Page 1 GATE EE - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 In a series RLC circuit at resonance, the magnitude of the voltage developed across the capacitor (a) is always zero (b) can never be greater than the input voltage (c) can be greater than the input voltage, however, it is 90° out of phase with the input voltage (d) can be greater than the input voltage, and is in phase with the input voltage. 1.2 Two incandescent light bulbs of 40 W and 60 W rating are connected in series across the mains. Then (a) the bulbs together consume 100 W (b) the bulbs together consume 50W (c) the 60 W bulb glows brighter (d) the 40 W bulb glows brighter 1.3 A unit step voltage is applied at t = 0 to a series RL circuit with zero initial conditions. (a) It is possible for the current to be oscillatory. (b) The voltage across the resistor at t = 0 + is zero. (c) The energy stored in the inductor in the steady state is zero. (d) The resistor current eventually falls to zero. 1.4 Given two coupled inductors L 1 and L 2 , their mutual inductance M satisfies (a) 2 2 1 2 M L L = + (b) ( ) 1 2 2 L L M + > (c) M > 1 2 L L (d) 1 2 M L L = 1.5 A passive 2-port network is in a steady-state. Compared to its input, the steady state output can never offer (a) higher voltage (b) lower impedance (c) greater power (d) better regulation Page 2 GATE EE - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 In a series RLC circuit at resonance, the magnitude of the voltage developed across the capacitor (a) is always zero (b) can never be greater than the input voltage (c) can be greater than the input voltage, however, it is 90° out of phase with the input voltage (d) can be greater than the input voltage, and is in phase with the input voltage. 1.2 Two incandescent light bulbs of 40 W and 60 W rating are connected in series across the mains. Then (a) the bulbs together consume 100 W (b) the bulbs together consume 50W (c) the 60 W bulb glows brighter (d) the 40 W bulb glows brighter 1.3 A unit step voltage is applied at t = 0 to a series RL circuit with zero initial conditions. (a) It is possible for the current to be oscillatory. (b) The voltage across the resistor at t = 0 + is zero. (c) The energy stored in the inductor in the steady state is zero. (d) The resistor current eventually falls to zero. 1.4 Given two coupled inductors L 1 and L 2 , their mutual inductance M satisfies (a) 2 2 1 2 M L L = + (b) ( ) 1 2 2 L L M + > (c) M > 1 2 L L (d) 1 2 M L L = 1.5 A passive 2-port network is in a steady-state. Compared to its input, the steady state output can never offer (a) higher voltage (b) lower impedance (c) greater power (d) better regulation GATE EE - 2001 1.6 A single-phase transformer is to be switched to the supply to have minimum inrush current. The switch should be closed at (a) maximum supply voltage (b) zero supply voltage (c) 1 2 maximum supply voltage (d) 1 2 maximum supply voltage 1.7 It is desirable to eliminate 5 th harmonic voltage from the phase voltage of an alternator. The coils should be short-pitched by an electrical angle of (a) 30° (b) 36° (c) 72° (d) 18° 1.8 Fig.P1.8 shows the magnetization curves of an alternator at rated armature current, unity power factor and also at no load. The magnetization curve for rated armature current, 0.8 power factor leading is given by (a) curve A (b) curve B (c) curve C (d) curve D 1.9 The core flux of a practical transformer with a resistive load (a) is strictly constant with load changes (b) increases linearly with load (c) increases as the square root of the load (d) decreases with increased load 1.10 , and d d d X X X ' '' are steady state d-axis synchronous reactance, transient d-axis reactance and sub-transient d-axis reactance of a synchronous machine respectively. Which of the following statements is true? (a) > d d d X X X ' '' > (b) > d d d X X X '' ' > (c) d d d X X X ' '' > > (d) d d d X X X '' ' > > 1.11 A 50 Hz balanced three-phase, Y-connected supply is connected to a balanced three phase Y-connected load. If the instantaneous phase-a of the supply voltage is Vcos(?t) and the phase-a of the load current is Icos(?t-f), the instantaneous three-phase power is (a) a constant with a magnitude of VIcosf A B C D No load Rated armature current unit pf Exciting current Page 3 GATE EE - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 In a series RLC circuit at resonance, the magnitude of the voltage developed across the capacitor (a) is always zero (b) can never be greater than the input voltage (c) can be greater than the input voltage, however, it is 90° out of phase with the input voltage (d) can be greater than the input voltage, and is in phase with the input voltage. 1.2 Two incandescent light bulbs of 40 W and 60 W rating are connected in series across the mains. Then (a) the bulbs together consume 100 W (b) the bulbs together consume 50W (c) the 60 W bulb glows brighter (d) the 40 W bulb glows brighter 1.3 A unit step voltage is applied at t = 0 to a series RL circuit with zero initial conditions. (a) It is possible for the current to be oscillatory. (b) The voltage across the resistor at t = 0 + is zero. (c) The energy stored in the inductor in the steady state is zero. (d) The resistor current eventually falls to zero. 1.4 Given two coupled inductors L 1 and L 2 , their mutual inductance M satisfies (a) 2 2 1 2 M L L = + (b) ( ) 1 2 2 L L M + > (c) M > 1 2 L L (d) 1 2 M L L = 1.5 A passive 2-port network is in a steady-state. Compared to its input, the steady state output can never offer (a) higher voltage (b) lower impedance (c) greater power (d) better regulation GATE EE - 2001 1.6 A single-phase transformer is to be switched to the supply to have minimum inrush current. The switch should be closed at (a) maximum supply voltage (b) zero supply voltage (c) 1 2 maximum supply voltage (d) 1 2 maximum supply voltage 1.7 It is desirable to eliminate 5 th harmonic voltage from the phase voltage of an alternator. The coils should be short-pitched by an electrical angle of (a) 30° (b) 36° (c) 72° (d) 18° 1.8 Fig.P1.8 shows the magnetization curves of an alternator at rated armature current, unity power factor and also at no load. The magnetization curve for rated armature current, 0.8 power factor leading is given by (a) curve A (b) curve B (c) curve C (d) curve D 1.9 The core flux of a practical transformer with a resistive load (a) is strictly constant with load changes (b) increases linearly with load (c) increases as the square root of the load (d) decreases with increased load 1.10 , and d d d X X X ' '' are steady state d-axis synchronous reactance, transient d-axis reactance and sub-transient d-axis reactance of a synchronous machine respectively. Which of the following statements is true? (a) > d d d X X X ' '' > (b) > d d d X X X '' ' > (c) d d d X X X ' '' > > (d) d d d X X X '' ' > > 1.11 A 50 Hz balanced three-phase, Y-connected supply is connected to a balanced three phase Y-connected load. If the instantaneous phase-a of the supply voltage is Vcos(?t) and the phase-a of the load current is Icos(?t-f), the instantaneous three-phase power is (a) a constant with a magnitude of VIcosf A B C D No load Rated armature current unit pf Exciting current GATE EE - 2001 (b) a constant with a magnitude of (3/2)VIcosf (c) time-varying with an average value of (3/2) VIcosf and a frequency of 100 Hz. (d) time-varying with an average value of VIcosf and a frequency of 50 Hz. 1.12 In the protection of transformers, harmonic restraint is used to guard aainst (a) magnetizing inrush current (b) unbalanced operation (c) lightning (d) switching over-voltages 1.13 A lossless radial transmission line with surge impedance loading (a) takes negative VAR at sending end and zero VAR at receiving end (b) takes positive VAR at sending end and zero VAR at receiving end (c) has flat voltage profile and unity power factor at all points along it (d) has sending end voltage higher than receiving end voltage and unity power factor at sending end 1.14 The polar plot of a type-1, 3-pole, open-loop system is shown in Fig.P1.14. the closed loop system is (a) always stable (b) marginally stable (c) unstable with one pole on the right half s-plane (d) unstable with two poles on the right half s-plane 1.15 Given the homogeneous state-space equaion 3 1 0 2 x x - ? ? = ? ? - ? ? & the steady state value ( ) lim , ss t x x t ?8 = given the initial state value of x(0) = [10 – 10] T , is (a) 0 0 ss x ? ? = ? ? ? ? (b) 3 2 ss x - ? ? = ? ? - ? ? (c) 10 10 ss x - ? ? = ? ? ? ? (d) ss x 8 ? ? = ? ? 8 ? ? GH - plane -1.42 0 o w=8 w=0 Page 4 GATE EE - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 In a series RLC circuit at resonance, the magnitude of the voltage developed across the capacitor (a) is always zero (b) can never be greater than the input voltage (c) can be greater than the input voltage, however, it is 90° out of phase with the input voltage (d) can be greater than the input voltage, and is in phase with the input voltage. 1.2 Two incandescent light bulbs of 40 W and 60 W rating are connected in series across the mains. Then (a) the bulbs together consume 100 W (b) the bulbs together consume 50W (c) the 60 W bulb glows brighter (d) the 40 W bulb glows brighter 1.3 A unit step voltage is applied at t = 0 to a series RL circuit with zero initial conditions. (a) It is possible for the current to be oscillatory. (b) The voltage across the resistor at t = 0 + is zero. (c) The energy stored in the inductor in the steady state is zero. (d) The resistor current eventually falls to zero. 1.4 Given two coupled inductors L 1 and L 2 , their mutual inductance M satisfies (a) 2 2 1 2 M L L = + (b) ( ) 1 2 2 L L M + > (c) M > 1 2 L L (d) 1 2 M L L = 1.5 A passive 2-port network is in a steady-state. Compared to its input, the steady state output can never offer (a) higher voltage (b) lower impedance (c) greater power (d) better regulation GATE EE - 2001 1.6 A single-phase transformer is to be switched to the supply to have minimum inrush current. The switch should be closed at (a) maximum supply voltage (b) zero supply voltage (c) 1 2 maximum supply voltage (d) 1 2 maximum supply voltage 1.7 It is desirable to eliminate 5 th harmonic voltage from the phase voltage of an alternator. The coils should be short-pitched by an electrical angle of (a) 30° (b) 36° (c) 72° (d) 18° 1.8 Fig.P1.8 shows the magnetization curves of an alternator at rated armature current, unity power factor and also at no load. The magnetization curve for rated armature current, 0.8 power factor leading is given by (a) curve A (b) curve B (c) curve C (d) curve D 1.9 The core flux of a practical transformer with a resistive load (a) is strictly constant with load changes (b) increases linearly with load (c) increases as the square root of the load (d) decreases with increased load 1.10 , and d d d X X X ' '' are steady state d-axis synchronous reactance, transient d-axis reactance and sub-transient d-axis reactance of a synchronous machine respectively. Which of the following statements is true? (a) > d d d X X X ' '' > (b) > d d d X X X '' ' > (c) d d d X X X ' '' > > (d) d d d X X X '' ' > > 1.11 A 50 Hz balanced three-phase, Y-connected supply is connected to a balanced three phase Y-connected load. If the instantaneous phase-a of the supply voltage is Vcos(?t) and the phase-a of the load current is Icos(?t-f), the instantaneous three-phase power is (a) a constant with a magnitude of VIcosf A B C D No load Rated armature current unit pf Exciting current GATE EE - 2001 (b) a constant with a magnitude of (3/2)VIcosf (c) time-varying with an average value of (3/2) VIcosf and a frequency of 100 Hz. (d) time-varying with an average value of VIcosf and a frequency of 50 Hz. 1.12 In the protection of transformers, harmonic restraint is used to guard aainst (a) magnetizing inrush current (b) unbalanced operation (c) lightning (d) switching over-voltages 1.13 A lossless radial transmission line with surge impedance loading (a) takes negative VAR at sending end and zero VAR at receiving end (b) takes positive VAR at sending end and zero VAR at receiving end (c) has flat voltage profile and unity power factor at all points along it (d) has sending end voltage higher than receiving end voltage and unity power factor at sending end 1.14 The polar plot of a type-1, 3-pole, open-loop system is shown in Fig.P1.14. the closed loop system is (a) always stable (b) marginally stable (c) unstable with one pole on the right half s-plane (d) unstable with two poles on the right half s-plane 1.15 Given the homogeneous state-space equaion 3 1 0 2 x x - ? ? = ? ? - ? ? & the steady state value ( ) lim , ss t x x t ?8 = given the initial state value of x(0) = [10 – 10] T , is (a) 0 0 ss x ? ? = ? ? ? ? (b) 3 2 ss x - ? ? = ? ? - ? ? (c) 10 10 ss x - ? ? = ? ? ? ? (d) ss x 8 ? ? = ? ? 8 ? ? GH - plane -1.42 0 o w=8 w=0 GATE EE - 2001 1.16 If an energy meter disc makes 10 revolutions in 100 seconds when a load of 450 W is connected to it, the meter constant (in rev/kWh) is (a) 1000 (b) 500 (c) 1600 (d) 800 1.17 The minimum number of wattmeter (s) required to measure 3-phase, 3-wire balanced or unbalanced power is (a) 1 (b) 2 (c) 3 (d) 4 1.18 In the single-stage transistor amplifier circuit shown in Fig.P1.18, the capacitor C E is removed. Then, the ac small-signal midband voltage gain of the amplifier (a) increases (b) decreases (c) is unaffected (d) drops to zero 1.19. Among the following four, the slowest ADC (analog-to-digital converter) is (a) parallel comparator (i.e., flash) type (b) successive approximation type (c) integrating type (d) counting type 1.20. The output of a logic gate is “1” when all its inputs are at logic “0”. The gate is either (a) a NAND or an EX-OR gate (b) a NOR or an EX-OR gate (c) an AND or an EX-NOR gate (d) a NOR or an EX-NOR gate 1.21. The output f of the 4-to-1 MUX shown in Fig.P1.21 is (a) xy x + (b) x+y (c) x y + (d) xy+x C E +12V Input Output + - + V CC 2 1 0 S 1 S 0 X Y MUX Page 5 GATE EE - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 In a series RLC circuit at resonance, the magnitude of the voltage developed across the capacitor (a) is always zero (b) can never be greater than the input voltage (c) can be greater than the input voltage, however, it is 90° out of phase with the input voltage (d) can be greater than the input voltage, and is in phase with the input voltage. 1.2 Two incandescent light bulbs of 40 W and 60 W rating are connected in series across the mains. Then (a) the bulbs together consume 100 W (b) the bulbs together consume 50W (c) the 60 W bulb glows brighter (d) the 40 W bulb glows brighter 1.3 A unit step voltage is applied at t = 0 to a series RL circuit with zero initial conditions. (a) It is possible for the current to be oscillatory. (b) The voltage across the resistor at t = 0 + is zero. (c) The energy stored in the inductor in the steady state is zero. (d) The resistor current eventually falls to zero. 1.4 Given two coupled inductors L 1 and L 2 , their mutual inductance M satisfies (a) 2 2 1 2 M L L = + (b) ( ) 1 2 2 L L M + > (c) M > 1 2 L L (d) 1 2 M L L = 1.5 A passive 2-port network is in a steady-state. Compared to its input, the steady state output can never offer (a) higher voltage (b) lower impedance (c) greater power (d) better regulation GATE EE - 2001 1.6 A single-phase transformer is to be switched to the supply to have minimum inrush current. The switch should be closed at (a) maximum supply voltage (b) zero supply voltage (c) 1 2 maximum supply voltage (d) 1 2 maximum supply voltage 1.7 It is desirable to eliminate 5 th harmonic voltage from the phase voltage of an alternator. The coils should be short-pitched by an electrical angle of (a) 30° (b) 36° (c) 72° (d) 18° 1.8 Fig.P1.8 shows the magnetization curves of an alternator at rated armature current, unity power factor and also at no load. The magnetization curve for rated armature current, 0.8 power factor leading is given by (a) curve A (b) curve B (c) curve C (d) curve D 1.9 The core flux of a practical transformer with a resistive load (a) is strictly constant with load changes (b) increases linearly with load (c) increases as the square root of the load (d) decreases with increased load 1.10 , and d d d X X X ' '' are steady state d-axis synchronous reactance, transient d-axis reactance and sub-transient d-axis reactance of a synchronous machine respectively. Which of the following statements is true? (a) > d d d X X X ' '' > (b) > d d d X X X '' ' > (c) d d d X X X ' '' > > (d) d d d X X X '' ' > > 1.11 A 50 Hz balanced three-phase, Y-connected supply is connected to a balanced three phase Y-connected load. If the instantaneous phase-a of the supply voltage is Vcos(?t) and the phase-a of the load current is Icos(?t-f), the instantaneous three-phase power is (a) a constant with a magnitude of VIcosf A B C D No load Rated armature current unit pf Exciting current GATE EE - 2001 (b) a constant with a magnitude of (3/2)VIcosf (c) time-varying with an average value of (3/2) VIcosf and a frequency of 100 Hz. (d) time-varying with an average value of VIcosf and a frequency of 50 Hz. 1.12 In the protection of transformers, harmonic restraint is used to guard aainst (a) magnetizing inrush current (b) unbalanced operation (c) lightning (d) switching over-voltages 1.13 A lossless radial transmission line with surge impedance loading (a) takes negative VAR at sending end and zero VAR at receiving end (b) takes positive VAR at sending end and zero VAR at receiving end (c) has flat voltage profile and unity power factor at all points along it (d) has sending end voltage higher than receiving end voltage and unity power factor at sending end 1.14 The polar plot of a type-1, 3-pole, open-loop system is shown in Fig.P1.14. the closed loop system is (a) always stable (b) marginally stable (c) unstable with one pole on the right half s-plane (d) unstable with two poles on the right half s-plane 1.15 Given the homogeneous state-space equaion 3 1 0 2 x x - ? ? = ? ? - ? ? & the steady state value ( ) lim , ss t x x t ?8 = given the initial state value of x(0) = [10 – 10] T , is (a) 0 0 ss x ? ? = ? ? ? ? (b) 3 2 ss x - ? ? = ? ? - ? ? (c) 10 10 ss x - ? ? = ? ? ? ? (d) ss x 8 ? ? = ? ? 8 ? ? GH - plane -1.42 0 o w=8 w=0 GATE EE - 2001 1.16 If an energy meter disc makes 10 revolutions in 100 seconds when a load of 450 W is connected to it, the meter constant (in rev/kWh) is (a) 1000 (b) 500 (c) 1600 (d) 800 1.17 The minimum number of wattmeter (s) required to measure 3-phase, 3-wire balanced or unbalanced power is (a) 1 (b) 2 (c) 3 (d) 4 1.18 In the single-stage transistor amplifier circuit shown in Fig.P1.18, the capacitor C E is removed. Then, the ac small-signal midband voltage gain of the amplifier (a) increases (b) decreases (c) is unaffected (d) drops to zero 1.19. Among the following four, the slowest ADC (analog-to-digital converter) is (a) parallel comparator (i.e., flash) type (b) successive approximation type (c) integrating type (d) counting type 1.20. The output of a logic gate is “1” when all its inputs are at logic “0”. The gate is either (a) a NAND or an EX-OR gate (b) a NOR or an EX-OR gate (c) an AND or an EX-NOR gate (d) a NOR or an EX-NOR gate 1.21. The output f of the 4-to-1 MUX shown in Fig.P1.21 is (a) xy x + (b) x+y (c) x y + (d) xy+x C E +12V Input Output + - + V CC 2 1 0 S 1 S 0 X Y MUX GATE EE - 2001 1.22. An op-amp has an open-loop gain of 10 5 and an open-loop upper cutoff frequency of 10 Hz. If this op-amp is connected as an amplifier with a closed-loop gain of 100, then the new upper cutoff frequency is (a) 10 Hz (b) 100 Hz (c) 10 kHz (d) 100 kHz 1.23. The main reason for connecting a pulse transformer at the output stage of a thyristor triggering circuit is to (a) amplifying the power of the triggering pulse (b) provide electrical isolation (c) reduce the turn on time of the thyristor (d) avoid spurious triggering of the thyristor due to noise 1.24. AC-to-DC circulating current dual converters are operated with the following relationship between their triggering angles (a 1 and a 2 ). (a) a 1 + a 2 = 180° (b) a 1 + a 2 = 360° (c) a 1 - a 2 = 180° (d) a 1 + a 2 = 90° 1.25 In case of an armature controlled separately excited dc motor drive with closed- loop speed control, an inner current loop is useful because it (a) limits the speed of the motor to a safe value (b) helps in improving the drive energy efficiency (c) limits the peak current of the motor to the permissible value (d) reduces the steady state speed error 2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 2.1 The electric field E ur (in volts/metre) at the point (1,1,0) due to a point charge of +1µC located at (-1,1,1) (coordinates in metres)is (a) ( ) 6 0 10 2 20 5 i k pe - - (b) ( ) 6 0 10 2 20 i k pe - - (c) ( ) 6 0 10 2 20 5 i k pe - - - (d) ( ) 6 0 10 2 20 i k pe - - - 2.2. A connected network of N>2 nodes has at most one branch directly connecting any pair of nodes. The graph of the network (a) must have at least N branches for one or more closed paths to existRead More

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