Page 1 ?EE ? GATE Paper 2010 Q. No. 1 â€“ 25 Carry One Mark Each 1. The value of the quantity P, where 1 x 0 Pxedx,isequalto = ? (A) 0 (B) 1 (C) e (D) 1/e 2. Divergence of the three-dimensional radial vector field r is (A) 3 (B) 1/r (C) Ë† Ë†Ë† ij k + + (D) ( ) Ë† Ë†Ë† 3i j k ++ 3. The period of the signal () xt 8sin 0.8 t 4 p ?? =p+ ?? ?? is (A) 0.4 s p (B) 0.8 s p (C) 1.25s (D) 2.5s 4. The system represented by the input-output relationship () ( ) 5t yt x d,t 0 -8 =tt> ? is (A) Linear and causal (B) Linear but not causal (C) Causal but not linear (D) Neither linear nor causal 5. The switch in the circuit has been closed for a long time. It is opened at t = 0. At t = 0 + , the current through the 1F µ capacitor is (A) 0A (B) 1A (C) 1.25A (D) 5A 6. The second harmonic component of the periodic waveform given in the figure has an amplitude of (A) 0 (B) 1 (C) 2/ p (D) 5 7. As shown in the figure, a 1 O resistance is connected across a source that has a load line v + i = 100. The current through the resistance is (A) 25A (B) 50A (C) 100A (D) 200A 5V 1 O t0 = 1F µ 4 O 1 + 0 1 - T /2 T t Source v + - i 1 O Page 2 ?EE ? GATE Paper 2010 Q. No. 1 â€“ 25 Carry One Mark Each 1. The value of the quantity P, where 1 x 0 Pxedx,isequalto = ? (A) 0 (B) 1 (C) e (D) 1/e 2. Divergence of the three-dimensional radial vector field r is (A) 3 (B) 1/r (C) Ë† Ë†Ë† ij k + + (D) ( ) Ë† Ë†Ë† 3i j k ++ 3. The period of the signal () xt 8sin 0.8 t 4 p ?? =p+ ?? ?? is (A) 0.4 s p (B) 0.8 s p (C) 1.25s (D) 2.5s 4. The system represented by the input-output relationship () ( ) 5t yt x d,t 0 -8 =tt> ? is (A) Linear and causal (B) Linear but not causal (C) Causal but not linear (D) Neither linear nor causal 5. The switch in the circuit has been closed for a long time. It is opened at t = 0. At t = 0 + , the current through the 1F µ capacitor is (A) 0A (B) 1A (C) 1.25A (D) 5A 6. The second harmonic component of the periodic waveform given in the figure has an amplitude of (A) 0 (B) 1 (C) 2/ p (D) 5 7. As shown in the figure, a 1 O resistance is connected across a source that has a load line v + i = 100. The current through the resistance is (A) 25A (B) 50A (C) 100A (D) 200A 5V 1 O t0 = 1F µ 4 O 1 + 0 1 - T /2 T t Source v + - i 1 O ?EE ? GATE Paper 2010 8. A wattmeter is connected as shown in the figure. The wattmeter reads (A) Zero always (B) Total power consumed by Z 1 and Z 2 (C) Power consumed by Z 1 (D) Power consumed by Z 2 9. An ammeter has a current range of 0 - 5 A, and its internal resistance is 0.2 O . In order to change the range to 0 - 25 A, we need to add a resistance of (A)0.8 O in series with the meter (B) 1.0 O in series with the meter (C)0.04 O in parallel with the meter (D) 0.05 O in parallel with the meter 10. As shown in the figure, a negative feedback system has an amplifier of gain 100 with ±10% tolerance in the forward path, and an attenuator of value 9/100 in the feedback path. The overall system gain is approximately: (A) 10±1% (B) 10 ±2% (C) 10 ±5% (D) 10 ±10% 11. For the system () 2 , s1 + the approximate time taken for a step response to reach 98% of its final value is (A) 1s (B) 2s (C) 4s (D) 8s 12. If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then (A) A, B are resistances and C, D capacitances (B) A, C are resistances and B, D capacitances (C) A, B are capacitances and C, D resistances (D) A, C are capacitances and B, D resistances Current coil Potential coil Wattmeter 1 Z 2 Z 100 10% ± 9 100 + - 1 h 2 h A C B D () aCoupledtank ( ) bElectricalequivalent Page 3 ?EE ? GATE Paper 2010 Q. No. 1 â€“ 25 Carry One Mark Each 1. The value of the quantity P, where 1 x 0 Pxedx,isequalto = ? (A) 0 (B) 1 (C) e (D) 1/e 2. Divergence of the three-dimensional radial vector field r is (A) 3 (B) 1/r (C) Ë† Ë†Ë† ij k + + (D) ( ) Ë† Ë†Ë† 3i j k ++ 3. The period of the signal () xt 8sin 0.8 t 4 p ?? =p+ ?? ?? is (A) 0.4 s p (B) 0.8 s p (C) 1.25s (D) 2.5s 4. The system represented by the input-output relationship () ( ) 5t yt x d,t 0 -8 =tt> ? is (A) Linear and causal (B) Linear but not causal (C) Causal but not linear (D) Neither linear nor causal 5. The switch in the circuit has been closed for a long time. It is opened at t = 0. At t = 0 + , the current through the 1F µ capacitor is (A) 0A (B) 1A (C) 1.25A (D) 5A 6. The second harmonic component of the periodic waveform given in the figure has an amplitude of (A) 0 (B) 1 (C) 2/ p (D) 5 7. As shown in the figure, a 1 O resistance is connected across a source that has a load line v + i = 100. The current through the resistance is (A) 25A (B) 50A (C) 100A (D) 200A 5V 1 O t0 = 1F µ 4 O 1 + 0 1 - T /2 T t Source v + - i 1 O ?EE ? GATE Paper 2010 8. A wattmeter is connected as shown in the figure. The wattmeter reads (A) Zero always (B) Total power consumed by Z 1 and Z 2 (C) Power consumed by Z 1 (D) Power consumed by Z 2 9. An ammeter has a current range of 0 - 5 A, and its internal resistance is 0.2 O . In order to change the range to 0 - 25 A, we need to add a resistance of (A)0.8 O in series with the meter (B) 1.0 O in series with the meter (C)0.04 O in parallel with the meter (D) 0.05 O in parallel with the meter 10. As shown in the figure, a negative feedback system has an amplifier of gain 100 with ±10% tolerance in the forward path, and an attenuator of value 9/100 in the feedback path. The overall system gain is approximately: (A) 10±1% (B) 10 ±2% (C) 10 ±5% (D) 10 ±10% 11. For the system () 2 , s1 + the approximate time taken for a step response to reach 98% of its final value is (A) 1s (B) 2s (C) 4s (D) 8s 12. If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then (A) A, B are resistances and C, D capacitances (B) A, C are resistances and B, D capacitances (C) A, B are capacitances and C, D resistances (D) A, C are capacitances and B, D resistances Current coil Potential coil Wattmeter 1 Z 2 Z 100 10% ± 9 100 + - 1 h 2 h A C B D () aCoupledtank ( ) bElectricalequivalent ?EE ? GATE Paper 2010 13. A single-phase transformer has a turns ratio of 1:2, and is connected to a purely resistive load as shown in the figure. The magnetizing current drawn is 1A, and the secondary current is 1A. If core losses and leakage reactanceâ€™s are neglected, the primary current is (A) 1.41A (B) 2A (C) 2.24 A (D) 3 A 14. Power is transferred from system A to system B by an HVDC link as shown in the figure. If the voltages V AB and V CD are as indicated in the figure, and I > 0, then (A) V AB <0, V CD <0, V AB >V CD (B) V AB >0, V CD >0, V AB >V CD (C) V AB >0, V CD >0, V AB <V CD (D) V AB >0, V CD <0 15 A balanced three-phase voltage is applied to a star-connected induction motor, the phase to neutral voltage being V. The stator resistance, rotor resistance referred to the stator, stator leakage reactance, rotor leakage reactance referred to the stator, and the magnetizing reactance are denoted by sr s r m r,r,x ,x and X , respectively. The magnitude of the starting current of the motor is given by (A) () ( ) 22 sr s r V rr x x ++ + (B) () 2 2 ss m V rx X ++ (C) () ( ) 22 sr m r V rr X x ++ + (D) () 2 2 sm r V rX x ++ 16. Consider a step voltage wave of magnitude 1pu travelling along a lossless transmission line that terminates in a reactor. The voltage magnitude across the reactor at the instant the travelling wave reaches the reactor is (A) â€“1pu (B) 1pu (C) 2pu (D) 3pu 1.2 1A AC System A Rectifier A B AB V l CD V Inverter AC System B C D Power Flow ????? ? ? A Reactor Page 4 ?EE ? GATE Paper 2010 Q. No. 1 â€“ 25 Carry One Mark Each 1. The value of the quantity P, where 1 x 0 Pxedx,isequalto = ? (A) 0 (B) 1 (C) e (D) 1/e 2. Divergence of the three-dimensional radial vector field r is (A) 3 (B) 1/r (C) Ë† Ë†Ë† ij k + + (D) ( ) Ë† Ë†Ë† 3i j k ++ 3. The period of the signal () xt 8sin 0.8 t 4 p ?? =p+ ?? ?? is (A) 0.4 s p (B) 0.8 s p (C) 1.25s (D) 2.5s 4. The system represented by the input-output relationship () ( ) 5t yt x d,t 0 -8 =tt> ? is (A) Linear and causal (B) Linear but not causal (C) Causal but not linear (D) Neither linear nor causal 5. The switch in the circuit has been closed for a long time. It is opened at t = 0. At t = 0 + , the current through the 1F µ capacitor is (A) 0A (B) 1A (C) 1.25A (D) 5A 6. The second harmonic component of the periodic waveform given in the figure has an amplitude of (A) 0 (B) 1 (C) 2/ p (D) 5 7. As shown in the figure, a 1 O resistance is connected across a source that has a load line v + i = 100. The current through the resistance is (A) 25A (B) 50A (C) 100A (D) 200A 5V 1 O t0 = 1F µ 4 O 1 + 0 1 - T /2 T t Source v + - i 1 O ?EE ? GATE Paper 2010 8. A wattmeter is connected as shown in the figure. The wattmeter reads (A) Zero always (B) Total power consumed by Z 1 and Z 2 (C) Power consumed by Z 1 (D) Power consumed by Z 2 9. An ammeter has a current range of 0 - 5 A, and its internal resistance is 0.2 O . In order to change the range to 0 - 25 A, we need to add a resistance of (A)0.8 O in series with the meter (B) 1.0 O in series with the meter (C)0.04 O in parallel with the meter (D) 0.05 O in parallel with the meter 10. As shown in the figure, a negative feedback system has an amplifier of gain 100 with ±10% tolerance in the forward path, and an attenuator of value 9/100 in the feedback path. The overall system gain is approximately: (A) 10±1% (B) 10 ±2% (C) 10 ±5% (D) 10 ±10% 11. For the system () 2 , s1 + the approximate time taken for a step response to reach 98% of its final value is (A) 1s (B) 2s (C) 4s (D) 8s 12. If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then (A) A, B are resistances and C, D capacitances (B) A, C are resistances and B, D capacitances (C) A, B are capacitances and C, D resistances (D) A, C are capacitances and B, D resistances Current coil Potential coil Wattmeter 1 Z 2 Z 100 10% ± 9 100 + - 1 h 2 h A C B D () aCoupledtank ( ) bElectricalequivalent ?EE ? GATE Paper 2010 13. A single-phase transformer has a turns ratio of 1:2, and is connected to a purely resistive load as shown in the figure. The magnetizing current drawn is 1A, and the secondary current is 1A. If core losses and leakage reactanceâ€™s are neglected, the primary current is (A) 1.41A (B) 2A (C) 2.24 A (D) 3 A 14. Power is transferred from system A to system B by an HVDC link as shown in the figure. If the voltages V AB and V CD are as indicated in the figure, and I > 0, then (A) V AB <0, V CD <0, V AB >V CD (B) V AB >0, V CD >0, V AB >V CD (C) V AB >0, V CD >0, V AB <V CD (D) V AB >0, V CD <0 15 A balanced three-phase voltage is applied to a star-connected induction motor, the phase to neutral voltage being V. The stator resistance, rotor resistance referred to the stator, stator leakage reactance, rotor leakage reactance referred to the stator, and the magnetizing reactance are denoted by sr s r m r,r,x ,x and X , respectively. The magnitude of the starting current of the motor is given by (A) () ( ) 22 sr s r V rr x x ++ + (B) () 2 2 ss m V rx X ++ (C) () ( ) 22 sr m r V rr X x ++ + (D) () 2 2 sm r V rX x ++ 16. Consider a step voltage wave of magnitude 1pu travelling along a lossless transmission line that terminates in a reactor. The voltage magnitude across the reactor at the instant the travelling wave reaches the reactor is (A) â€“1pu (B) 1pu (C) 2pu (D) 3pu 1.2 1A AC System A Rectifier A B AB V l CD V Inverter AC System B C D Power Flow ????? ? ? A Reactor ?EE ? GATE Paper 2010 17. Consider two buses connected by an impedance of (0+j5) O. The bus 1 voltage is o 100 30 V ? , and bus 2 voltage is o 100 0 V. ? The real and reactive power supplied by bus 1, respectively, are (A) 1000W, 268VAr (B) â€“1000W, â€“134Var (C) 276.9W, â€“56.7Var (D) â€“276.9W, 56.7Var 18. A three-phase, 33kV oil circuit breaker is rated 1200A, 2000MVA, 3s. The symmetrical breaking current is (A) 1200 A (B) 3600 A (C) 35 kA (D) 104.8 kA 19. Consider a stator winding of an alternator with an internal high-resistance ground fault. The currents under the fault condition are as shown in the figure. The winding is protected using a differential current scheme with current transformers of ratio 400/5 A as shown. The current through the operating coil is (A) 0.17875 A (B) 0.2A (C) 0.375A (D) 60 kA 20. The zero-sequence circuit of the three phase transformer shown in the figure is (A) (B) (C) (D) CT ratio 400 /5 CT ratio 400 /5 () 220 j0 A + ( ) 250 j0 A + Operating coil R Y B r b y R r G R r G R r G R r G Page 5 ?EE ? GATE Paper 2010 Q. No. 1 â€“ 25 Carry One Mark Each 1. The value of the quantity P, where 1 x 0 Pxedx,isequalto = ? (A) 0 (B) 1 (C) e (D) 1/e 2. Divergence of the three-dimensional radial vector field r is (A) 3 (B) 1/r (C) Ë† Ë†Ë† ij k + + (D) ( ) Ë† Ë†Ë† 3i j k ++ 3. The period of the signal () xt 8sin 0.8 t 4 p ?? =p+ ?? ?? is (A) 0.4 s p (B) 0.8 s p (C) 1.25s (D) 2.5s 4. The system represented by the input-output relationship () ( ) 5t yt x d,t 0 -8 =tt> ? is (A) Linear and causal (B) Linear but not causal (C) Causal but not linear (D) Neither linear nor causal 5. The switch in the circuit has been closed for a long time. It is opened at t = 0. At t = 0 + , the current through the 1F µ capacitor is (A) 0A (B) 1A (C) 1.25A (D) 5A 6. The second harmonic component of the periodic waveform given in the figure has an amplitude of (A) 0 (B) 1 (C) 2/ p (D) 5 7. As shown in the figure, a 1 O resistance is connected across a source that has a load line v + i = 100. The current through the resistance is (A) 25A (B) 50A (C) 100A (D) 200A 5V 1 O t0 = 1F µ 4 O 1 + 0 1 - T /2 T t Source v + - i 1 O ?EE ? GATE Paper 2010 8. A wattmeter is connected as shown in the figure. The wattmeter reads (A) Zero always (B) Total power consumed by Z 1 and Z 2 (C) Power consumed by Z 1 (D) Power consumed by Z 2 9. An ammeter has a current range of 0 - 5 A, and its internal resistance is 0.2 O . In order to change the range to 0 - 25 A, we need to add a resistance of (A)0.8 O in series with the meter (B) 1.0 O in series with the meter (C)0.04 O in parallel with the meter (D) 0.05 O in parallel with the meter 10. As shown in the figure, a negative feedback system has an amplifier of gain 100 with ±10% tolerance in the forward path, and an attenuator of value 9/100 in the feedback path. The overall system gain is approximately: (A) 10±1% (B) 10 ±2% (C) 10 ±5% (D) 10 ±10% 11. For the system () 2 , s1 + the approximate time taken for a step response to reach 98% of its final value is (A) 1s (B) 2s (C) 4s (D) 8s 12. If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then (A) A, B are resistances and C, D capacitances (B) A, C are resistances and B, D capacitances (C) A, B are capacitances and C, D resistances (D) A, C are capacitances and B, D resistances Current coil Potential coil Wattmeter 1 Z 2 Z 100 10% ± 9 100 + - 1 h 2 h A C B D () aCoupledtank ( ) bElectricalequivalent ?EE ? GATE Paper 2010 13. A single-phase transformer has a turns ratio of 1:2, and is connected to a purely resistive load as shown in the figure. The magnetizing current drawn is 1A, and the secondary current is 1A. If core losses and leakage reactanceâ€™s are neglected, the primary current is (A) 1.41A (B) 2A (C) 2.24 A (D) 3 A 14. Power is transferred from system A to system B by an HVDC link as shown in the figure. If the voltages V AB and V CD are as indicated in the figure, and I > 0, then (A) V AB <0, V CD <0, V AB >V CD (B) V AB >0, V CD >0, V AB >V CD (C) V AB >0, V CD >0, V AB <V CD (D) V AB >0, V CD <0 15 A balanced three-phase voltage is applied to a star-connected induction motor, the phase to neutral voltage being V. The stator resistance, rotor resistance referred to the stator, stator leakage reactance, rotor leakage reactance referred to the stator, and the magnetizing reactance are denoted by sr s r m r,r,x ,x and X , respectively. The magnitude of the starting current of the motor is given by (A) () ( ) 22 sr s r V rr x x ++ + (B) () 2 2 ss m V rx X ++ (C) () ( ) 22 sr m r V rr X x ++ + (D) () 2 2 sm r V rX x ++ 16. Consider a step voltage wave of magnitude 1pu travelling along a lossless transmission line that terminates in a reactor. The voltage magnitude across the reactor at the instant the travelling wave reaches the reactor is (A) â€“1pu (B) 1pu (C) 2pu (D) 3pu 1.2 1A AC System A Rectifier A B AB V l CD V Inverter AC System B C D Power Flow ????? ? ? A Reactor ?EE ? GATE Paper 2010 17. Consider two buses connected by an impedance of (0+j5) O. The bus 1 voltage is o 100 30 V ? , and bus 2 voltage is o 100 0 V. ? The real and reactive power supplied by bus 1, respectively, are (A) 1000W, 268VAr (B) â€“1000W, â€“134Var (C) 276.9W, â€“56.7Var (D) â€“276.9W, 56.7Var 18. A three-phase, 33kV oil circuit breaker is rated 1200A, 2000MVA, 3s. The symmetrical breaking current is (A) 1200 A (B) 3600 A (C) 35 kA (D) 104.8 kA 19. Consider a stator winding of an alternator with an internal high-resistance ground fault. The currents under the fault condition are as shown in the figure. The winding is protected using a differential current scheme with current transformers of ratio 400/5 A as shown. The current through the operating coil is (A) 0.17875 A (B) 0.2A (C) 0.375A (D) 60 kA 20. The zero-sequence circuit of the three phase transformer shown in the figure is (A) (B) (C) (D) CT ratio 400 /5 CT ratio 400 /5 () 220 j0 A + ( ) 250 j0 A + Operating coil R Y B r b y R r G R r G R r G R r G ?EE ? GATE Paper 2010 21. Given that the op-amp is ideal, the output voltage V 0 is (A) 4V (B) 6V (C) 7.5V (D) 12.12V 22. Assuming that the diodes in the given circuit are ideal, the voltage V 0 is (A) 4V (B) 5V (C) 7.5V (D) 12.12V 23. The power electronic converter shown in the figure has a single-pole double-throw switch. The pole P of the switch is connected alternately to throws A and B. The converter shown is a (A) step-down chopper (buck converter) (B) half-wave rectifier (C) step-up chopper (boost converter) (D) full-wave rectifier 24. Figure shows a composite switch consisting of a power transistor (BJT) in series with a diode. Assuming that the transistor switch and the diode are ideal, the I-V characteristic of the composite switch is (A) (B) (C) (D) 0 V 10V 15V 10k O 10k O 10k O IN V A P B L + - OUT V + V I - V I V I V I V I R 2V + 2R 10V + 10V - 0 V - +Read More

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