Electrical Engineering - unsolved - 2005

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GATE –Past papers:

GATE –Past papers ELECTRICAL ENGINEERING - UNSOLVED PAPER - 2005

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

Problem:

01 In the figure given below the value of R is 2.5 Ω 5.0 Ω 7.5 Ω 10.0 Ω Problem

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Problem 02 The RMS value of the voltage u(t) = 3 + 4cos (3t) is √l7 V 5 V 7 V (3 + 2√2)V

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Problem 03 For the two port network shown in the figure the Z-matrix is given by b. c. d.

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Problem 04 In the figure given below, 4 the initial capacitor voltage is zero. The switch is closed at t = 0. The final steady-state voltage across the capacitor is 20 V 10 V 5 V 0 V

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Problem 05 If Ē is the electric field intensity, ( × Ē) is equal to Ē I Ē l null vector zero

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Problem 06 A system with zero initial conditions has the closed loop transfer function. T(s) = (s 2 + 4)/((s + 1) (s + 4)). The system output is zero at the frequency 0.5 rad /sec 1 rad /sec 2 rad /sec 4 rad /sec

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Problem 07 Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is K/s 3 K/(s 2 (s+ 1)) K/(s(s 2 + 1)) K/(s(s 2 - 1))

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Problem 08 The gain margin of a unity feedback control system with the open loop transfer function G (s) = (s + 1 )/s 2 is 0 1/√2 √2

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Problem 09 In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x : Augmented matrix [ Pq ] must have the same rank as matrix P Vector q must have only non-zero elements Matrix P must be singular Matrix P must be square

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Problem 10 If P and Q are two random events, then the following is TRUE Independence of P and Q implies that probability (P Q ) = 0 Probability (P Q) ≥ Probability (P) + Probability (Q) If P and Q are mutually exclusive, then they must be independent Probability (P Q) ≤ Probability (P)

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Problem 11 If S = , then S has the value (-1)/3 1/4 1/2 1

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Problem 12 The solution of the first order differential equation x(t) = -3x(t), x (0) = x 0 is x (t) = x 0 e -3t x (t) = x 0 e -3 x (t) = x 0 e -1/3 x (t) = x 0 e -1

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Problem 13 The equivalent circuit of a transformer has leakage reactances X 1 , X' 2 and magnetizing reactance X m . Their magnitudes satisfy X 1 >> X' 2 >>X M X 1 << X' 2 << X M X 1 ≈ X‘ 2 >>X M X 1 ≈ X' 2 >> X M

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Problem 14 Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and corresponding input time voltages Star - Star Star - Delta Delta - Delta Delta - Zigzag

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Problem 15 On the torque/speed curve of induction motor shown in the figure four points of operation are marked as W, X, Y and Z. Which one of them represents the operation at a slip greater than 1 ? W X Y Z

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Problem 16 For an induction motor, operating at a slip s, the ratio of gross power output to air gap power is equal to (1-s) 2 (1 - s) √(1- s) (1 - √s)

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Problem 17 The p.u . parameters for a 500 MVA machine on its own base are : inertia, M = 20 p.u . ; reactance, X = 2 p.u . The p.u . values of inertia and reactance on 100 MVA common base, respectively, are 4, 0.4 100, 10 4, 10 100, 0.4

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Problem 18 An 800 kV transmission line has a maximum power transfer capacity of P. If it is operated at 400 kV with the series reactance unchanged, then new maximum power transfer capacity is approximately P 2P P/2 P/4

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Problem 19 The insulation strength of an EHV transmission line is mainly governed by load power factor switching over-voltages harmonics corona

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Problem 20 High Voltage DC (HVDC) transmission is mainly used for bulk power transmission over very long distances inter-connecting two systems with the same nominal frequency eliminating reactive power requirement in the operation minimizing harmonics at the converter stations

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Problem 21 The Q - meter works on the principle of mutual inductance self inductance series resonance parallel resonance

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Problem 22 A PMMC voltmeter is connected across a series combination of a DC voltage source V 1 =2 V and an AC voltage source V 2 (t) = 3 sin (4t) V. The meter reads 2 V 5 V (2 + √ 3/2) V ( √ 17/2) V

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Problem 23 Assume that D 1 and D 2 in figure are ideal diodes. The value of current I is 0 mA 0.5 mA 1 mA 2 mA

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Problem 24 The 8085 assembly language instruction that stores the content of H and L registers into the memory locations 2050 h and 2051 h , respectively, is SPHL 2050 H SPHL 2051 H SHLD 2050 H STAX 2050 H

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Problem 25 Assume that the N-channel MOSFET shown in the figure is ideal, and that its thereshold voltage is + 1.0 V. the voltage V ab between nodes a and b is 5 V 2 V 1 V 0 V

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Problem 26 The digital circuit shown in the figure works as a JK flip-flop Clocked RS flip-flop T flip-flop Ring counter

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Problem 27 A digital-to-analog converter with a full-scale output voltage of 3.5 V has a resolution close to 14 m V. Its bit size is 4 8 16 32

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Problem 28 The conduction loss versus device current characteristic of a power MOSFET is best approximated by a parabola a straight line a rectangular hyperbola an exponentially decaying function

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Problem 29 A three-phase diode bridge rectifier is fed from a 400 V RMS, 50 Hz, three-phase AC source. If the load is purely resistive, then peak instantaneous output voltage is equal to 400V 400 √ 2V 400 √ (2/3) V (400 √ 3) V

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Problem 30 The output voltage waveform of a three-phase square-wave inverter contains only even harmonics both odd and even harmonics only odd harmonics only triple harmonics

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Problem 31 The RL circuit of the figure is fed from a constant magnitude, variable frequency sinusoidal voltage source V IN - At 100 Hz, the R and L elements each have a voltage drop u rms - if the frequency of the source is changed to 50Hz, then new voltage drop across R is √(5/8) u RMS √(2/3) u RMS √(8/5) u RMS √(3/2) u RMS

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Problem 32 For the three-phase circuit shown in the figure the ratio of the currents I r : l y : I B is given by 1 : 1 : √3 1 : 1 : 2 1 : 1 : 0 1 : 1 : √3/2

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Problem 33 For the triangular wave form shown in the figure, the RMS value of the voltage is equal to √(1/6) √(1/3) 1/3 √(2/3)

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Problem 34 The circuit shown in the figure is in steady state, when the switch is closed at t = 0. Assuming that the inductance is ideal, the current through the inductor at t = 0 + equals 0 A 0.5 A 1 A 2 A

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Problem 35 The charge distribution in a metal-dielectric semiconductor specimen is shown in the figure. The negative charge density decreases linearly in the semiconductor as shown. The electric field distribution is as shown in a. b. c. d.

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Problem 36 In the given figure, the Thevenin's equivalent pair (voltage, impedance), as seen at the (2V, 5 Ω ) (2 V, 7.5 Ω ) (4V, 5 Ω ) (4 V, 7.5 Ω )

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Problem 37 A unity feedback system, having an open loop gain G(s)H(s) = (K(1 - s))/(1 + s), becomes stable when |K|>1 K > 1 |K|<1 K < - 1

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Problem 38 When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error of -1.0 -0.5 0 0.5

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Problem 39 In the GH(s) plane, the Nyquist plot of the loop transfer function G(s)H(s) π =e( -0.25 )/s passes through the negative real axis at the point (-0.25, j0) (-0.5, j0) (-1, j0) (-2, j0)

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Problem 40 If the compensated system shown in the figure has a phase margin of 60° at the crossover frequency of 1 rad /sec, then value of the gain K is 0.366 0.732 1.366 2.738

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Problem 41 For the matrix P = one of the eigen values is equal to -2. Which of the following is an eigen vector? b. c. d.

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Problem 42 If R = , then top row of R -1 is [5 6 4] [5 -3 1] [2 0 -1] [2 -1 1/2]

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Problem 43 A fair coin is tossed three times in succession. If the first toss poduces a head, then the probability of getting exactly two heads in three tosses is 1/8 1/2 3/8 3/4

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Problem 44 For the function f(x) = x 2 e -x , the maximum occurs when x is equal to 2 1 0 -1

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Problem 45 For the scalar field u = (x 2 /2) + (y 2 /3), magnitude of the gradient at the point (1, 3) is √(13/9) √(9/2) √5 9/2

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Problem 46 For the equation (t) +3 (t) + 2x(t) = 5, the solution x (t) approaches which of the following values as t → ∞? 0 5/2 5 10

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Problem 47 The Laplace transform of a function f(t) is F(s) = (5s 2 + 23s + 6)/(s(s 2 + 2s + 2)). As t → ∞, f(t) approaches ? 3 5 17/2 ∞

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Problem 48 The Fourier series for the function f(x) = sin 2 x is sin x + sin 2x 1 - cos 2x sin 2x + cos 2x 0.5 - 0.5 cos 2x

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Problem 49 If u(t) is the unit step and δ (t) is the unit impulse function, the inverse z-transform of F(z) = (1/(z + 1)) for k > 0 is (-1) k δ (k) δ (k) - (-1) k (-1) k u(k) u(k) - (-1) k

Problem:

Problem 50 Two magnetic poles revolve around a stationary armature carrying two coil (c 1 – c 1 ’ , c 2 – c 2 ’) as shown in the figure. Consider the instant when the poles are in a position as shown. Identify the correct statement regarding the polarity of the induced emf at this instant in coilsides c 1 and c 2 . in c 1 , no emf in c 2 in c 1 , no emf in c 2 in c 2 , no emf in c 1 in c 2 , no emf in c 1

Problem:

Problem 51 A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven ( i ) at half the rated speed by armature voltage control and (ii) at 1.5 times the rated speed by field control, the respective output powers delivered by the motor are approximately. 25 kW in ( i ) and 75 kW in (ii) 25 kW in ( i ) and 50 kW in (ii) 50 kW in ( i ) and 75 kW in (ii) 50 kW in ( i ) and 50 kW in (ii)

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Problem 52 In relation to DC machines, match the following and choose the correct combination P-3, Q-3, R-1 P-2, Q-5, R-4 P-3, Q-5, R-4 P-2, Q-3, R-1 Group - 1 Performance Variables Group – 2 Proportional to P Armature emf (E) 1 Flux ( Ф ), speed ( ω ) and armatrue current (la) Q Developed torque (T) 2 Ф and ω only R Developed power (P) 3 Ф and l a only 4 l a and ω only 5 l a only

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Problem 53 In relation to the synchronous machines, which one of the following statements is false? In salient pole machines, the direct-axis synchronous reactance is greater than the quadrature -axis synchronous reactance The damper bars help the synchronous motor self start Short circuit ratio is the ratio of the field current required to produce the rated voltage on open circuit to the rated armature current The V-curve of a synchronous motor represents the variation in the armature current with field excitation, at a given output power.

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Problem 54 Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value, the speed decreases and the stator current increases both the speed and the stator current decrease the speed and the stator current remain practically constant there is negligible change in the speed but the stator current decreases

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Problem 55 A three-phase cage induction motor is started by direct-on-line (DOL) switching at the rated voltage. If the starting current drawn is 6 times the full load current, and the full load slip is 4%, then ratio of the starting developed torque to the full load torque is approximately equal to 0.24 1.44 2.40 6.00

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Problem 56 In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve low starting torque uick acceleration high efficiency reduced size

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Problem 57 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r] Assertion : Under V/f control of induction motor, the maximum value of the developed torque remains constant over a wide range of speed in the sub- synchrbnous region. Reason : The magnetic flux is maintained almost constant at the rated value by keeping the ratio V/f constant over the considered speed range. Both (a) and (r) are true and (r) is the correct reason for (a) Both (a) and (r) are true but (r) is not the correct reason for (a) Both (a) and (r) are false (a) is true but (r) is false

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Problem 58 The parameters of a transposed overhead transmission line are given as : Self reactance x s = 0.4 Ω /km and Mutual reactance x m = 0.1 Ω /km The positive sequence reactance x 1 and zero sequence reactance x 0 , respectively, in Ω /km are 0.3, 0.2 0.5, 0.2 0.5, 0.6 0.3, 0.6

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Problem 59 At an industrial sub-station with a 4 MW load, a capacitor of 2 MVAR is installed to maintain the load power factor at 0.97 lagging. If the capacitor goes out of service, the load power factor becomes 0.85 1.00 0.80 lag 0.90 lag

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Problem 60 The network shown in the given figure has impedances in p.u . as indicated. The diagonal element Y 22 of the bus admittance matrix Y BUS of the network is -j 19.8 + j 20.0 +j 0.2 - j 19.95

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Problem 61 A load centre is at an equidistant from the two thermal generating stations G 1 and G 2 as shown in the figure. The fuel cost characteristics of the generating stations are given by F 1 = a + bP 1 + cP 1 2 Rs/hour F 1 = a + bP 2 + 2 cP 2 2 Rs/hour where P 1 and P 2 are the generation in MW of G 1 and G 2 , respectively. For most economic generation to meet 300 MW of load, P 1 and P 2 , respectively, are 150, 150 100, 200 200, 100 175, 125

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Problem 62 Two networks are connected in cascade as shown in the figure. With the usual notations the equivalent A, B, C and D constants are obtained. Given that, C = 0.025 45°, the value of Z 2 is 10 30 0 Ω 40 -45 0 Ω 1 Ω 0 Ω

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Problem 63 A generator with constant 1.0 p.u . terminal voltage supplies power through a step-up transformer of 0.12 p.u . reactance and a double-circuit line to an infinite bus bar as shown in the figure. The infinite bus voltage is maintained at 1.0 p.u . Neglecting the resistances and susceptances of the system, the steady state stability power limit of the system is 6.25 p.u . If one of the double-circuit is tripped, then resulting steady state stability power limit in p.u . will be 12.5 p.u . 3.125 p.u . 10.0 p.u . 5.0 p.u .

Problem:

Problem 64 The simultaneous application of signals x(t) and y(t) to the horizontal and vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-8 display. If P and Q are constants, and x(t) = P sin (4t + 30), then y(t) is equal to Q sin (4t - 30) Q sin (2t+ 15) Q sin (8t + 60) Q sin (4t + 30)

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Problem 65 A DC ammeter has a resistance of 0.1 Ω and its current range is 0-100A. If the range is to be extended to 0-500A, then meter requires the following shunt resistance 0.010 Ω 0.011 Ω 0.025 Ω 1.0 Ω

Problem:

Problem 66 The set-up in the figure is used to measure resistance R. The ammeter and voltmeter resistances are 0.01 Ω and 2000 Ω , respectively. Their readings are 2 A and 180 V, respectively, giving a measured resistance Ω 90. The percentage error in the measurement is 2.25 % 2.35 % 4.5 % 4.71 %

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Problem 67 A 1000 V DC supply has two 1-core cables as its positive and negative leads: their insulation resistances to earth are 4 M Ω and 6 M Ω , respectively, as shown in the figure. A voltmeter with resistance 50 Ω is used to measure the insulation of the cable. When connected between the positive core and earth, then voltmeter reads 8 V 16 V 24 V 40 V

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Problem 68 Two wattmeters , which are connected to measure the total power on a three - phase system supplying a balanced load, read 10.5 kW and - 2.5 kW, respectively. The total powere and the power factor, respectively, are 13.0 kW, 0.334 13.0 kW, 0.684 8.0 kW, 0.52 8.0 kW, 0.334

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Problem 69 The common emitter amplifier shown in the figure is biased using a 1 mA ideal current source. The approximate base current value is 0 μ A 10 μ A 100 μ A 1000 μ A

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Problem 70 Consider the inverting amplifier, using an ideal operational amplifier shown in the figure. The designer wishes to realize the input resistance seen by the small-signal source to be as large as possible, while keepiong the voltage gain between -10 and -25. The upper limit on R F is 1 M Ω . The value of R 1 should be Infinity 1 M Ω 100 k Ω 40 k Ω

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Problem 71 The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in a. b. c. d.

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Problem 72 In the given figure, if the input is a sinusoidal signal, the output will appear as shown in a. b. c. d.

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Problem 73 Select the circuit which will produce the given output Q for the input signals X 1 and X 2 given in the figure a. b. c. d.

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Problem 74 If X 1 and X 2 are the inputs to the circuit shown in the figure, the output Q is b. c. d.

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Problem 75 In the figure, as long as X 1 =1 and X 2 = 1, the output Q remains at 1 at 0 at its initial value unstable

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Problem 76 The figure shows the voltage across a power semiconductor device and the current through the device during a switching transitions. It the transition a turn ON transition or a turn OFF transition? What is the energy lost during the transition? Turn ON, VI/2 (t 1 + t 2 ) Turn OFF, VI (t 1 + t 2 ) Turn ON, VI (t 1 + t 2 ) Turn OFF, VI/2 (t 1 + t 2 )

Problem:

Problem 77 An electronic switch S is required to block voltages of either polarity during its OFF state as shown in the fig. (a). This switch is required to conduct in only one direction during its ON state as shown in the figure (b) Which of the following are valid realizations of the switch S? Only P P and Q P and R R and S

Problem:

Problem 78 The given figure shows a step-down chopper switched at 1kHz with a duty ratio D = 0.5. The peak-peak ripple in the load current is close to 10 A 0.5 A 0.125 A 0.25 A

Problem:

Problem 79 An electric motor, developing a starting torque of 15 Nm, starts with a load torque of 7Nm on its shaft. If the acceleration at start is 2 rad /sec 2 , the moment of inertia of the systems must be (neglecting viscous and Coulomb friction) 0.25 kg m 2 0.25 Nm 2 4 kg m 2 4 Nm 2

Problem:

Problem 80 Consider a phase-controlled converter shown in the figure. The thyristor is fired at an angle a in every postive half cycle of the input voltage. If the peak value of the instantaneous output voltage equals 230 V, the firing angle α is close to 45° 135° 90° 83.6°

Problem:

Problem 81a If, at t = 0 + , the voltage across the coil is 120 V, the value of resistance R is 0 Ω 20 Ω 40 Ω 60 Ω

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Problem 81b For the value of obtained in (a), the time taken for 95% of the stored energy to be dissipated is close to 0.10 sec 0.15 sec 0.50 sec 1.0 sec

Problem:

Problem 82a The state transition matrix a. b. c. d.

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Problem 82b The state transition equation a. X(t) = b. X(t) = c. X(t) = d. X(t) =

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Problem 83a The induced emf (line-to-line) is close to 5.5 kV 7.2 kV 9.6 kV 12.5 kV

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Problem 83b The power (or torque) angle is close to 13.9° 18.3° 24.6° 33.0°

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Problem 84a the positive sequence driving point reactance at the bus is 2.5 Ω 4.033 Ω 5.5 Ω 12.1 Ω

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Problem 84b and the zero sequence driving point reactance at the bus is 2.2 Ω 4.84 Ω 18.18 Ω 22.72 Ω

Problem:

Problem 85a The transconductance of the MOSFET is 0.75 ms 1 ms 2 ms 10 ms

Problem:

Problem 85b The voltage gain of the amplifier is +5 -7.5 +10 -10

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