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GATE 2015 : Electrical Engineering (Set 2)

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GATE 2015 SET2 ELECTRICAL EE Q. 1 Q. 25 carry one mark each. Q.1 Given ( ) = ( ) + ( ), where , , are complex valued functions of a complex variable . Which one of the following statements is TRUE? (A) If (B) If (C) If (D) If Q.2 ( ) is differentiable at 0 , then ( ) and ( ) are also differentiable at 0 . ( ) and ( ) are differentiable at 0 , then ( ) is also differentiable at 0 . ( ) is continuous at 0 , then it is differentiable at 0 . ( ) is differentiable at 0 , then so are its real and imaginary parts. We have a set of 3 linear equations in 3 unknowns. means and are equivalent statements and means and are not equivalent statements. P: There is a unique solution. Q: The equations are linearly independent. R: All eigenvalues of the coefficient matrix are nonzero. S: The determinant of the coefficient matrix is nonzero. Which one of the following is TRUE? Q.3 (A) (C) (B) (D) Match the following. P. Stokes s Theorem Q. Gauss s Theorem R. Divergence Theorem S. Cauchy s Integral Theorem (A) P-2 Q-1 R-4 S-3 Q.4 Q.5 (B) P-4 Q-1 R-3 S-2 1. . = 2. ( ) = 0 3. ( . ) = . 4. ( ). = . (C) P-4 Q-3 R-1 S-2 The Laplace transform of ( ) = 2 is 3 2 . The Laplace transform of ( ) = 1 is (A) 3 5 2 2 Match the following. (B) 1 2 (C) 1 2 Instrument Type P. Permanent magnet moving coil Q. Moving iron connected through current transformer R. Rectifier S. Electrodynamometer (A) P-1 Q-2 R-1 S-3 EE (D) P-3 Q-4 R-2 S-1 (B) P-1 Q-3 R-1 S-2 (C) P-1 Q-2 R-3 S-3 (D) 3 2 Used for 1. DC Only 2. AC Only 3. AC and DC (D) P-3 Q-1 R-2 S-1 1/15 GATE 2015 Q.6 Q.7 SET2 ELECTRICAL EE A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The readings of the two wattmeters are (A) 3.94 kW and 1.06 kW (C) 5.00 kW and 0.00 kW (B) 2.50 kW and 2.50 kW (D) 2.96 kW and 2.04 kW A capacitive voltage divider is used to measure the bus voltage in a high-voltage 50 Hz AC system as shown in the figure. The measurement capacitors 1 and 2 have tolerances of 10% on their nominal capacitance values. If the bus voltage is 100 kV rms, the maximum rms output voltage (in kV), considering the capacitor tolerances, is __________. C1 1 F 10% C2 9 F 10% v bus Q.8 v out In the following circuit, the input voltage Vin is 100 sin(100 ). For 100 = 50, the average voltage across (in Volts) under steady-state is nearest to Vin C C (A) 100 Q.9 (B) 31.8 (D) 63.6 Two semi-infinite dielectric regions are separated by a plane boundary at = 0. The dielectric constants of region 1 ( < 0) and region 2 ( > 0) are 2 and 5, respectively. Region 1 has uniform = 3 + 4 + 2 , where , , and are unit vectors along the , and electric field axes, respectively. The electric field in region 2 is (A) 3 + 1.6 + 2 (C) 1.2 + 4 + 0.8 EE (C) 200 R (B) 1.2 + 4 + 2 (D) 3 + 10 + 0.8 2/15 GATE 2015 Q.10 SET2 ELECTRICAL EE A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown = in the figure. The value of 0 is 4 10 7 in SI unit. If a uniform magnetic field intensity 7 10 A/m is applied, then the peak value of the induced voltage, Vturn ( in Volts), is _________. Z H Vturn Q.11 X The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is = 2 sin(2 2000t). The amplitude of the output voltage (in Volt) is _______. 0.1 F Vi 1 k - 1 k Vo + Q.12 In the following circuit, the transistor is in active mode and = 2 V. To get = 4 V, we replace with . Then the ratio / is ______. +10 V RC RB Q.13 VC Consider the following Sum of Products expression, F. + + = + + The equivalent Product of Sums expression is (A) (B) (C) (D) EE = ( + + )( + + ) ( + = ( + + )( + + )( + = ( + + )( + + ) ( + = ( + + )( + + ) ( + + + + + ) ) ) ) 3/15 GATE 2015 Q.14 SET2 ELECTRICAL EE The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown in Figure (c). F1 vo/vi vo/vi vi vo F2 vi vo f1 f2 f f (a) (b) R/2 +Vsat R - R + F1 vi F2 vo -Vsat (c) The cut-off frequencies of F1 and F2 are f1 and f2 respectively. If f1 < f2 , the resultant circuit exhibits the characteristic of a (A) Band-pass filter (C) All pass filter Q.15 (B) Band-stop filter (D) High-Q filter When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions? (A) The CB junction is forward biased and the BE junction is reverse biased. (B) The CB junction is reverse biased and the BE junction is forward biased. (C) Both the CB and BE junctions are forward biased. (D) Both the CB and BE junctions are reverse biased. EE 4/15 GATE 2015 Q.16 SET2 ELECTRICAL EE The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time 1 by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle shows the transient correctly? Synchronous generator Line 1 Xs Infinite Bus 10 Line 2 (A) (B) =0 =0 time time t1 (C) (D) =0 EE t1 t1 time =0 t1 time 5/15 GATE 2015 Q.17 SET2 ELECTRICAL EE A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is 6 3 4 3 7 5 pu. 4 5 8 If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3rd row 3rd column element (in pu) of the bus admittance matrix after compensation is Q.18 (A) 7.0 (B) 8.5 (C) 7.5 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero initial conditions, the value of 2 2 at t = 0+ is R L V (A) Q.19 (D) 9.0 (B) (C) 0 (D) The current i (in Ampere) in the 2 resistor of the given network is ______. 2 1 i 5V 1 1 2 1 Q.20 Find the transformer ratios and such that the impedance ( ) is resistive and equals 2.5 when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s. L=1 mH C=10 uF Zin R=2.5 1:b Q.21 EE (A) = 0.5, = 2.0 (C) = 1.0, = 1.0 1:a (B) = 2.0, = 0.5 (D) = 4.0, = 0.5 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200 radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to directly drive a load whose load torque TL depends on its rotational speed (in radian/second), such that = 2.78 . Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is _______. 6/15 GATE 2015 Q.22 SET2 ELECTRICAL EE The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 50 Hz. The air-gap voltage, across the magnetizing inductance, is 210 V rms, and the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________. 0.04 j0.22 j6.28 Vs Q.23 j0.22 0.05 s Vg A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the reconnected machine if the field circuit is left unchanged ? (A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5 Q.24 An open loop control system results in a response of 2 (sin 5 + cos 5 ) for a unit impulse input. The DC gain of the control system is ______. Q.25 Nyquist plots of two functions G1(s) and G2(s) are shown in figure. Im Im = G1(s) G2(s) Re = 0 Re 0 Nyquist plot of the product of G1(s) and G2(s) is (A) (B) Im Im = 0 1 Re (C) Re (D) Im Im Re Re 0 EE 7/15 GATE 2015 SET2 ELECTRICAL EE Q. 26 Q. 55 carry two mark each. Q.26 Q.27 The volume enclosed by the surface ( , ) = over the triangle bounded by the lines = ; = 0; = 1 in the plane is ______. Two coins R and S are tossed. The 4 joint events , , , have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where represents head and represents tail. Which one of the following is TRUE? (A) The coin tosses are independent. (B) R is fair, S is not. (C) S is fair, R is not. (D) The coin tosses are dependent. Q.28 A differential equation _____. Q.29 Consider a signal defined by Its Fourier Transform is (A) (C) Q.30 2 sin ( 10) 10 2 sin 10 0.2 = 0 is applicable over 10 < < 10. If (4) = 10, then ( 5) is 10 for |t| 1 ( ) = 0 for |t| > 1 (B) 2 10 (D) 10 sin ( 10) 10 2 sin The coils of a wattmeter have resistances 0.01 and 1000 ; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The percentage error on the wattmeter reading is _________. Load EE 8/15 GATE 2015 Q.31 SET2 ELECTRICAL EE A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage is 36 V. Assume that all the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that will make the inductor current (iL) just continuous is _______. S iL 60 V + Q.32 36 V Vo L Vin Vo R S 15 V R C VL t Ts -45 V In the given rectifier, the delay angle of the thyristor T1 measured from the positive going zero crossing of Vs is 30o. If the input voltage Vs is 100 sin(100 ) V, the average voltage across R (in Volt) under steady-state is _______. T1 D4 Q.34 + For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is Ts. If the voltage VL is as shown, the duty cycle of the switch S is ______. VL Q.33 5 mH Vs + D3 R Vo D2 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE? (A) The impulse response will be integrable, but may not be absolutely integrable. (B) The unit impulse response will have finite support. (C) The unit step response will be absolutely integrable. (D) The unit step response will be bounded. Q.35 EE The -Transform of a sequence [ ] is given as ( ) = 2 + 4 4/ + 3/ 2 . If [ ] is the first difference of [ ], then ( ) is given by (A) 2 + 2 8/ + 7/ 2 3/ 3 (B) 2 + 2 6/ + 1/ 2 3/ 3 (C) 2 2 + 8/ 7/ 2 + 3/ 3 (D) 4 2 8/ 1/ 2 + 3/ 3 9/15 GATE 2015 Q.36 SET2 ELECTRICAL EE Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of + is placed at a distance of from both sheets. The net force on the charge is 2 , 4 0 2 where is given by y +Q d d x Q.37 (A) 0 (B) 1 4 1 4 1 (C) 8 1 8 (D) 1 2 2 8 2 + 1 2 2 8 2 In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is 1 = 00. The state ( 1 ), immediately after the 333rd clock pulse is Q1 Q0 J0 Q0 J1 Q1 K0 Q0 K1 Q1 CLK (A) 00 Q.38 (B) 01 (C) 10 (D) 11 A Boolean function ( , , , ) = (1,5,12,15) is to be implemented using an 8 1 multiplexer (A is MSB). The inputs ABC are connected to the select inputs S2 S1 S0 of the multiplexer respectively. Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order? (A) , 0, , 0, 0, 0, , (B) , 1, , 1, 1, 1, , (C) , 1, , 1, 1, 1, , (D) , 0, , 0, 0, 0, , EE 10/15 GATE 2015 Q.39 SET2 ELECTRICAL EE The saturation voltage of the ideal op-amp shown below is 10 V. The output voltage 0 of the following circuit in the steady-state is 1 k + 10 V 0.25 F + - 10 V v0 2 k 2 k (A) square wave of period 0.55 ms. (C) square wave of period 0.25 ms. Q.40 (B) triangular wave of period 0.55 ms. (D) triangular wave of period 0.25 ms. The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers 1 and 2 in MW, and are given by where 1 = 0.2 1 + 50 1 2 = 0.24 2 + 40 2 20 MW 1 150 MW 20 MW 2 150 MW. Q.41 For a certain load demand, 1 and 2 have been chosen such that 1 1 = 76 Rs/MWh and 2 2 = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then 2 is ________. A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is . The value of is ______. 3R R 60 60 EE 11/15 GATE 2015 Q.42 SET2 ELECTRICAL EE A 3-phase transformer rated for 33 kV/11 kV is connected in delta/star as shown in figure. The current transformers (CTs) on low and high voltage sides have a ratio of 500/5. Find the currents 1 and 2 , if the fault current is 300 A as shown in figure. a b c 300 A i2 i1 Q.43 (B) 1 = 0 , 2 = 0 (D) 1 = 1/ 3 , 2 = 1/ 3 (A) 1 = 1/ 3 , 2 = 0 (C) 1 = 0 , 2 = 1/ 3 A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. The line-to-line voltage rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected and = 100 0 A, then what is the value of in Ampere? Ip Is a A R B R b R C c Q.44 (A) 50 30 (B) 50 30 (C) 50 3 30 (D) 200 30 In the given network 1 = 100 0 V, 2 = 100 120 V, 3 = 100 + 120 V. The phasor current (in Ampere) is V1 -j1 V2 j1 V3 (A) 173.2 60 EE (B) 173.2 120 i (C) 100.0 60 (D) 100.0 120 12/15 GATE 2015 Q.45 SET2 ELECTRICAL EE A symmetrical square wave of 50% duty cycle has amplitude of 15 V and time period of 0.4 ms. This square wave is applied across a series RLC circuit with = 5 , = 10 mH, and = 4 F. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is ______. L C R Q.46 Q.47 Two identical coils each having inductance L are placed together on the same core. If an overall inductance of is obtained by interconnecting these two coils, the minimum value of is ____. A three-winding transformer is connected to an AC voltage source as shown in the figure. The number of turns are as follows: 1 = 100, 2 = 50, 3 = 50. If the magnetizing current is neglected, and the currents in two windings are 2 = 2 30 A and 3 = 2 150 A, then what is the value of the current 1 in Ampere? N2 I1 I2 I3 N1 (A) 1 90 (B) 1 270 N3 (C) 4 90 (D) 4 270 Q.48 With an armature voltage of 100 V and rated field winding voltage, the speed of a separately excited DC motor driving a fan is 1000 rpm, and its armature current is 10 A. The armature resistance is 1 . The load torque of the fan load is proportional to the square of the rotor speed. Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to 500 rpm is ______. Q.49 A three-phase, 11 kV, 50 Hz, 2 pole, star connected, cylindrical rotor synchronous motor is connected to an 11 kV, 50 Hz source. Its synchronous reactance is 50 per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is 100 A at unity power factor. If the load torque is increased so that the stator current is 120 A, then the load angle (in degrees) at this load is ________. Q.50 A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is 225 % of full load torque and it occurs at 15% slip. The actual rotor resistance is 0.03 /phase. The value of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is ______. EE 13/15 GATE 2015 Q.51 SET2 ELECTRICAL EE Two three-phase transformers are realized using single-phase transformers as shown in the figure. A2 a1 A1 B2 B1 C1 C2 b1 C1 B2 a1 B1 A2 c1 A1 C2 b1 c1 a2 b2 V1 c2 a2 b2 V2 c2 The phase difference (in degree) between voltages V1 and V2 is _______. Q.52 The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables and . The integration time step is h. +1 = +1 = For this discrete-time system, which one of the following statements is TRUE? (A) The system is not stable for > 0 1 (B) The system is stable for > 1 2 1 < (C) The system is stable for 0 < < (D) The system is stable for EE 1 2 < 14/15 GATE 2015 Q.53 SET2 ELECTRICAL EE The unit step response of a system with the transfer function ( ) = the following waveforms? (A) 1 2 1+ is given by which one of (B) y y 1 2 0 5 t 1 0 (C) t 5 -2 (D) y y 2 1 1 0 0 5 5 t t -0.75 -2 Q.54 An open loop transfer function G(s) of a system is ( ) = ( + 1)( + 2) For a unity feedback system, the breakaway point of the root loci on the real axis occurs at, (B) 1.58 (D) none of the above (A) 3(s+1)/( 2 2s + 2) (C) (s+1)/( 2 2s + 1) Q.55 (A) 0.42 (C) 0.42 and 1.58 (B) 3(2s+1)/( 2 2s + 1) (D) 3(2s+1)/( 2 2s + 2) For the system governed by the set of equations: 1 / dt = 2 1 + 2 + u 2 / dt = 2 1 + u y = 3 1 the transfer function Y(s)/U(s) is given by END OF THE QUESTION PAPER EE 15/15

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