constant f W n n f as 'f ' increased by W also n W W n e f f W e e f e W.f W by 4. A synchronous generator is connected to an infinite bus with excitation voltage Ef.3 pu. The generator has a synchronous reactance of. pu and is delivering real power (P) of.6 pu to the bus. Assume the infinite bus voltage to be. pu. Neglect stator resistance. The reactive power (Q) in pu supplied by the generator to the bus under this condition is.

60 Answer:.9 Exp: Given, E f.3 P.u X s.p.u P. 6pu V. pu Q? We know that,.3.6 sin δ. δ 3.5 s EV P sin δ X V Q [ Ecosδ V].9 X s 4. There are two generators in a power system. No-load frequencies of the generators are 5.5 Hz and 5Hz, respectively, and both are having droop constant of Hz/MW. Total load in the system is.5 MW. Assuming that the generators are operating under their respective droop characteristics, the frequency of the power system in Hz in the steady state is. Answer: 5 Exp: Given, two generators in a power system has no load frequency of 5.5 & 5 Hz. drop constanthz/mw Total load.5 mw for generator '', f x 5.5 generator '' f x 5 x 5.5 x 5 x x.5...() Total load x x.5...() 3 By solving () & () x.5 f Hz 4. The horizontally placed conductors of a single phase line operating at 5 Hz are having outside diameter of.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is The capacitance to ground per kilometer of each line is (A) F (B) F (C) 4. - F (D) F

61 Answer: (B) Exp: Given, diameters of conductor.6m radius, r.8cm Spacing between conductors, d6m Permitivity capacitance to ground per km? π π 8.85 d 6 ln ln r.8 o C C / km 8.4 F 43. A three phase, MVA, 5 kv generator has solidly grounded neutral. The positive, negative, and the zero sequence reactances of the generator are. pu,. pu, and.5 pu, respectively, at the machine base quantities. If a bolted single phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is. Answer: 55 Exp: Single line to ground fault, Fault current in If 3Ia positive sub transient circuit, Ea Ia z z z jo j. j. j.5 j.3pu j.45 Fault current Base current I 3 I f a 3 j. j6.666 pu pu Fault circuit pu fault circuit in pu x Base circuit in Amp If 5396A 44. A system with the open loop transfer function: G s K s s s s ( )( ) is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of K is