GATE 2011 Electrical Engineering Set C

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1 Electrical Engineering Set C Q. - Q.25 Carry One Mark each.. A three-phase current source inverter used for the speed control of an induction motor is to be realized using MOSFET switches as shown below. Switches to are identical switches. The proper configuration for realizing switches to is A A A A B B B B 2. A low-pass filter with a cut-off frequency of 3 Hz is cascaded with a high-pass filter with a cut-off frequency of 2 Hz. The resultant system of filters will function as an all-pass filter a band stop (band-reject) filter an all-stop filter a band-pass filter lpf 3 X f(in Hz) 3. Consider the following statements: Page

2 (i) The compensating coil of a low power factor wattmeter compensates the effect of the impedance of the current coil. (ii) The compensating coil of a low power factor wattmeter compensates the effect of the impedance of the voltage coil circuit. (i) is true but (ii) is false (i) is false but (ii) is true both (i) and (ii) are true both (i) and (ii) are false 4. For the circuit shown below, R R R R R R the CORRECT transfer characteristic is It is Schmitt trigger and phase shift is zero. 5. The steady state error of a unity feedback linear system for a unit step input is.. The steady state error of the same system, for a pulse input r(t) having a magnitude of and a duration of one second, as shown in the figure is r(t). s t Page 2

3 r(t) = As system is linear, = 6. The frequency response of a linear system G(j ) is provided in the tabular form below G(j ) The gain margin and phase margin of the system are 6 db and 3 6 db and 3 From table, at Similarly, G(j ) at is.5 GM = 2 6 db and 3 6 db and 3 db PM = 8 5 = 3 7. A nuclear power station of 5 MW capacity is located at 3 km away from a load center. Select the most suitable power evacuation transmission configuration among the followings options. Load center 32 kv, 3 km double circuit Load center 32 kv, 3 km single circuit with 4% series capacitor compensation Load center 4 kv, 3 km single circuit Load center 4 kv, 3 km double circuit 8. A three-phase, salient pole synchronous motor is connected to an infinite bus. It is operated at no load at normal excitation. The field excitation of the motor is first reduced to zero and then increased in the reverse direction gradually. Then the armature current increases continuously first decreases and then increases steeply first increases and then decreases steeply remains constant 9. A 4-point starter is used to start and control the speed of a dc shunt motor with armature resistance control dc shunt motor with field weakening control dc series motor dc compound motor. The Fourier series expansion f(t) = will contain the following nonzero terms of the periodic signal shown below Page 3

4 f(t) t and, n =, 3, 5,.... and, n =, 2, 3,.... and, n =, 2, 3,.... and, n =, 3, 5,.... Signal is even Also = for even n. The r.m.s value of the current i(t) in the circuit shown below is F H Ω i(t) Ω A A A A A 2. Roots of the algebraic equation are 3. Circuit turn-off time of an SCR is defined as the time taken by the SCR to turn off required for the SCR current to become zero for which the SCR is reverse biased by the commutation circuit for which the SCR is reverse biased to reduced its current below the holding current From the definition, it s the time for which SCR is reverse biased. 4. With K as a constant, the possible solution for the first order differential equation is Page 4

5 Integrate on both sides y = 5. The output Y of the logic circuit given below is X Y Y = X 6. A dual trace oscilloscope is set to operate in the ALTernate mode. The control input of the multiplexer used in the y-circuit is fed with a signal having a frequency equal to the highest frequency that the multiplexer can operate properly twice the frequency of the time base (sweep) oscillator the frequency of the time base (sweep) oscillator half the frequency of the time base (sweep) oscillator It is dependent on the frequency of time base oscillator. 7. The bridge circuit shown in the figure below is used for the measurement of an unknown element. The bridge circuit is best suited when is a low resistance high resistance Balance Condition: Balance condition: low Q inductor lossy capacitor is an inductor. 8. An open loop system represented by the transfer function G(s) = is stable and of the minimum phase type stable and of the non-minimum phase type unstable and of the minimum phase type unstable and of the non-minimum phase type For G(s), poles are at 2 and 3 Stable Page 5

6 Also, zeroes are to the right of S-plane non-minimum phase type 9. For enhancing the power transmission in a long EHV transmission line, the most preferred method is to connect a series inductive compensator in the line shunt inductive compensator at the receiving end series capacitive compensator in the line shunt capacitive compensator at the sending end Pα Where, X = 2. A negative sequence relay is commonly used to protect an alternator a transformer a transmission line a bus bar 2. A single-phase air core transformer, fed from a rated sinusoidal supply, is operating at no load. The steady state magnetizing current drawn by the transformer from the supply will have the waveform i i t t i i t t It is an air core transformer. So, there is no saturation effect. 22. Given two continuous time signals x(t) = * y(t) is and y(t) = which exist for t > the convolution z(t) = x(t) X(s) = Z(s) = X(s).Y(s) = 23. In the circuit given below, the value of R required for the transfer of maximum power of the load having a resistance of 3 Ω is Page 6

7 R 6Ω 3Ω V Load 6 Ω infinity zero 3 Ω 24. The voltage applied to a circuit is volts and the circuit draws a current of amperes. Taking the voltage as the reference phasor, the phasor representation of the current in amperes is 25. A point z has been plotted in the complex plane, as shown in figure below. Unit circle Im z Re The plot of the complex number y = is Unit circle Im y Im Unit circle Re Re y Im Unit circle Im Unit circle y Re Re y Z is having +ve real part and positive imaginary part ( from the characteristics). So Y should have +ve real part and negative imaginary part. Page 7

8 Q.26 - Q.55 Carry Two Marks each. 26. A voltage commutated chopper circuit, operated at 5 Hz, is shown below. M.µF A 2V LOAD mh If the maximum value of load current is A, then the maximum current through the main (M) and auxiliary thyristors will be = 2A 27. The transistor used in the circuit shown below has a β of 3 and is negligible. 2.2k 5k k D =.7V If the forward voltage drop of diode is.7v, then the current through collector will be 68 ma 2.54 ma 8 ma 5.36 ma Transistor is in Saturation region = 5.36 ma 28. A portion of the main program to call a subroutine SUB in an 885 environment is given below. : : LXI D, DISP LP: CALL SUB : Page 8

9 : It is desired that control be returned to LP + DISP + 3 when the RET instruction is executed in the subroutine. The set of instructions that precede the RET instruction in the subroutine are POP D POP H DAD H DAD D PUSH D PUSH H POP H XTHL DAD D INX D INX H INX D INX H INX D INX H XTHL PUSH H 29. The open loop transfer function G(s) of a unity feedback control system is given as, G(s) = From the root locus, it can be inferred that when k tends to positive infinity. three roots with nearly equal real parts exist on the left half of the s-plane one real root is found on the right half of the s-plane the root loci cross the j axis for a finite value of k; k three real roots are found on the right half of the s-plane RL starts from and 2 and ends at or Number of RL branches = 3 RL exists to the left of 2 on real axis one poles tends to Angle of asymptotes = = is not correct. Intersection of RL branches on real axis = C.E is S K 2 as real part is not correct. For marginal stability, K = is not correct. 3. A load center of 2 MW derives power from two stations connected by 22 kv transmission lines of 25 km and 75 km and 75 km as shown in the figure below. The three generators G, G2 and G3 are of MW capacity each and have identical fuel cost characteristics. The minimum loss generation schedule for supplying the 2 MW load is G 25 km 2 MW 75 km G2 G3 P = 8 MW + losses P2 = 2 MW P3 = 2 MW P = 6 MW Page 9 P2 = 3 MW + losses P3 = 3 MW P = 4 MW P2 = 4 MW

10 P3 = 4 MW + losses P = 3 MW + losses Loss α ; Loss α length For checking all options only option A gives less losses. P2 = 45 MW P3 = 45 MW 3. A 22 V, DC shunt motor is operating at a speed of 44 rpm. The armature resistance is. and armature current is A. If the excitation of the machine is reduced by %, the extra resistance to be put in the armature circuit to maintain the same speed and torque will be.79 Ω 3. Ω 2. Ω 8.9 Ω Now flux is decreased by %, so Torque is constant so Nα = 32. A zero mean random signal is uniformly distributed between limits a and equal to its variance. Then the r.m.s value of the signal is a a a and its mean square value is Variance = R.M.S value = 33. Let the Laplace transform of a function f(t) which exists for t > be and the Laplace transform of its delayed version f be. Let (s) be the complex conjugate of with the Laplace variable set as a s = σ + j. If G(s) =, then the inverse Laplace transform of G(s) is an ideal impulse δ(t) an ideal delayed impulse δ(t τ) an ideal step function u(t) an ideal delayed step function u(t τ) 34. A lossy capacitor, rated for operation at 5 kv, 5 Hz is represented by an equivalent circuit with an ideal capacitor in parallel with a resistor. The value of is found to be.2 µf and the value of MΩ. Then the power loss and of the lossy capacitor operating at the rated voltage, respectively, are W and.2 2 W and.25 W and.25 2 W and The function f(x) = 2x has a maxima at x = and a minima at x = 5 a maxima at x = and a minima at x = 5 f(x) = only a maxima at x = only a minima at x = So the equation f(x) have only a maxima at x = Page

11 36. Solution of the variables and for the following equations is to be obtained by employing the Newton- Raphson iterative method. equation (i) equation (ii) Assuming the initial values and =., the Jacobian matrix is..... (i)..... (ii) J = at and J = 37. A clipper circuit is shown below. k D 5V Assuming forward voltage drops of the diodes to be.7 V, the input-output transfer characteristics of the circuit is When output will follow input, because zener diode and normal diodes are off When V Zener diode forward bias and V When V Diode is forward bias and Page

12 38. A two-bit counter circuit is shown below. J Q Q T K CLK is then the state If the state of the counter at the clock time (after three clock cycles) will be Clock Input Initial state 2 3 of the counter at Output 39. A two-loop position control system is shown below. Motor R(s) Y(s) ks Tacho-generator The gain k of the Tacho-generator influences mainly the peak overshoot natural frequency of oscillation phase shift of the closed loop transfer function at very low frequencies phase shift of the closed loop transfer function at very high frequencies T(s) = = rad/sec; ξ = is dependent on K is correct is independent of K is not correct T(J ) = At low frequencies, T(J ) At high frequencies, T(J ) and are partially correct 4. A three-bus network is shown in the figure below indicating the p.u. impedance of each element. Page 2

13 2 j.2 3 j.8 j. j. The bus admittance matrix, Y-bus, of the network is j j j j h(t) = 4. A 4½ digit DMM has the error specification as:.2% of reading + counts. If a dc voltage of V is read on its 2 V full scale, the maximum error that can be expected in the reading is ±.% ±.3% ±.2% ±.4% Error specification :.2% of reading + counts..2% of reading: counts : =.V Total error In terms of % 42. The direct axis and quadrature axis reactances of a salient pole alternator are.2 p.u and. p.u respectively. The armature resistance is negligible. If this alternator is delivering rated kva at upf and at rated voltage then its power angle is Power factor angle = 43. The response h(t) of a linear time invariant system to an impulse δ(t), under initially relaxed condition is h(t) =. The response of this system for a unit step input u(t) is u(t) + L(Impulse response) = T.F = Page 3

14 Step response = = 44. A capacitor is made with a polymeric dielectric having an of 2.26 and a dielectric breakdown strength of 5 kv/cm. The permittivity of free space is 8.85 pf/m. If the rectangular plates of the capacitor have a width of 2 cm and a length of 4 cm, then the maximum electric charge in the capacitor is 2 µc 8 µc 4 µc µc q = CV = 45. A three-phase 44V, 6 pole, 5 Hz, squirrel cage induction motor is running at a slip of 5%. The speed of stator magnetic field with respect to rotor magnetic field and speed of rotor with respect to stator magnetic field are zero, 5 rpm zero, 955 rpm [Ans. *] rpm, 5 rpm rpm, 955 rpm 46. The two vectors [,, ] and [, a, ], where a =, are orthonormal orthogonal Dot product of two vectors = + a + = So orthogonal parallel collinear 47. The matrix[a] = is decomposed into a product of a lower triangular matrix [L] and an upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are and and and and Options D is correct Common Data Questions Common Data for Questions 48 and 49: An RLC circuit with relevant data is given below. R L C 48. The power dissipated in the resistor R is.5 W W W 2 W Page 4

15 49. The current in the figure above is j2 A Common Data for Questions 5 and 5: The input voltage given to a converter is V The current drawn by the converter is 5. The input power factor of the converter is Input pf = 5. The active power drawn by the converter is 8 W 5 W 77 W 887 W P = Linked Answer Questions Statement for Linked Answer Questions 52 and 53: Two generator units G and G2 are connected by 5 kv line with a bus at the mid-point as shown below. 3 km 2 km G2 G 5 kv 5 kv G = 25 MVA, 5 kv, positive sequence reactance X = 25 % on its own base G2 = MVA, 5 kv, positive sequence reactance X = % on its own base and = km, positive sequence reactance X =.225 Ω/km 52. For the above system, the positive sequence diagram with the p.u values on the MVA common base is j. j. j. 3 2 j. Page 5

16 j.25 j. j. 3 2 j. j. j2.25 j j. j.25 j2.25 j j. Take MVAs 5 kv as base For generator (G) For Transmission Line (L and L2) For generator (G2) p.u 53. In the above system, the three-phase fault MVA at the bus 3 is MVA 7.9 MVA 85. MVA 8.82 MVA =.55 Fault (MVA) = = 8.82 MVA Statement for Linked Answer Questions 54 and 55: A solar energy installation utilizes a three-phase bridge converter to feed energy into power system through a transformer of 4 V/4 V, as shown below. Page 6

17 Filter Choke Battery The energy is collected in a bank of 4 V battery and is connected to converter through a large filter choke of resistance Ω. 54. The maximum current through the battery will be 4 A 8 A 4 A 94 A = 54.2 = = 4A 55. The kva rating of the input transformer is 53.2 kva 46. kva [Ans. *] 22.6 kva 9.6 kva General Aptitude (GA) Questions Q.56 Q. 6 carry one mark each. 56. Choose the word from the options given below that is most nearly opposite in meaning to the given word: Frequency periodicity gradualness rarity persistency The best antonym here is rarity which means shortage or scarcity. 57. There are two candidates P and Q in an election. During the campaign, 4% of the voters promised to vote for P, and rest for Q. However, on the day of election 5% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters? 9 95 P Q 4% 6% +6% 6% +5% 5% 49% 5% 2% = 2 % = 58. Choose the most appropriate word from the options given below to complete the following sentence: Under ethical guidelines recently adopted by the Indian Medical Association, human genes are to be manipulated only to correct diseases for which treatments are unsatisfactory. similar uncommon most available Page 7

18 Fuel consumption (kilometers per litre) The context seeks to take a deviation only when the existing/present/current/alternative treatments are unsatisfactory. So the word for the blank should be a close synonym of existing/present/alternative. Available is the closest of all. 59. Choose the most appropriate word from the options given below to complete the following sentence: It was her view that the country s problems had been by foreign technocrats, so that to invite them to come back would be counter-productive. identified ascertained exacerbated analysed The clues in the question are ---foreign technocrats did something negatively to the problems so it is counter-productive to invite them. All other options are non-negative. The best choice is exacerbated which means aggravated or worsened. 6. The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair: Gladiator : Arena dancer : stage commuter : train teacher : classroom lawyer : courtroom The given relationship is worker: workplace. A gladiator is (i) a person, usually a professional combatant trained to entertain the public by engaging in mortal combat with another person or a wild. (ii) A person engaged in a controversy or debate, especially in public. Q. 6 to Q. 65 carry two marks each. 6. Given that f(y) =, and q is any non-zero real number, the value of is 2 Given, f(y) = 62. The fuel consumed by a motorcycle during a journey while travelling at various speeds is indicated in the graph below Speed (kilometers per hour) The distances covered during four laps of the journey are listed in the table below Lap Distance (Kilometres) Average speed (Kilometres per hour) Page 8

19 5 5 P Q 4 75 R S From the given data we can conclude that the fuel consumed per kilometre was least during the lap P R Q S Fuel consumption Actual P 6km/l Q 9km/l R 75km/l S 3km/l l 63. The sum of n terms of series is Let S = 4 ( ) = ( ) = = 64. Three friends, R, S and T shared toffee from a bowl. R took of the toffees, but returned four to the bowl. S took of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 7 toffees left, how many toffees were originally there in the bowl? Let the total number of toffees is bowl e x R took of toffees and returned 4 to the bowl Number of toffees with R = Remaining of toffees in bowl = Number of toffees with S = Remaining toffees in bowl = Number of toffees with T = Remaining toffees in bowl = Given, 65. The horse has played a little known but very important role in the field of medicine. Horses were injected with toxins of diseases until their blood built up immunities. Then a serum was made from their blood. Serums to fight with diphtheria and tetanus were developed this way. It can be inferred from the passage, that horses were given immunity to diseases given medicines to fight toxins generally quite immune to diseases given diphtheria and tetanus serums Page 9

20 From the passage it cannot be inferred that horses are given immunity as in, since the aim is to develop medicine and in turn immunize humans. is correct since it is given that horses develop immunity after some time. Refer unit their blood built up immunities. Even is invalid since medicine is not built till immunity is developed in the horses. is incorrect since specific examples are cited to illustrate and this cannot capture the essence. Page 2

(B) 1 A 2 2 (C) 1 A (D) 2 A

(B) 1 A 2 2 (C) 1 A (D) 2 A GATE SOLVED PAPER - EE 0 Q. No. 5 Carry One Mark Each Q. Roots of the algebraic equation x + x + x+ 0 are (A) ( +, + j, - j) (B) ( +, -, + ) (C) ( 000,, ) (D) (-, + j, -j) Q. With K as a constant, the