GATE –Past papers ELECTRICAL ENGINEERING - UNSOLVED PAPER - 2007

SECTION – I :

SECTION – I Single Correct Answer Type There are five parts in this question. Four choices are given for each part and one of them is correct. Indicate you choice of the correct answer for each part in your answer-book by writing the letter (a), (b), (c) or (d) whichever is appropriate

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01 The common emitter forward current gain of the transistor shown is β F = 100. The transistor is operating in Saturation region Cutoff region Reverse active region Forward active region Problem

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Problem 02 The three-terminal linear voltage regulator is connected to a 10 Ω load resistor as shown in the figure. If V in is 10 V, what is the power dissipated in the transistor ? 0.6 W 2.4 W 4.2 W 5.4 W

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Problem 03 Consider the transformer connections in a part of a power system shown in the figure. The nature of transformer connections and phase shifts are indicated for all but one transformer. Which of the following connections, and the corresponding phase shift θ , should be used for the transformer between A and B? Star-Star ( θ = 0°) Star - Delta ( θ = -30°) Delta - Star ( θ = 30°) Star-Zigzag ( θ = 30°)

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Problem 04 The incremental cost curves in Rs/MW hr for two generators supplying a common load of 700 MW are shown in the figures. The maximum and minimum generation limits are also indicated. The optimum generation schedule is : Generator A : 400 MW, Generator B : 300 MW Generator A : 350 MW, Generator B : 350 MW Generator A : 450 MW, Generator B : 250 MW Generator A : 425 MW, Generator B : 275 MW

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Problem 05 Two regional systems, each having several synchronous generators and loads are interconnected by an ac line and a HVDC link as shown in the figure. Which of the following statements is true in the steady state : Both regions need not have the same frequency The total power flow between the regions (P ac + P dc ) can be changed by controlling the HVDC converters alone The power sharing between the ac line and the HVDC link can be changed by controlling the HVDC converters alone. The direction of power flow in the HVDC ling ( P dc ) cannot be reversed.

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Problem 06 Consider a bundled conductor of an overhead line, consisting of three identical sub conductors placed at the corners of an equilateral triangle as shown in the figure. If we neglect the charges on the other phase conductors and ground, and assume that spacing between sub-conductors is much larger than their radius, the maximum electric field intensity is experienced at Point X Point Y Point Z Point W

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Problem 07 The circuit shown in the figure is a voltage source with voltage ( rV )//(R 1 //R 2 ) a voltage source with voltage ((r // R 2 )/(R 1 ))V a current source with current ((r//R 2 )/(R 1 + R 2 )).V/r a current source with current (R 2 /(R 1 + R 2 )).V/r

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Problem 08 The system shown in the figure is Stable Unstable conditionally stable stable for input u 1 , but unstable for input u 2

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Problem 09 Let a signal a 1 sin ( ω 1 t + 1 ) be applied to a stable linear time - invariant system. Let the corresponding steady state output be represented as a 2 F ( ω 2 t + 2 ). Then which of the following statements is true ? F is not necessarily a "sine" or "cosine" function but must be periodic with ω 1 = ω 2 F must be a "sine" or "cosine" function with a 1 = a2 F must be a "sine" function with ω 1 = ω 2 and 1 = 2 F must be a "sine" or "cosine" function with ω 1 = ω 2

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Problem 10 The frequency spectrum of a signal is shown in the figure. If this signal is ideally sampled at intervals of 1 ms, then the frequency spectrum of the sampled signal will be b. c. d.

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Problem 11 Divergence of the vector field V (x, y, z) = - (x cos xy + y) i + (y cos xy ) j + (sin z 2 + x 2 + y 2 ) k is 2z cos z 2 sin xy + 2z cos z 2 x sin xy - cos z none of these

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Problem 12 x = [x 1 x 2 ... x n ] T is an n- tuple nonzero vector. The n x n matrix V = xx T has rank zero has rank / is orthogonal has rank n

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Problem 13 A single - phase fully controlled thyristor bridge ac - dc converter is operating at a firing angle of 25° and an overlap angle 10° with constant dc output current of 20 A. The fundamental power factor (displacement factor) at input ac mains is 0.78 0.827 0.866 0.9

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Problem 14 A three - phase, fully controlled thyristor bridge converter is used as line commutated inverter to feed 50 kW power at 420 V dc to a three - phase, 415 V (line), 50 Hz ac mains. Consider dc link current to be constant. The rms current of the thyristor is 119.05 A 79.37 A 68.73 A 39.68 A

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Problem 15 In a transformer zero voltage regulation at full load is not possible possible at unity power factor load possible at leading power factor load possible at lagging power factor load

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Problem 16 The dc motor, which can provide zero speed regulation at full load without any controller, is series shunt cumulative compound differential compound

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Problem 17 The probes of a non - isolated, two - channel oscilloscope are clipped to points A, B and C in the circuit of the adjacent figure. V in is a square wave of a suitable low frequency. The display on Ch 1 and Ch 2 are as shown on the right. Then the "Signal" and "Ground" probes S 1 , G 1 and S 2 , G 2 of Ch 1 and Ch 2 respectively are connected to points. A, B, C, A A, B, C, B C, B, A, B B, A, B, C

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Problem 18 A single phase full-wave half-controlled bridge converter feeds an inductive load. The two SCRs in the converter are connected to a common DC bus. The converter has to have a freewheeling diode because the converter inherently does not provide for free-wheeling because the converter does not provide for free-wheeling for high values of triggering angles or else the free-wheeling action of the converter will cause shorting of the AC supply or else if a gate pulse to one of the SCRs is missed, it will subsequently cause a high load current in the other SCR

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Problem 19 The electromagnetic torque T e of a drive, and its connected load torque T L are as shown below. Out of the operating points A, B, C and D, the stable ones are a. b. c. d.

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Problem 20 "Six MOSFETs connected in a bridge configuration (having no other power device) MUST be operated as a Voltage Source Inverter (VSI)". This statement is True, because being majority carier devices, MOSFETs are voltage driven True, because MOSFETs have inherently anti-parallel diodes False, because it can be operated both as Current Source Inverter (CSI) or a VSI False, because MOSFETs can be operated as excellent constant current sources in the saturation region

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Problem 21 The input signal V in shown in the figure is a 1 kHz square wave voltage that alternates between +7V and -7V with a 50% duty cycle. Both transistors have the same current gain, which is large. The circuit delivers power to the load resistor R L . What is the efficiency of this circuit for the given input ? Choose the closest answer. 1) 46 % 2) 55 % 3) 63 % 4) 92 %

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Problem 22 A, B, C and D are input bits, and Y is the output bit in the XOR gate circuit of the figure below. Which of the following statements about the sum S of A, B, C, D and Y is correct? S is always either zero or odd S is always either zero or even S = 1 only if the sum of A, B, C and D is even S = 1 only if the sum of A, B C and D is odd

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Problem 23 The differential equation dx / dt = ((1 )/ discretised using Euler's numerical integration method with a time step T > 0. What is the maximum permissible value of T to ensure stability of the solution of the corresponding discrete time equation ? 1 /2 2

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Problem 24 The switch S is the circuit of the figure is initially closed. It is opened at time t = 0. You may neglect the Zener diode forward voltage drops. What is the behaviour of V OUT for t > 0? It makes a transition from - 5 V to + 5 V at t = 1 2.98 μ s It makes a transition from - 5 V to + 5 V at t = 2.57 μ s It makes a transition from + 5 V to - 5 V at t = 12.98 μ s It makes a transition from + 5 V to - 5 V at t = 2.57 μ s

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Problem 25 A solid sphere made of insulating material has a radius R and has a total charge Q distributed uniformly in its volume. What is the magnitude of the electric field intensity, E, at a distance r (0 < r < R) inside the sphere ? (1/4 πε 0 )( Qr /R 3 ) (3/4 πε 0 )( Qr /R 3 ) (1/4 πε o )(Q/r 2 ) (1/4 πε 0 )(QR/r 3 )

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Problem 26 The figure below shows a three phase self-commutated voltage source converter connected to a power system. The converter's dc bus capacitor is marked as C in the figure. The circuit is initially operating in steady state with δ = 0 and the capacitor dc voltage is equal to V dco . You may neglect all losses and harmonics. What action should be taken to increase the capacitor dc voltage slowly to a new steady state value ? Make δ positive and maintain it at a positive value Make δ positive and return it to its original value Make δ negative and maintain it at a negative value Make δ negative and return it to its original value

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Problem 27 The total reactance and total susceptance of a lossless overhead EHV line, operating at 50 Hz, are given by 0.045 pu and 1.2 pu respectively. If the velocity of wave propagation is 3 x 10 5 km/s, then the approximate length of the line is 122 km 172 km 222 km 272 km

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Problem 28 Consider the protection system shown in the figure below. The circuit breakers, numbered from 1 to 7 are of identical type. A single line to ground fault with zero fault impedance occurs at the midpoint of the line (at point F), but circuit breaker 4 fails to operate ("stuck breaker"). If the relays are coordinated correctly, a valid sequence of circuit breaker operations is 1,2,6,7,3,5 1,2,5,6,7,3 5,6,7,3,1,2 5, 1,2,3,6,7

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Problem 29 A three phase balanced star connected voltage source with frequency ω rad / s is connected to a star connected balanced load which is purely inductive. The instantaneous line currents and phase to neutral voltages are denoted by ( i a , i b , i c ) and (v an, v bn , v cn ) respectively and their rms values are denoted by V and 1. If R = [v an v bn v cn ] = then the magnitude of R is 3 VI VI 0.7 VI 0

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Problem 30 Consider a synchronous generator connected to an infinite bus by two identical parallel transmission lines. The transient reactance x of the generator is 0.1 pu and the mechanical power input to it is constant at 1.0 pu . Due to some previous disturbance, the rotor angle ( δ ) is undergoing an undamped oscillation, with the maximum value δ (t) equal to 130°. One of the parallel lines trips due to relay maloperation at an instant when δ (t) = 130° as shown in the figure. The maximum value of the per unit line reactance, x, such that the system does not lose synchronism subsequent to this tripping is 1) 0.87 2) 0.74 3) 0.67 4) 0.54

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Problem 31 Suppose we define a sequence transformation between "a-b-c" and "p-n-o" variables as follows: = k where α = ej (2 π /3) and k is constant. Now if it is given that : = and = Z then, a. Z = Z = Z = 3k 2 Z =

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Problem 32 Consider the two power systems shown in figure A below, which are initially not interconnected, and are operating in steady state at the same frequency. Separate load flow solutions are computed individually for the two systems, corresponding to this scenario. The bus voltage phasors so obtained are indicated on figure A. These two isolated systems are now interconnected by a short transmission line as shown in figure B, and it is found that P 1 = P 2 = Q 1 = Q 2 = 0: The bus voltage phase angular difference between generator bus X and generator bus Y after the interconnection is 10° 25° -30° 30°

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Problem 33 The octal equivalent of the HEX number AB.CD is 253.314 253.632 526.314 526.632

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Problem 34 If x = Re G(j θ ), and y = /m G(j ω ) then for a ω → 0 + , the Nyquist plot for G(s) = 1 /s(s + 1) (s + 2) becomes asymptotic to the line x = 0 x = -3/4 x = y - 1/6 x = y/ √ 3

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Problem 35 The system 900/s(s + 1) (s + 9) is to be compensated such that its gain-crossover frequency becomes same as its uncompensated phase-crossover frequency and provides a 45° phase margin. To achieve this, one may use a lag compensator that provides an attenuation of 20 dB and a phase lag of 45° at the frequency of 3 √ 3 rad /s a lead compensator that provides an amplification of 20 dB and a phase lead of 45° at the frequency of 3 rad /s a lag-lead compensator that provides an amplification of 20 dB and a phase lag of 45° at the frequency of √ 3 rad /s a lag-lead compensator that provides an attenuation of 20 dB and phase lead of 45° at the frequency of 3 rad /s

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Problem 36 Consider the discrete-time system shown in the figure where the impulse response of G(z) is g(0) = 0, g(1) = g(2) = 1, g(3) = g(4) = ... = 0. This system is stable for range of values of K [-1,1/2] [-1,1] [- 1/2, 1] [-1/2, 2]

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Problem 37 A signal x(t) is given by x(t) = Which among the following gives the fundamental Fourier term of x(t) ? (4/ π ) cos (( π t /T) - ( π /4)) (4/ π ) cos (( π t /2T) + ( π /4)) (4/ π ) sin (( π t /T) - ( π /4)) (4/ π ) sin (( π t /2T) + ( π /4))

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Problem 38 If the loop gain K of a negative feedback system having a loop transfer function K(s + 3)/(s + 8) 2 is to be adjusted to induce a sustained oscillation then The frequency of this oscillation must be 4/√3 rad /s The frequency of this oscillation must be must be 4 rad /s The frequency of this oscillation must be must be 4 or 4/√3 rad /s such a K does not exist

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Problem 39 The system shown in figure below with X = c 0 s + c 1 , Y = 1 /(s 2 + a 0 s + a 1 ), Z = b 0 s + b 1 X = 1, Y = (c 0 s + c 1 )/(s 2 + a 0 s + a 1 ), Z = b 0 s + b 1 X = c 1 s + c 0 , Y = (b 1 s + b 0 ) /(s 2 + a 1 s + a 0 ), Z = 1 X = c 1 s + c 0 , Y = 1/(s 2 + a 1 s + a 0 ), Z = b 1 s + b 0

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Problem 40 The value of where C is the contour |z - i /2| = 1 is 2 π i π Tan -1 z π i tan -1 z

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Problem 41 A single-phase voltage source inverter is controlled in a single pulse-width modulated mode with a pulse width of 150° in each half cycle. Total harmonic distortion is defined as THD = ( √ (V rms 2 - 1 V 2 )/V 1 ) x 100, where V 1 is the rms value of the fundamental component of the output voltage. The THD of output ac voltage wave form is 65.65 % 48.42 % 31.83% 30.49 %

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Problem 42 A voltage source inverter is used to control the speed of a three-phase, 50 Hz, squirrel cage induction motor. Its slip for rated torque is 4%. The flux is maintained at rated value. If the stator resistance and rotational losses are neglected, then the frequency of the impressed voltage to obtain twice the rated torque at starting should be 10 Hz 5 Hz 4 Hz 2 Hz

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Problem 43 A three-phase, 440 V, 50 Hz ac mains fed thyristor bridge is feeding a 440 V dc, 15 kW. 1500 rpm separately excited dc motor with a ripple free continuous current in the dc link under all operating conditions. Neglecting the losses, the power factor of the ac mains at half the rated speed, is 0.354 0.372 0.90 0.955

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Problem 44 A single-phase, 230 V, 50 Hz ac mains fed step down transformer (4 : 1) is supplying power to a half-wave uncontrolled ac-dc converter used for charging a battery (12 V dc) with the series current limiting resistor being 19.04 Ω . The charging current is 2.43 A 1.65 A 1.22 A 1.0 A

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Problem 45 A three-phase synchronous motor connected to ac mains is running at full load and unity power factor. If its shaft load is reduced by half, with field current held constant, its new power factor will be unity leading lagging dependent on machine parameters

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Problem 46 A 100 kVA . 415 V (line), star-connected synchronous machine generates rated open circuit voltage of 415 V at a field current of 15 A. The short circuit armature current at a field current of 10 A is equal to the rated armature current. The per unit saturated synchronous reactance is 1.731 1.5 0.666 0.577

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Problem 47 A three-phase, three-stack, variable reluctance step motor has 20 poles on each rotor and stator stack. The step angle of this step motor is 3° 6° 9° 18°

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Problem 48 A single - phase 50 - kVA , 250V/500 V two winding transformer has an efficiency of 95 % at full load, unity power factor. If it is reconfigured as a 500 V/750 V autotransformer, its efficiency at its new rated load at unity power factor will be 95.752% 97.851 % 98.276 % 99.241 %

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Problem 49 A 230 V (phase), 50 Hz, three - phase, 4 - wire system has a phase sequence ABC. A unity power - factor load of 4 kW is connected between phase A and neutral N. It is desired to achieve zero neutral current through the use of a pure inductor and a pure capacitor in the other two phase. The value of inductor and capacitor is 72.95 mH in phase C and 139.02 μ F in phase B 72.95 mH in phase B and 139.02 μ F in phase C 42.12 mH in phase C and 240.79 μ F in phase B 42.12 mH in phase B and 240.79 μ F in phase C

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Problem 50 The state equation for the current l 1 shown in the network shown below in terms of the voltage V x and the independent source V, is given by dl 1 / dt = -1.4V x -3.75l 1 + (5/4)V dl 1 / dt = -1.4V x -3.75l 1 - (5/4)V dl 1 / dt = -1.4V x + 3.75l 1 + (5/4)V dl 1 / dt = -1.4V x + 3.75l 1 - (5/4)V

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Problem 51 If u(t), r(t) denote the unit step and unit ramp functions respectively and u(t) * r(t) their convolution, then the function u(t + 1) * r(t - 2) is given by (1/2)(t-1)(t-2) (1/2)(t- 1) 2 (t- 2) (1/2)(t- 1) 2 u(t - 1) none of these

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Problem 52 The integral sin (t - ) cos d equals sin t cos t 0 (1/2) cost (1/2) sin t

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Problem 53 X(z) = 1 – 3z -1 , Y(z) = 1 + 2z -2 are Z- transforms of two signals x[n], y[n] respectively. A linear time invariant system has the impulse response h[n] defined by these two signals as h[n] = x[n -1] *y [n] where * denotes discrete time convolution. Then the output of the system for the input δ [n -1] has Z - transform z -1 X (z) Y(z) equals δ [n - 2] - 3 δ [n - 3] + 2 δ [n - 4] - 6 δ [n - 5] has Z - transform 1 – 3z -1 + 2z -2 – 6z -3 does not satisfy any of the above three.

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Problem 54 A loaded dice has following probability distribution of occurrences if three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is same as that of occurrence of 3, 4, 5 same as that of occurrence of 1, 2, 5 1/128 5/8 Dice value 1 2 3 4 5 6 Probability 1/4 1/8 1/8 1/8 1/8 1/4

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Problem 55 Let x and y be two vectors in a 3 dimensional space and <x, y> denote their dot product. Then the determinant det is zero when x and y are linearly independent is positive when x and y are linearly independent is non-zero for all non-zero x and y is zero only when either x or y is zero

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Problem 56 The linear operation L(x) is defined by the cross product L(x) = bxx , where b = [0 1 0] T and x = [x 1 x 2 x 3 ] T are three dimensional vectors. The 3x3 matrix M of this operation satisfies L(x) = M Then the eigenvalues of M are 0,+1,-1 1,-1, 1 i , - i , 1 i , - i , 0

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Problem 57 In the figure, transformer Ti has two secondaries , all three windings having the same number of turns and with polarities as indicated. One secondary is shorted by a 10 Ω resistor R, and the other by a 15 μ F capacitor. The switch SW is opened (t = 0) when the capacitor is charged to 5 V with the left plate as positive. At t = 0+ the voltage Vp and current I r are -25 V, 0.0 A very large voltage, very large current 5.0 V, 0.5 A -5.0 V,-0.5 A

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Problem 58 IC 555 in the adjacent figure is configured as an astable multivibrator . It is enabled to oscillate at t = 0 by applying a high input to pin 4. The pin description is : 1 and 8 - supply ; 2 - trigger; 4 - reset; 6 - threshold; 7- discharge. The waveform appearing across the capacitor starting from t = 0, as observed on a storage CRC is b. c. d.

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Problem 59 In the circuit of adjacent figure the diode connects the ac source to a pure inductance L. The diode conducts for 90° 180° 270° 360°

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Problem 60 The circuit in the figure is a current commutated dc - dc chopper where, Th M is the main SCR and Th AUX is the auxiliary SCR. The load current is constant at 10 A. Th M is ON. Th AUX is triggered at t = 0. Th M is turned OFF between 0 μ s < t ≤ 25 μ s 25 μ s < t ≤ 50 μ s 50 μ s < t ≤ 75 μ s 75 μ s < t ≤ 100 μ s

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Problem 61 In the circuit shown in figure switch SW 1 is initially CLOSED and SW 2 is OPEN. The inductor L carries a current of 10 A and the capacitor is charged to 10 V with polarities as indicated. SW 2 is initially CLOSED at t = 0 - and SW 1 is OPENED at t = 0. The current through C and the voltage across L at t = 0 + is 55 A, 4.5 V 5.5 A, 45 V 45 A, 5.5 V 4.5 A, 5.5 V

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Problem 62 The R-L-C series circuit shown is supplied from a variable frequency voltage source. The admittance-locus of the R-L-C network at terminals AB for increasing frequency ω is a. b. d.

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Problem 63 In the figure given below all phasors are with reference to the potential at point "O". The locus of voltage phasor V YX as R is varied from zero to infinity is shown by b. d.

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Problem 64 A 3 V dc supply with an internal resistance of Ω supplies a passive non-linear resistance characterized by the relation V nL = I 2 nl . The power dissipated in the non-linear resistance is 1.0 W 1.5 W 2.5 W 3.0 W

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Problem 65 Consider the feedback control system shown below which is subjected to a unit step input. The system is stable and has the following parameters k p = 4, k i = 10 ω = 500 and = 0.7 The steady state value of z is 1 0.25 0.1 0

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Problem 66 A three-phase squirrel cage induction motor has a starting torque of 150 % and a maximum torque of 300 % with respect to rated torque at rated voltage and rated frequency. Neglect the stator resistance and rotational losses. The value of slip for maximum torque is 13.48 % 16.24 % 18.92 % 26.79 %

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Problem 67 The matrix A given below is the node incidence matrix of a network. The columns correspond to branches of the network while the rows correspond to nodes. Let V = [v 1 v 2 ... v 6 ] T denote the vector of branch voltages while I = [i 1 i 2 .... i 6 ] T that of branch currents. The vector E = [e 1 e 2 e 3 e 4 ] T denotes the vector of node voltages relative to a common ground. A = Which of the following statements is true? The equations v 1 -v 2 + v 3 = 0, v 3 + v 4 - v 5 = 0 are KVL equations for the network for some loops 0 The equations v 1 -v 3 - v 6 = 0, v 4 + v 5 – v 6 = 0 are KVL equations for the network for some loops 0 E = AV AV = 0 are KVL equations for the network

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Problem 68 An isolated 50 Hz synchronous generator is rated at 15 MW which is also the maximum continuous power limit of its prime mover. It is equipped with a speed governor with 5% droop. Initially, the generator is feeding three loads of 4 MW each at 50 Hz. One of these loads is programmed to trip permanently if the frequency falls below 48 Hz. If an additional load of 3.5 MW is connected then the frequency will settle down to 49.417 Hz 49.917 Hz 50.083 Hz 50.580 Hz

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Problem 69 Which one of the following statements regarding the INT (interrupt) and the BRQ (but request) pins in a CPU is true ? The BRQ pin is sampled after every instruction cycle, but the INT is sampled after every machine cycle Both INT and BRQ are sampled after every machine cycle The INT pin is sampled after every instruction cycle, but the BRQ is sampled after every machine cycle Both INT and BRQ are sampled after every instruction cycle

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Problem 70 A bridge circuit is shown in the figure below. Which one of the sequences given below is most suitable for balancing the bridge ? First adjust R 4 and then adjust R 1 First adjust R 2 and then adjust R 3 First adjust R 2 and then adjust R 4 First adjust R 4 and then adjust R 2

Directions for question 71 to 73::

Directions for question 71 to 73: A three phase squirrel cage induction motor has a starting current of seven times the full load current and full load slip of 5 %

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Problem 71 If an autotransformer is used for reduced voltage starting to provide 1.5 per unit starting torque, the autotransformer ratio (%) should be 57.77 % 72.56 % 78.25 % 81.33 %

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Problem 72 If a star-delta starter is used to start this induction motor, the per unit starting torque will be 0.607 0.816 1.225 1.616

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Problem 73 If a starting torque of 0.5 per unit is required then the per unit starting current should be 4.65 3.75 3.16 2.13

Directions for question 74 to 75 : :

Directions for question 74 to 75 : A 1 : 1 pulse Transformer (PT) is used to trigger the SCR in the adjacent figure . The SCR is rated at 1.5kV , 250 A with lL = 250mA, lH = 150 mA , and l Gmax = 150 mA , l Gmin =100 mA . The SCR is connected to an inductive load , Where L = 150 mH in series with a small resistance and the supply voltage is 200 V dc . The forward drops of all transistors / diodes and gate – cathode junction during ON state are 1.0 v

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Problem 74 The resistance R should be 4.7 k Ω 470 Ω 47 Ω 4.7 Ω

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Problem 75 The minimum approximate volt - second rating of the pulse transformer suitable for triggering the SCR should be : (volt - second rating is the maximum of product of the voltage and the width of the pulse that may be applied) 2000 μ V - s 200 μ V - s 20 μ V - s 2.0 μ V - s

Directions for question 76 to 77::

Directions for question 76 to 77: An inductor designed with 400 turns coil wound on an iron core of 16 cm 2 cross sectional area and with a cut of an air gap length of 1 mm the coil is connected to a 230 V, 50Hz ac supply Neglect coil resistance, core loss, iron reluctance and leakage inductance. (u 0 = 4 x 10 -7 H/m)

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Problem 76 The current in the inductor is 18.08 A 9.04 A 4.56 A 2.28 A

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Problem 77 The average force on the core to reduce the air gap will be 832.29 N 1666.22 N 3332.47 N 6664.84 N

Directions for question 78 to 79::

Directions for question 78 to 79: Cayley – Hamilton Theorem states that a square matrix satisfies its own characteristic equation. Consider a matrix

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Problem 78 A satisfies the relation A + 3I + 2A -1 =0 A 2 + 2A + 21 = 0 (A + I) (A + 2I) = 0 exp(A) = 0

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Problem 79 A 9 equals 511 A + 510 I 309 A + 104 I 154 A + 155 I exp (9 A)

Directions for question 80 to 81 : :

Directions for question 80 to 81 : Consider the R-L-C circuit shown in figure.

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Problem 80 For a step - input e i , the overshoot in the output e 0 will be 0, since the system is not under-damped 5 % 16 % 48 %

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Problem 81 If the above step response is to be observed on a non- storage CRO, then it would be best to have the e i as a step function square wave of frequency 50 Hz square wave of frequency 300 Hz square wave of frequency 2.0 kHz The associated figure shows the two types of rotate right instructions R1 , R2 Available in a microprocessor where Reg is a 8 – bit register and C is the carry Bit. The rotate left instructions Ll and L2 are similar except that C now links the most significant bit of Rrg instead of the least significant one.

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Problem 82 Suppose Reg contains the 2's complement number 11010110. If this number is divided by 2 the answer should be 01101011 10010101 11101001 11101011

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Problem 83 Such a division can be correctly performed by the following set of operations L2, R2, R1 L2, R1, R2 R2, L1, R1 R1, L2, R2

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Problem 84 A signal is processed by a causal filter with transfer function G(s). For a distortion free output signal waveform, G(s) must provide zero phase shift for all frequency Provide constant phase shift for all frequency provide linear phase shift that is proportional to frequency Provide a phase shift that is inversely proportional to frequency

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Problem 85 G(z) = α z -1 + β z -3 is a low-pass digital filter with a phase characteristics same as that of the above question if α = β α = - β α = β (1/3) α = β -(1/3)

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