Saturday, October 31, 2009
GATE Syllabus for Electrical Engineering
ENGINEERING MATHEMATICS
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.
Complex variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue theorem, solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.
Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.
Transform Theory: Fourier transform, Laplace transform, Z-transform.
ELECTRICAL ENGINEERING
Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, basic filter concepts; ideal current and voltage sources, Thevenin’s, Norton’s and Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions; Ampere’s and Biot-Savart’s laws; inductance; dielectrics; capacitance.
Signals and Systems: Representation of continuous and discrete-time signals; shifting and scaling operations; linear, time-invariant and causal systems; Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms.
Electrical Machines: Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation; autotransformer; energy conversion principles; DC machines - types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors - principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications; servo and stepper motors.
Power Systems: Basic power generation concepts; transmission line models and performance; cable performance, insulation; corona and radio interference; distribution systems; per-unit quantities; bus impedance and admittance matrices; load flow; voltage control; power factor correction; economic operation; symmetrical components; fault analysis; principles of overcurrent, differential and distance protection; solid state relays and digital protection; circuit breakers; system stability concepts, swing curves and equal area criterion; HVDC transmission and FACTS concepts.
Control Systems: Principles of feedback; transfer function; block diagrams; steady-state errors; Routh and Niquist techniques; Bode plots; root loci; lag, lead and lead-lag compensation; state space model; state transition matrix, controllability and observability.
Electrical and Electronic Measurements: Bridges and potentiometers; PMMC, moving iron, dynamometer and induction type instruments; measurement of voltage, current, power, energy and power factor; instrument transformers; digital voltmeters and multimeters; phase, time and frequency measurement; Q-meters; oscilloscopes; potentiometric recorders; error analysis.
Analog and Digital Electronics: Characteristics of diodes, BJT, FET; amplifiers - biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers; operational amplifiers - characteristics and applications; simple active filters; VCOs and timers; combinational and sequential logic circuits; multiplexer; Schmitt trigger; multi-vibrators; sample and hold circuits; A/D and D/A converters; 8-bit microprocessor basics, architecture, programming and interfacing.
Power Electronics and Drives: Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and principles of operation; triggering circuits; phase control rectifiers; bridge converters - fully controlled and half controlled; principles of choppers and inverters; basis concepts of adjustable speed dc and ac drives.
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.
Complex variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue theorem, solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.
Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.
Transform Theory: Fourier transform, Laplace transform, Z-transform.
ELECTRICAL ENGINEERING
Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, basic filter concepts; ideal current and voltage sources, Thevenin’s, Norton’s and Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions; Ampere’s and Biot-Savart’s laws; inductance; dielectrics; capacitance.
Signals and Systems: Representation of continuous and discrete-time signals; shifting and scaling operations; linear, time-invariant and causal systems; Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms.
Electrical Machines: Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation; autotransformer; energy conversion principles; DC machines - types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors - principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications; servo and stepper motors.
Power Systems: Basic power generation concepts; transmission line models and performance; cable performance, insulation; corona and radio interference; distribution systems; per-unit quantities; bus impedance and admittance matrices; load flow; voltage control; power factor correction; economic operation; symmetrical components; fault analysis; principles of overcurrent, differential and distance protection; solid state relays and digital protection; circuit breakers; system stability concepts, swing curves and equal area criterion; HVDC transmission and FACTS concepts.
Control Systems: Principles of feedback; transfer function; block diagrams; steady-state errors; Routh and Niquist techniques; Bode plots; root loci; lag, lead and lead-lag compensation; state space model; state transition matrix, controllability and observability.
Electrical and Electronic Measurements: Bridges and potentiometers; PMMC, moving iron, dynamometer and induction type instruments; measurement of voltage, current, power, energy and power factor; instrument transformers; digital voltmeters and multimeters; phase, time and frequency measurement; Q-meters; oscilloscopes; potentiometric recorders; error analysis.
Analog and Digital Electronics: Characteristics of diodes, BJT, FET; amplifiers - biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers; operational amplifiers - characteristics and applications; simple active filters; VCOs and timers; combinational and sequential logic circuits; multiplexer; Schmitt trigger; multi-vibrators; sample and hold circuits; A/D and D/A converters; 8-bit microprocessor basics, architecture, programming and interfacing.
Power Electronics and Drives: Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and principles of operation; triggering circuits; phase control rectifiers; bridge converters - fully controlled and half controlled; principles of choppers and inverters; basis concepts of adjustable speed dc and ac drives.
Friday, October 30, 2009
GATE EE – 2002 Electrical Engineering Question Paper
SECTION – A
1. This question consists of TWENTY-FIVE sub-questions (1.1 œ 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 A current impulse, 5 d (t), is forced through a capacitor C. The voltage, V (t), across the capacitor is given by
1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is
1.3 The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by
(a) B œ N + 1 (b) B + N
(c) N œ B + 1 (d) N œ 2B -1
1.4 Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode?
(a) A circle of unit radius (b) An ellipse
(c) A parabola
(d) A straight line inclined at 45° with respect to the x-axis
1.5 Given a vector field the divergence theorem states that
1.6 If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply?
(a) reduces (b) increases
(c) remains the same
(d) increase or reduces depending upon the rotor resistance
1.7 A dc series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque-speed characteristic of this motor will be approximately represented by which curve
(a) Curve A
(b) Curve B
(c) Curve C
(d) Curve D
1.8 A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply is connected to the high voltage winding. A resistive load is connected to the low voltage winding which draws rated current. Which one of the following quantities will not be sinusoidal?
(a) Voltage induced across the low voltage winding
(b) Core flux
(c) Load current
(d) Current drawn from the source
1.9 A 400V/200V/200V, 50 Hz three winding transformer is connected as shown in 400V
Fig.1.9. The reading of the voltmeter, V, ~ V 50 Hz will be
(a) 0 V (b) 400 V
(c) 600 V (d) 800 V 4
1.10 The frequency of the clock signal applied to the rising edge triggered D flip-flop shown in Fig.1.10 is 10 kHz. The frequency of the signal
available at Q is
(a) 10 kHz
(b) 2.5 kHz
(c) 20 kHz
(d) 5 kHz
1.11 The forward resistance of the diode shown in Fig.1.11 is 5 and the remaining parameters are same as those of an ideal diode. The dc component of the source current is
1.12 The cut-in voltage of both Zener diode D and diode D shown in Fig.1.12 is 0.7 V, while break down voltage of D is 3.3 V and reverse breakdown voltage of D is 50 V. the other parameters can be assumed to be the same as those of an ideal diode. The values of the peak output voltage (V ) are
(a) 3.3 V in the positive half cycle and 1.4 V in the negative half cycle
(b) 4 V in the positive half cycle and 5 V in the negative half cycle
(c) 3.3 V in both positive and negative half cycles
(d) 4 V in both positive and negative half cycles
1.13 The line-to-line input voltage to the 3 R
phase, 50 Hz, ac circuit shown in Fig.1.13 is 100 V rms. Assuming that the phase sequence is RYB, the
wattmeters would read.
(a) W = 886 W and W = 886 W
(b) W = 500 W and W = 500 W
(c) W = 0 W and W = 1000 W
(d) W = 250 W and W = 750 W
1.14 The logic circuit used to generate the active low chip select (CS) by an 8085 microprocessor to address a peripheral is shown in Fig.1.14. The peripheral will respond to addresses in the range.
(a) E000-EFFF
(b) 000E-FFFE
(c) 1000-FFFF
(d) 0001-FFF1
1.15 Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is 0.25 cm and the distance between their centers is 1m. If this distance is doubled, then the inductance per unit length
(a) doubles (b) halves
(c) increases but does not double (d) decreases but does not halve
1.16 Consider a power system with three identical generators. The transmission losses are negligible. One generator (G1) has a speed governor which maintains its speed constant at the rated value, while the other generators (G2 and G3) have governors with a droop of 5%. If the load of the system is increased, then in steady state.
(a) generation of G2 and G3 is increased equally while generation of G1 is
unchanged.
(b) generation of G1 alone is increased while generation of G2 and G3 is
unchanged.
(c) generation of G1, G2 and G3 is increased equally.
(d) generation of G1, G2 and G3 is increased in the ratio 0.5:0.25:0.25.
1.17 A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exists between the conductor and the ground. The maximum electric stress occurs at
(a) the upper surface of the conductor
(b) the lower surface of the conductor
(c) the ground surface
(d) midway between the conductor and ground
1.18 Consider the problem of relay co-ordination for the distance relays R1 and R2 on adjacent lines of a transmission system (Fig.1.18). The Zone 1 and Zone settings for both the relays are indicated on the diagram. Which of the following indicates the correct time setting for the Zone 2 of relays R1 and R2.
1.19. Let s(t) be the step response of a linear system with zero initial conditions; then the response of this system to an input u(t) is
1.20. Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is
1.22. The state transition matrix for the system with initial state X(0) is X AX =
(a) sI A – - (b) e X (c) Laplace inverse
(d) Laplace inverse of [ sI A X(0)]
1.23. A six pulse thyristor rectifier bridge is connected to a balanced 50 Hz three phase ac source. Assuming that the dc output current of the rectifier is constant, the lowest frequency harmonic component in the ac source line current is
(a) 100 Hz (b) 150 Hz (c) 250 Hz (d) 300 Hz
1.24. What is the rms value of the voltage waveform shown in Fig.1.24?
(a) 200 V (b) 100 V (c) 200 V (d) 100 V
1.25 A step down chopper is operated in the continuous conduction mode in steady state with a constant duty ratio D. If V is the magnitude of the dc output voltage 0 and if V is the magnitude of the dc input voltage, the ratio
V is given by
(a) D (b) 1 – D (c) 1 (d) 1
2. This question consists of TWENTY-FIVE sub-questions (2.1 œ 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 A two port network, shown in Fig.2.1 is described by the following equations.
The admittance parameters Y , Y Y for the network shown are
(a) 0.5 mho, 1 mho, 2 mho and 1 mho respectively
(b) 1
3 mho, – 1 6 mho, – 1 6 mho and 1 3 mho respectively
(c) 0.5 mho, 0.5 mho, 1.5 mho and 2 mho respectively
(d) 2 – mho, 3 – mho, 3
7 7 mho and 2 5 5 mho respectively
2.2. In the circuit shown in Fig.2.2, what value of C will cause a unity power factor at the ac source?
(a) 68.1 F
230V (b) 165 F C Z
=30 40°
L ~
50Hz (c) 0.681 F
(d) 6.81 F
2.3. A first order, low pass filter is given with R = 50 and C = 5 F. What is the
frequency at which the gain of the voltage transfer function of the filter is 0.25?
(a) 4.92 kHz (b) 0.49 kHz (c) 2.46 kHz (d) 24.6 kHz
2.4. A series R-L-C circuit has R = 50 , L = 100 H and C = 1 F. the lower half
power frequency of the circuit is
(a) 30.55 kHz (b) 3.055 kHz (c) 51.92 kHz (d) 1.92 kHz
2.5. A 200 V, 2000 rpm, 10A, separately excited dc motor has an armature resistance of 2 . Rated dc voltage is applied to both the armature and field winding of the motor. If the armature drawn 5A from the source, the torque developed by the motor is
(a) 4.30 Nm (b) 4.77 Nm (c) 0.45 Nm (d) 0.50 Nm
2.6. The rotor of a three phase, 5 kW, 400V, 50 Hz, slip ring induction motor is wound for 6 poles while its stator is wound for 4 poles. The approximate average no load steady state speed when this motor is connected to 400V, 50 Hz supply is
(a) 1500 rpm (b) 500 rpm (c) 0 rpm (d) 1000 rpm
2.7. The flux per pole in a synchronous motor with the field circuit ON and the stator disconnected from the supply is found to be 25 mWb. When the stator is connected to the rated supply with the field excitation unchanged, the flux per pole in the machine is found to be 20 mWb while the motor is running on no load. Assuming no load losses to be zero, the no load current down by the motor from the supply
(a) lags the supply voltage (b) leads the supply voltage
(c) is in phase with the supply voltage (d) is zero
2.8. An 11 V pulse of 10 s duration is applied to the circuit shown in Fig.2.8.
Assuming that the capacitor is completely discharged prior to applying the pulse, the peak value of the capacitor voltage is
(a) 11 V (b) 5.5 V
(c) 6.32 V (d) 0.96 V
2.9. The output voltage (V ) of the Schmitt trigger shown in Fig.2.9 swings between +15V and – 15V. Assume that the operational amplifier is ideal. The output will change from +15V to œ15V when
the instantaneous value of the input sine wave is
(a) 5 V in the positive slope only
(b) 5 V in the negative slope only
(c) 5 V in the positive and negative slopes
(d) 3 V in the positive and negative slopes
2.10. For the circuit shown in Fig.2.10, the Boolean expression for the output Y in terms of inputs P, Q, R and S is
2.11. In the circuit shown in Fig.2.11, it is found that the input ac voltage (v) and current i are in phase. The coupling coefficient is K = , where M is the
mutual inductance between the two coils. The value of K and the dot polarity of K the coil P-Q are
(a) K = 0.25 and dot at P
(b) K = 0.5 and dot at P
(c) K = 0.25 and dot at Q
(d) K = 0.5 and dot at Q
2.12. Consider the circuit shown in Fig.2.12. If the frequency of the source is 50 Hz, then a value of t which results in a transient free response is
(a) 0 ms
(b) 1.78 ms
(c) 2.71 ms
(d) 2.91 ms
2.13. A three phase thyristor bridge rectifier is used in a HVDC link. The firing angle a (as measured from the point of natural commutation) is constrained to lie between 5° and 30°. If the dc side current and ac side voltage magnitudes are constant, which of the following statements is true (neglect harmonics in the ac side currents and commutation overlap in your analysis)
(a) Reactive power absorbed by the rectifier is maximum when a = 5°
(b) Reactive power absorbed by the rectifier is maximum when a = 30°
(c) Reactive power absorbed by the rectifier is maximum when a = 15°
(d) Reactive power absorbed by the rectifier is maximum when a = 10°
2.14. A power system consists of 2 areas (Area 1 and Area 2) connected by a single tie line (Fig.2.14). It is required to carry out a load flow study on this system. While entering the network data, the tie-line data (connectivity and parameters) is inadvertently left out. If the load flow program is run with this incomplete data
(a) The load-flow will converge only if the slack bus is specified in Area 1
(b) The load-flow will converge only if the slack bus is specified in Area 2
(c) The load-flow will converge if the slack bus is specified in either Area 1 or
Area 2
(d) The load-flow will not converge if only one slack bus is specified.
2.15. A transmission line has a total series reactance of 0.2 pu. Reactive power compensation is applied at the midpoint of the line and it is controlled such that the midpoint voltage of the transmission line is always maintained at 0.98 pu. If voltage at both ends of the line are maintained at 1.0 pu, then the steady state power transfer limit of the transmission line is
(a) 9.8 pu (b) 4.9 pu (c) 19.6 pu (d) 5 pu
2.16. A generator is connected to a transformer which feeds another transformer through a short feeder (see Fig.2.16). The zero sequence impedance values are expressed in pu on a common base and are indicated in Fig.2.16. the Thevenin equivalent zero sequence impedance at point B is
(a) 0.8 + j0.6 (b) 0.75 + j0.22 (c) 0.75 + j0.25 (d) 1.5 + j0.25
» ÿ » ÿ ” which of the following statements is true?
2.17. For the system 2 3 1 , X X u = + … Ÿ … Ÿ
(a) The system is controllable but unstable
(b) The system is uncontrollable but unstable
(c) The system is controllable but stable
(d) The system is uncontrollable but stable
The root 2.18. A unity feedback system has an open loop transfer function,
2.19. The transfer function of the system described
” 2.20. For the system 2 0 1 ; 4 0 , X X u y X = + = with u as unit impulse and with » ÿ … Ÿ … Ÿ zero initial state, the output, y, becomes
(a) 2 e (b) 4 e (c) 2 e (d) 4 e 2t 2t 4t 4t
2.21. The eigen values of the system represented by are X X =
(a) 0, 0, 0, 0 (b) 1, 1, 1, 1 (c) 0, 0, 0, -1 (d) 1, 0, 0, 0
2.22. In the chopper circuit shown in Fig.2.22 the input dc voltage has a constant . the output voltage V is assumed ripple-free. The V switch S is operated with a switching time period T and a duty ratio D. what is the value of D at the boundary of continuous and discontinuous conduction of the inductor current i ?
2.23. Fig. 2.23 (a) shows an inverter circuit with a dc source voltage V . The
semiconductor switches of the inverter are operated in such a manner that the pole voltages v and v are as shown in Fig.2.23 (b). What is the rms value of the pole-to-pole voltage v ?
2.24. In the circuit shown in Fig.2.24, the switch is closed at time t = 0. The steady state value of the voltage v is
(a) 0 V
(b) 10 V -
(c) 5 V
(d) 2.5 V
2.25. In the single phase diode bridge rectifier shown in figure 2.25, the load resistor is R = 50 . The source voltage is =200 sin( t), where =2 50 radians per second. The power dissipated in the load resistor R is
(a) 3200
(b) 400
(c) 400 W
(d) 800 W
SECTION – B
This section consists of TWENTY questions of FIVE marks each. ANY FIFTEEN out of them have to be answered. If more than fifteen questions are attempted, score off answers that are not to be evaluated. Otherwise only the first fifteen unscored answers will be considered.
3. The magnetic vector potential in a region is defined by sin . . An – y A e x a = infinitely long conductor, having ac ross section area, a = 5mm and carrying a dc current, I = 5A in they y direction, passes through this region as shown in Fig.P3. Determine the expression for (a) and (b) force density exerted on the B conductor.
4. A constant current source is supplying 10A to a circuit shown in Fig.P4. the switch S, which is initially closed for a sufficiently long time, is suddenly opened. Obtain the differential equation governing the behaviour of R the inductor current and hence obtain the complete time response of the inductor current. What is the 5H energy stored in L, a long time after the switch is opened?
5. An electrical network is fed by two ac sources, as shown Fig.P5. Given that Z =
Obtain the Thevenin equivalent circuit (Thevenin voltage and impedance) across terminals x and y, and y determine the current I through the load Z
6. In the resistor network shown in Fig.P6, all resistor values are 1 . A current of 1A passes from terminal a to terminal b, as shown in the figure. Calculate the voltage between terminals and . [Hint: You may exploit the symmetry of the a b circuit].
7. A 230V, 250 rpm. 100A separately excited dc motor has an armature resistance of 0.5 . the motor is connected to 230V dc supply and rated dc voltage is applied to the field winding. It is driving a load whose torque speed characteristic is given by T = 500 – 10 , where is the rotational speed expressed in rad/sec and T is
the load torque in Nm. Find the steady state speed at which the motor will drive the load and the armature current drawn by it from the source. Neglect the rotational losses of the machine.
8. A single phase 6300 kVA, 50 Hz, 3300V/400V distribution transformer is connected between two 50 Hz supply systems, A and B as shown in Fig.P8. the transformer has 12 and 99 turns in the low and high voltage windings
respectively. The magnetizing reactance of the transformer referred to the high voltage side is 500 . The leakage reactance of the high and low voltage
windings are 1.0 and 0.012 respectively. Neglect the winding resistance and
core losses of the transformer. The Thevenin voltage of system A is 3300V while that of system B is 400V. the short circuit reactance of systems A and B are 0.5 and 0.010 respectively. If no power is transferred between A and B, so that the two system voltages are in phase, find the magnetizing ampere turns of the transformer.
9. A 440 V, 50 Hz, 6 pole and 960 rpm star connected induction machine has the following per phase parameters referred to the stator:
R = 0.6 R = 0.3 X = 1
The magnetizing reactance is very high and is neglected. The machine is
connected to the 440V, 50 Hz supply and a certain mechanical load is coupled to it. It is found that the magnitude of the stator current is equal to the rated current of the machine but the machine is running at a speed higher than its rated speed. Find the speed at which the machine is running. Also find the torque developed by the machine.
10. A 415 V, 2 pole, 3 phase, 50 Hz, star connected, non-salient pole synchronous motor has synchronous reactance of 2 per phase and negligible stator resistance. At a particular field excitation, it draws 20 A at unity power factor from a 415 V, 3 phase, 50 Hz supply. The mechanical load on the motor is now increased till the stator current is equal to 50A. The field excitation remains unchanged. Determine:
(a) the per phase open circuit voltage E
(b) the developed power for the new operating condition and corresponding
power factor.
11. For the circuit shown in Fig.P11, I = 1mA, = 99 and V = 0.7 V. Determine ß
(a) the current through R and R .
(b) the output voltage V
(c) the value of R
12. Determine the transfer function for the RC network shown in Fig.P12(a).
This network is used as a feedback circuit in an oscillator circuit shown in
Fig.P12(b) to generate sinusoidal oscillations. Assuming that the operational
amplifier is ideal, determine R for generating these oscillations. Also, determine the oscillation frequency if R = 10 k and C = 100 pF.
13. The ripple counter shown in Fig.P13 is made up negative edge triggered J-E flips flops. The signal levels at J and K inputs of all the flip-flops are maintained at logic 1. Assume that all outputs are cleared just prior to applying the clock signal.
(a) Create a table of Q ,Q ,Q and A in the format given below for 10 successive input cycles of the clock CLK1.
(b) Determine the module number of the counter.
(c) Modify the circuit of Fig.P13 to create a modulo-6 counter using the same components used in the figure.
14. A long lossless transmission line has a unity power factor (UPF) load at the receiving end and an ac voltage source at the sending end (Fig.P14). the
parameters of the transmission line are as follows:
Characteristic impedance Z =400 , propagation constant =1.2 10 rad/km, and length l = 100 km. The equation relating sending and receiving end
questions is V V l jZc lI cos sin ß ß = +
Complete the maximum power that can be transferred to the UPF load at the
receiving end if 230 . V kV
15. Two transposed 3 phase lines run parallel to each other as shown in Fig.P15. the equation describing the voltage drop in both lines is given below.
Compute the self and mutual zero sequence impedances of this system i.e.
compute Z , Z , Z in the following equations
V = Z I + Z I Í
V = Z I + Z I Í
Where V , V , I , I are the zero sequence voltage drops and currents for Í Í
the two lines respectively.
16. A synchronous generator is to be connected to an infinite bus through a
transmission line of reactance X = 0.2 pu, as shown in Fig.P16. the generator
data is as follows:
0.1 , 1.0 , x pu E pu H=5MJ/MVA, mechanical power P = 0.0 pu, = 2 50 ‘ ‘ = = p ×rad/sec. All quantities are expressed on a common base.
The generator is initially running on open circuit with the frequency of the open circuit voltage slightly higher than that of the infinite bus. If at the instant of switch closure d 0 and , compute the maximum value of so = = =
that the generator pulls into synchronism.
17. A single input single output system with y as output and u as input, is described
d y dy du 2
by + + = – 2 10 5 3 y u .
dt dt dt For the above system find an input u(t), with zero initial condition, that produces the same output as with no input and with the initial conditions.
18. Obtain a state variable representation of the system governed by the differential
d y dy y u t e 2 ( )
equation + – = 2 , with the choice of state variables as – 1
dt dt 2 ˜ ’ dy
x y x y e = = – , . Also find x (t), given that u(t) is a unit step function
19. The open loop transfer function of a unity feedback system is given by
Sketch the root locus as a varies from 0 to 8 . Find the angle and real axis
intercept of the asymptotes, breakaway points and the imaginary axis crossing points, if any.
20. In Fig.P20, the ideal switch S is switched on and off with a switching frequency f = 10 kHz. The switching time period is T = t + t = 100 s. The circuit is O N OF F operated in steady state at the boundary of continuous and discontinuous conduction, so that the inductor current i is as shown in Fig.P20. Find
(a) The on-time t of the switch.
ON
(b) The value of the peak current I .
21. In the circuit shown in Fig.P21, the source I is a dc current source. The switch S is operated with a time period T and a duty ratio D. You may assume that the capacitance C has a finite value which is large enough so that the voltage. V has negligible ripple. Calculate the following under steady state conditions, in terms of D, I and R.
(a) The voltage V , with the polarity shown in Figure P21.
(b) The average output voltage V , with the polarity shown.
22. The semiconductor switch S in the circuit of Fig.P22 is operated at a frequency of 20 kHz and a duty ratio D = 0.5. The circuit operates in the steady state. Calculate the power-transferred form the dc voltage source V to the dc voltage source V.
1. This question consists of TWENTY-FIVE sub-questions (1.1 œ 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 A current impulse, 5 d (t), is forced through a capacitor C. The voltage, V (t), across the capacitor is given by
1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is
1.3 The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by
(a) B œ N + 1 (b) B + N
(c) N œ B + 1 (d) N œ 2B -1
1.4 Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode?
(a) A circle of unit radius (b) An ellipse
(c) A parabola
(d) A straight line inclined at 45° with respect to the x-axis
1.5 Given a vector field the divergence theorem states that
1.6 If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply?
(a) reduces (b) increases
(c) remains the same
(d) increase or reduces depending upon the rotor resistance
1.7 A dc series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque-speed characteristic of this motor will be approximately represented by which curve
(a) Curve A
(b) Curve B
(c) Curve C
(d) Curve D
1.8 A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply is connected to the high voltage winding. A resistive load is connected to the low voltage winding which draws rated current. Which one of the following quantities will not be sinusoidal?
(a) Voltage induced across the low voltage winding
(b) Core flux
(c) Load current
(d) Current drawn from the source
1.9 A 400V/200V/200V, 50 Hz three winding transformer is connected as shown in 400V
Fig.1.9. The reading of the voltmeter, V, ~ V 50 Hz will be
(a) 0 V (b) 400 V
(c) 600 V (d) 800 V 4
1.10 The frequency of the clock signal applied to the rising edge triggered D flip-flop shown in Fig.1.10 is 10 kHz. The frequency of the signal
available at Q is
(a) 10 kHz
(b) 2.5 kHz
(c) 20 kHz
(d) 5 kHz
1.11 The forward resistance of the diode shown in Fig.1.11 is 5 and the remaining parameters are same as those of an ideal diode. The dc component of the source current is
1.12 The cut-in voltage of both Zener diode D and diode D shown in Fig.1.12 is 0.7 V, while break down voltage of D is 3.3 V and reverse breakdown voltage of D is 50 V. the other parameters can be assumed to be the same as those of an ideal diode. The values of the peak output voltage (V ) are
(a) 3.3 V in the positive half cycle and 1.4 V in the negative half cycle
(b) 4 V in the positive half cycle and 5 V in the negative half cycle
(c) 3.3 V in both positive and negative half cycles
(d) 4 V in both positive and negative half cycles
1.13 The line-to-line input voltage to the 3 R
phase, 50 Hz, ac circuit shown in Fig.1.13 is 100 V rms. Assuming that the phase sequence is RYB, the
wattmeters would read.
(a) W = 886 W and W = 886 W
(b) W = 500 W and W = 500 W
(c) W = 0 W and W = 1000 W
(d) W = 250 W and W = 750 W
1.14 The logic circuit used to generate the active low chip select (CS) by an 8085 microprocessor to address a peripheral is shown in Fig.1.14. The peripheral will respond to addresses in the range.
(a) E000-EFFF
(b) 000E-FFFE
(c) 1000-FFFF
(d) 0001-FFF1
1.15 Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is 0.25 cm and the distance between their centers is 1m. If this distance is doubled, then the inductance per unit length
(a) doubles (b) halves
(c) increases but does not double (d) decreases but does not halve
1.16 Consider a power system with three identical generators. The transmission losses are negligible. One generator (G1) has a speed governor which maintains its speed constant at the rated value, while the other generators (G2 and G3) have governors with a droop of 5%. If the load of the system is increased, then in steady state.
(a) generation of G2 and G3 is increased equally while generation of G1 is
unchanged.
(b) generation of G1 alone is increased while generation of G2 and G3 is
unchanged.
(c) generation of G1, G2 and G3 is increased equally.
(d) generation of G1, G2 and G3 is increased in the ratio 0.5:0.25:0.25.
1.17 A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exists between the conductor and the ground. The maximum electric stress occurs at
(a) the upper surface of the conductor
(b) the lower surface of the conductor
(c) the ground surface
(d) midway between the conductor and ground
1.18 Consider the problem of relay co-ordination for the distance relays R1 and R2 on adjacent lines of a transmission system (Fig.1.18). The Zone 1 and Zone settings for both the relays are indicated on the diagram. Which of the following indicates the correct time setting for the Zone 2 of relays R1 and R2.
1.19. Let s(t) be the step response of a linear system with zero initial conditions; then the response of this system to an input u(t) is
1.20. Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is
1.22. The state transition matrix for the system with initial state X(0) is X AX =
(a) sI A – - (b) e X (c) Laplace inverse
(d) Laplace inverse of [ sI A X(0)]
1.23. A six pulse thyristor rectifier bridge is connected to a balanced 50 Hz three phase ac source. Assuming that the dc output current of the rectifier is constant, the lowest frequency harmonic component in the ac source line current is
(a) 100 Hz (b) 150 Hz (c) 250 Hz (d) 300 Hz
1.24. What is the rms value of the voltage waveform shown in Fig.1.24?
(a) 200 V (b) 100 V (c) 200 V (d) 100 V
1.25 A step down chopper is operated in the continuous conduction mode in steady state with a constant duty ratio D. If V is the magnitude of the dc output voltage 0 and if V is the magnitude of the dc input voltage, the ratio
V is given by
(a) D (b) 1 – D (c) 1 (d) 1
2. This question consists of TWENTY-FIVE sub-questions (2.1 œ 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 A two port network, shown in Fig.2.1 is described by the following equations.
The admittance parameters Y , Y Y for the network shown are
(a) 0.5 mho, 1 mho, 2 mho and 1 mho respectively
(b) 1
3 mho, – 1 6 mho, – 1 6 mho and 1 3 mho respectively
(c) 0.5 mho, 0.5 mho, 1.5 mho and 2 mho respectively
(d) 2 – mho, 3 – mho, 3
7 7 mho and 2 5 5 mho respectively
2.2. In the circuit shown in Fig.2.2, what value of C will cause a unity power factor at the ac source?
(a) 68.1 F
230V (b) 165 F C Z
=30 40°
L ~
50Hz (c) 0.681 F
(d) 6.81 F
2.3. A first order, low pass filter is given with R = 50 and C = 5 F. What is the
frequency at which the gain of the voltage transfer function of the filter is 0.25?
(a) 4.92 kHz (b) 0.49 kHz (c) 2.46 kHz (d) 24.6 kHz
2.4. A series R-L-C circuit has R = 50 , L = 100 H and C = 1 F. the lower half
power frequency of the circuit is
(a) 30.55 kHz (b) 3.055 kHz (c) 51.92 kHz (d) 1.92 kHz
2.5. A 200 V, 2000 rpm, 10A, separately excited dc motor has an armature resistance of 2 . Rated dc voltage is applied to both the armature and field winding of the motor. If the armature drawn 5A from the source, the torque developed by the motor is
(a) 4.30 Nm (b) 4.77 Nm (c) 0.45 Nm (d) 0.50 Nm
2.6. The rotor of a three phase, 5 kW, 400V, 50 Hz, slip ring induction motor is wound for 6 poles while its stator is wound for 4 poles. The approximate average no load steady state speed when this motor is connected to 400V, 50 Hz supply is
(a) 1500 rpm (b) 500 rpm (c) 0 rpm (d) 1000 rpm
2.7. The flux per pole in a synchronous motor with the field circuit ON and the stator disconnected from the supply is found to be 25 mWb. When the stator is connected to the rated supply with the field excitation unchanged, the flux per pole in the machine is found to be 20 mWb while the motor is running on no load. Assuming no load losses to be zero, the no load current down by the motor from the supply
(a) lags the supply voltage (b) leads the supply voltage
(c) is in phase with the supply voltage (d) is zero
2.8. An 11 V pulse of 10 s duration is applied to the circuit shown in Fig.2.8.
Assuming that the capacitor is completely discharged prior to applying the pulse, the peak value of the capacitor voltage is
(a) 11 V (b) 5.5 V
(c) 6.32 V (d) 0.96 V
2.9. The output voltage (V ) of the Schmitt trigger shown in Fig.2.9 swings between +15V and – 15V. Assume that the operational amplifier is ideal. The output will change from +15V to œ15V when
the instantaneous value of the input sine wave is
(a) 5 V in the positive slope only
(b) 5 V in the negative slope only
(c) 5 V in the positive and negative slopes
(d) 3 V in the positive and negative slopes
2.10. For the circuit shown in Fig.2.10, the Boolean expression for the output Y in terms of inputs P, Q, R and S is
2.11. In the circuit shown in Fig.2.11, it is found that the input ac voltage (v) and current i are in phase. The coupling coefficient is K = , where M is the
mutual inductance between the two coils. The value of K and the dot polarity of K the coil P-Q are
(a) K = 0.25 and dot at P
(b) K = 0.5 and dot at P
(c) K = 0.25 and dot at Q
(d) K = 0.5 and dot at Q
2.12. Consider the circuit shown in Fig.2.12. If the frequency of the source is 50 Hz, then a value of t which results in a transient free response is
(a) 0 ms
(b) 1.78 ms
(c) 2.71 ms
(d) 2.91 ms
2.13. A three phase thyristor bridge rectifier is used in a HVDC link. The firing angle a (as measured from the point of natural commutation) is constrained to lie between 5° and 30°. If the dc side current and ac side voltage magnitudes are constant, which of the following statements is true (neglect harmonics in the ac side currents and commutation overlap in your analysis)
(a) Reactive power absorbed by the rectifier is maximum when a = 5°
(b) Reactive power absorbed by the rectifier is maximum when a = 30°
(c) Reactive power absorbed by the rectifier is maximum when a = 15°
(d) Reactive power absorbed by the rectifier is maximum when a = 10°
2.14. A power system consists of 2 areas (Area 1 and Area 2) connected by a single tie line (Fig.2.14). It is required to carry out a load flow study on this system. While entering the network data, the tie-line data (connectivity and parameters) is inadvertently left out. If the load flow program is run with this incomplete data
(a) The load-flow will converge only if the slack bus is specified in Area 1
(b) The load-flow will converge only if the slack bus is specified in Area 2
(c) The load-flow will converge if the slack bus is specified in either Area 1 or
Area 2
(d) The load-flow will not converge if only one slack bus is specified.
2.15. A transmission line has a total series reactance of 0.2 pu. Reactive power compensation is applied at the midpoint of the line and it is controlled such that the midpoint voltage of the transmission line is always maintained at 0.98 pu. If voltage at both ends of the line are maintained at 1.0 pu, then the steady state power transfer limit of the transmission line is
(a) 9.8 pu (b) 4.9 pu (c) 19.6 pu (d) 5 pu
2.16. A generator is connected to a transformer which feeds another transformer through a short feeder (see Fig.2.16). The zero sequence impedance values are expressed in pu on a common base and are indicated in Fig.2.16. the Thevenin equivalent zero sequence impedance at point B is
(a) 0.8 + j0.6 (b) 0.75 + j0.22 (c) 0.75 + j0.25 (d) 1.5 + j0.25
» ÿ » ÿ ” which of the following statements is true?
2.17. For the system 2 3 1 , X X u = + … Ÿ … Ÿ
(a) The system is controllable but unstable
(b) The system is uncontrollable but unstable
(c) The system is controllable but stable
(d) The system is uncontrollable but stable
The root 2.18. A unity feedback system has an open loop transfer function,
2.19. The transfer function of the system described
” 2.20. For the system 2 0 1 ; 4 0 , X X u y X = + = with u as unit impulse and with » ÿ … Ÿ … Ÿ zero initial state, the output, y, becomes
(a) 2 e (b) 4 e (c) 2 e (d) 4 e 2t 2t 4t 4t
2.21. The eigen values of the system represented by are X X =
(a) 0, 0, 0, 0 (b) 1, 1, 1, 1 (c) 0, 0, 0, -1 (d) 1, 0, 0, 0
2.22. In the chopper circuit shown in Fig.2.22 the input dc voltage has a constant . the output voltage V is assumed ripple-free. The V switch S is operated with a switching time period T and a duty ratio D. what is the value of D at the boundary of continuous and discontinuous conduction of the inductor current i ?
2.23. Fig. 2.23 (a) shows an inverter circuit with a dc source voltage V . The
semiconductor switches of the inverter are operated in such a manner that the pole voltages v and v are as shown in Fig.2.23 (b). What is the rms value of the pole-to-pole voltage v ?
2.24. In the circuit shown in Fig.2.24, the switch is closed at time t = 0. The steady state value of the voltage v is
(a) 0 V
(b) 10 V -
(c) 5 V
(d) 2.5 V
2.25. In the single phase diode bridge rectifier shown in figure 2.25, the load resistor is R = 50 . The source voltage is =200 sin( t), where =2 50 radians per second. The power dissipated in the load resistor R is
(a) 3200
(b) 400
(c) 400 W
(d) 800 W
SECTION – B
This section consists of TWENTY questions of FIVE marks each. ANY FIFTEEN out of them have to be answered. If more than fifteen questions are attempted, score off answers that are not to be evaluated. Otherwise only the first fifteen unscored answers will be considered.
3. The magnetic vector potential in a region is defined by sin . . An – y A e x a = infinitely long conductor, having ac ross section area, a = 5mm and carrying a dc current, I = 5A in they y direction, passes through this region as shown in Fig.P3. Determine the expression for (a) and (b) force density exerted on the B conductor.
4. A constant current source is supplying 10A to a circuit shown in Fig.P4. the switch S, which is initially closed for a sufficiently long time, is suddenly opened. Obtain the differential equation governing the behaviour of R the inductor current and hence obtain the complete time response of the inductor current. What is the 5H energy stored in L, a long time after the switch is opened?
5. An electrical network is fed by two ac sources, as shown Fig.P5. Given that Z =
Obtain the Thevenin equivalent circuit (Thevenin voltage and impedance) across terminals x and y, and y determine the current I through the load Z
6. In the resistor network shown in Fig.P6, all resistor values are 1 . A current of 1A passes from terminal a to terminal b, as shown in the figure. Calculate the voltage between terminals and . [Hint: You may exploit the symmetry of the a b circuit].
7. A 230V, 250 rpm. 100A separately excited dc motor has an armature resistance of 0.5 . the motor is connected to 230V dc supply and rated dc voltage is applied to the field winding. It is driving a load whose torque speed characteristic is given by T = 500 – 10 , where is the rotational speed expressed in rad/sec and T is
the load torque in Nm. Find the steady state speed at which the motor will drive the load and the armature current drawn by it from the source. Neglect the rotational losses of the machine.
8. A single phase 6300 kVA, 50 Hz, 3300V/400V distribution transformer is connected between two 50 Hz supply systems, A and B as shown in Fig.P8. the transformer has 12 and 99 turns in the low and high voltage windings
respectively. The magnetizing reactance of the transformer referred to the high voltage side is 500 . The leakage reactance of the high and low voltage
windings are 1.0 and 0.012 respectively. Neglect the winding resistance and
core losses of the transformer. The Thevenin voltage of system A is 3300V while that of system B is 400V. the short circuit reactance of systems A and B are 0.5 and 0.010 respectively. If no power is transferred between A and B, so that the two system voltages are in phase, find the magnetizing ampere turns of the transformer.
9. A 440 V, 50 Hz, 6 pole and 960 rpm star connected induction machine has the following per phase parameters referred to the stator:
R = 0.6 R = 0.3 X = 1
The magnetizing reactance is very high and is neglected. The machine is
connected to the 440V, 50 Hz supply and a certain mechanical load is coupled to it. It is found that the magnitude of the stator current is equal to the rated current of the machine but the machine is running at a speed higher than its rated speed. Find the speed at which the machine is running. Also find the torque developed by the machine.
10. A 415 V, 2 pole, 3 phase, 50 Hz, star connected, non-salient pole synchronous motor has synchronous reactance of 2 per phase and negligible stator resistance. At a particular field excitation, it draws 20 A at unity power factor from a 415 V, 3 phase, 50 Hz supply. The mechanical load on the motor is now increased till the stator current is equal to 50A. The field excitation remains unchanged. Determine:
(a) the per phase open circuit voltage E
(b) the developed power for the new operating condition and corresponding
power factor.
11. For the circuit shown in Fig.P11, I = 1mA, = 99 and V = 0.7 V. Determine ß
(a) the current through R and R .
(b) the output voltage V
(c) the value of R
12. Determine the transfer function for the RC network shown in Fig.P12(a).
This network is used as a feedback circuit in an oscillator circuit shown in
Fig.P12(b) to generate sinusoidal oscillations. Assuming that the operational
amplifier is ideal, determine R for generating these oscillations. Also, determine the oscillation frequency if R = 10 k and C = 100 pF.
13. The ripple counter shown in Fig.P13 is made up negative edge triggered J-E flips flops. The signal levels at J and K inputs of all the flip-flops are maintained at logic 1. Assume that all outputs are cleared just prior to applying the clock signal.
(a) Create a table of Q ,Q ,Q and A in the format given below for 10 successive input cycles of the clock CLK1.
(b) Determine the module number of the counter.
(c) Modify the circuit of Fig.P13 to create a modulo-6 counter using the same components used in the figure.
14. A long lossless transmission line has a unity power factor (UPF) load at the receiving end and an ac voltage source at the sending end (Fig.P14). the
parameters of the transmission line are as follows:
Characteristic impedance Z =400 , propagation constant =1.2 10 rad/km, and length l = 100 km. The equation relating sending and receiving end
questions is V V l jZc lI cos sin ß ß = +
Complete the maximum power that can be transferred to the UPF load at the
receiving end if 230 . V kV
15. Two transposed 3 phase lines run parallel to each other as shown in Fig.P15. the equation describing the voltage drop in both lines is given below.
Compute the self and mutual zero sequence impedances of this system i.e.
compute Z , Z , Z in the following equations
V = Z I + Z I Í
V = Z I + Z I Í
Where V , V , I , I are the zero sequence voltage drops and currents for Í Í
the two lines respectively.
16. A synchronous generator is to be connected to an infinite bus through a
transmission line of reactance X = 0.2 pu, as shown in Fig.P16. the generator
data is as follows:
0.1 , 1.0 , x pu E pu H=5MJ/MVA, mechanical power P = 0.0 pu, = 2 50 ‘ ‘ = = p ×rad/sec. All quantities are expressed on a common base.
The generator is initially running on open circuit with the frequency of the open circuit voltage slightly higher than that of the infinite bus. If at the instant of switch closure d 0 and , compute the maximum value of so = = =
that the generator pulls into synchronism.
17. A single input single output system with y as output and u as input, is described
d y dy du 2
by + + = – 2 10 5 3 y u .
dt dt dt For the above system find an input u(t), with zero initial condition, that produces the same output as with no input and with the initial conditions.
18. Obtain a state variable representation of the system governed by the differential
d y dy y u t e 2 ( )
equation + – = 2 , with the choice of state variables as – 1
dt dt 2 ˜ ’ dy
x y x y e = = – , . Also find x (t), given that u(t) is a unit step function
19. The open loop transfer function of a unity feedback system is given by
Sketch the root locus as a varies from 0 to 8 . Find the angle and real axis
intercept of the asymptotes, breakaway points and the imaginary axis crossing points, if any.
20. In Fig.P20, the ideal switch S is switched on and off with a switching frequency f = 10 kHz. The switching time period is T = t + t = 100 s. The circuit is O N OF F operated in steady state at the boundary of continuous and discontinuous conduction, so that the inductor current i is as shown in Fig.P20. Find
(a) The on-time t of the switch.
ON
(b) The value of the peak current I .
21. In the circuit shown in Fig.P21, the source I is a dc current source. The switch S is operated with a time period T and a duty ratio D. You may assume that the capacitance C has a finite value which is large enough so that the voltage. V has negligible ripple. Calculate the following under steady state conditions, in terms of D, I and R.
(a) The voltage V , with the polarity shown in Figure P21.
(b) The average output voltage V , with the polarity shown.
22. The semiconductor switch S in the circuit of Fig.P22 is operated at a frequency of 20 kHz and a duty ratio D = 0.5. The circuit operates in the steady state. Calculate the power-transferred form the dc voltage source V to the dc voltage source V.
GATE EE – 2001 Electrical Engineering Question Paper
SECTION – A
1. This question consists of TWENTY-FIVE sub-questions (1.1 œ 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 and L , their mutual inductance M satisfies
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
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) maximum supply voltage (d) 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 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?
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 VIcos f
(b) a constant with a magnitude of (3/2)VIcos f
(c) time-varying with an average value of (3/2) VIcos f and a frequency of 100 Hz.
(d) time-varying with an average value of VIcos f 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
the steady state value x x t = lim , given the initial state value of x(0) = [10
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 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
1.22. An op-amp has an open-loop gain of 10 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 and a ).
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 œ 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 (in volts/metre) at the point (1,1,0) due to a point charge of +1 C located at (-1,1,1) (coordinates in metres)is
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 exist
(b) can have an unlimited number of branches
(c) can only have at most N branches
(d) can have a minimum number of branches not decided by N
2.3. Consider the star network shown in Fig.P2.3. The resistance between terminals A and B with C open is 6 , between terminals B and C with A open is 11 , and between terminals C and A with B open is 9 . Then
(a) 4 , 2 , 5 R R R = = = (b) 2 , 4 , 7 R R R = = =
(c) 3 , 3 , 4 R R R = = = (d) 5 , 1 , 10 R R R = = =
2.4. Given the potential function in free space to be V(x) =
the magnitude (in volts/metre) and the direction of the electric field at a point (1,-1,1), where the dimensions are in metres, are
(a) 100; (i + j + k) (b) 100
3 ;(i - j + k)
(c) 100
3 ;[(-i œ j œ k)/ 3 ] (d) 100 3 ;[(i œ j œ k)/ 3 ]
2.5. The hysteresis loop of a magnetic material has an area of 5 cm with the scales given as 1 cm = 2 AT and 1 cm = 50 mWb. At 50 Hz, the total hysteresis loss is
(a) 15 W (b) 20 W (c) 25 W (d) 50 W
2.6. An electric motor with ”constant output power‘ will have a torque speed
characteristic in the form of a
(a) straight line through the origin
(b) straight line parallel to the speed axis
(c) circle about the origin (d) rectangular hyperbola
2.7. A 3-phase transformer has rating of 20 MVA, 220 kV (star) œ 33 kV (delta) with leakage reactance of 12%. The transformer reactance (in ohms) referred to each phase of the L.V. delta-connected side is
(a) 23.5 (b) 19.6 (c) 18.5 (d) 8.7
2.8. A 75 NVA, 10 kV synchronous generator has X = 0.4 p.u. The X value (in p.u.)
is a base of 100 MVA, 11 kV is
(a) 0.578 (b) 0.279 (c) 0.412 (d) 0.44
2.9. A star-connected 440 V, 50 Hz alternators has per phase synchronous reactance of 10 . It supplies a balanced capacitive load current of 20 A, as shown in the per phase equivalent circuit of Fig.2.9. It is desirable to have zero voltage regulation. The load power factor should be
(a) 0.82 (b) 0.47 (c) 0.39 (d) 0.92
2.10. A 240 V single-phase ac source is connected to a load with an impedance of 10 60° . A capacitor is connected in parallel with the load. If the capacitor supplies 1250 VAR, the real power supplied by the source is
(a) 3600 W (b) 2880 W (c) 2400 W (d) 1200 W
2.11. A 50 Hz alternator is rated 500 MVA, 20 kV, with X = 1.0 per unit and
” = X 0.2 per unit. It supplies a purely resistive load of 400 MW at 20 kV. The load is connected directly across the generator terminals when a symmetrical fault occurs at the load terminals. The initial rms current in the generator in per unit is
(a) 7.22 (b) 6.4 (c) 3.22 (d) 2.2
2.12. Consider the model shown in Fig.P2.12 of a transmission line with a series capacitor at its mid-point. The maximum voltage on the line is at the location
2.13. A power system has two synchronous generators. The Governor-turbine characteristics corresponding to the generators are
P = 50(50 œ f), P = 100(51 œ f)
Where f denotes the system frequency in Hz, and P and P are, respectively, the power outputs (in MW) of turbines 1 and 2. assuming the generators and
transmission network to be lossless, the system frequency for a total load of 400 MW is
(a) 47.5 Hz (b) 48.0 Hz (c) 48.5 Hz (d) 49.0 Hz
2.14. The conductors of a 10 km long, single phase, two wire line are separated by a distance of 1.5m. The diameter of each conductor is 1 cm. If the conductors are of copper, the inductance of the circuit is
(a) 50.0 mH (b) 45.3 mH (c) 23.8 mH (d) 19.6 mH
2.15. Given the relationship between the input u(t) and the output y(t) to be
2.16. The asymptotic approximation of the log-magnitude versus frequency plot of a minimum phase system with real poles and one zero is shown in Fig.P2.16. Its transfer functions is
2.17. A 100 A ammeter has an internal resistance of 100 . For extending its range to measure 500 A, the shunt required is of resistance (in )
(a) 20.0 (b) 22.22 (c) 25.0 (d) 50.0
2.18. Resistances R and R have, respectively, nominal values of 10 and 5 , and tolerances of ±5% and ±10%. The range of values for the parallel combination of R and R is
(a) 3.077 to 3.636 (b) 2.805 to 3.371
(c) 3.237 to 3.678 (d) 3.192 to 3.435
2.19. For the oscillator circuit shown in Fig.P2.19, the expression for the time period of oscillation can be given by (where t =RC)
(a) t ln 3
(b) 2 t ln 3 -
(c) t ln 2
(d) 2 t ln 2
2.20. An Intel 8085 processor is executing the program given below.
MVI A, 10H
MVI B, 10H
BACK: NOP
ADD B
RLC
JNC BACK
HLT
The number of times that the operation NOP will be executed is equal to
(a) 1 (b) 2 (c) 3 (d) 4
2.21. A sample-and-hold (S/H) circuit, having a holding capacitor of 0.1 nF, is used at the input of an ADC (analog-to-digital converter). The conversion time of the ADC is 1 sec, and during this time, the capacitor should not lose more than 0.5% of the charge put across it during the sampling time. The maximum value of the input signal to the S/H circuit is 5V. The leakage current of the S/H circuit should be less than
(a) 2.5 mA (b) 0.25 mA (c) 25.0 A (d) 2.5 A
2.22. An op-amp, having a slew rate of 62.8 V/ sec, is connected in a voltage follower configuration. If the maximum amplitude of the input sinusoid is 10V, then the minimum frequency at which the slew rate limited distortion would set in at the output is
(a) 1.0 MHz (b) 6.28 MHz (c) 10.0 MHz (d) 62.8 MHz
2.23. An n-channel JFET, having a pinch-off voltage (V ) of œ5 V, shows a trans-p conductance (g ) of 1 mA/V when the applied gate-to-source voltage (V ) is m GS
3V. Its maximum transconductance (in mA/V) is
(a) 1.5 (b) 2.0 (c) 2.5 (d) 3.0
2.24. A half-wave thyristor converter supplies a purely inductive load, as shown in Fig.2.24. If the triggering angle of the thyristor is 120°, the extinction angle will be
(a) 240°
(b) 180°
(c) 200°
(d) 120°
2.25. A single-phase full-bridge voltage source inverter feeds a purely inductive load, as shown in Fig.P2.25, where T , T , T , T are 3
power transistors and D , D , D , D are L feedback diodes. The inverter is operated in square-wave mode with a frequency of 50 Hz. If the average load current is zero, what -
T D is the time duration of conduction of each D
T feedback diode in a cycle?
(a) 5 msec (b) 10 msec
(c) 20 msec (d) 2.5 msec
SECTION – B
This section consists of TWENTY questions of FIVE marks each. ANY FIFTEEN out of them have to be answered. If more number of questions are attempted, score off the answers not be evaluated, else, only the first fifteen unscored answers will be considered.
3. Determine the resonance frequency and the Q-factor of the circuit shown in Fig.P3. Data: R = 10 , C= 3 F, L = 40 mH, L = 10 mH and M = 10 mH
4. An ideal transformer has a linear B/H characteristic with a finite slope and a turns ratio of 1:1. The primary of the transformer is energized with an ideal current source, producing the signal i as shown in Fig.P4. Sketch the shape (neglecting the scale factor) of the following signals, labeling the time axis clearly:
(a) the core flux f with the secondary of the transformer open
(b) the open-circuited secondary terminal voltage v (t)
(c) the short-circuited secondary current i (t), and
(d) the core flux f with the secondary of the transformer short-circuited.
5. Consider the voltage waveform , shown
in Fig.P5. Find.
(a) the dc component of ,
(b) the amplitude of the fundamental
component of , and 0 3 t(ms) 5 8 10 13
(c) the rms value of the ac part of .
6. In a dc motor running at 2000 rpm, the hysteresis and eddy current losses are 500W and 200W respectively. If the flux remains constant, calculate the speed at which the total iron losses are halved.
7. A dc series motor is rated 230V, 1000 rpm, 80 A (refer to Fig.P7). the series field resistance is 0.11 , and the armature resistance is 0.14 . If the flux at an armature current of 20A is 0.4 times of that under rated condition, calculate the speed at this reduced armature current of 20A.
8. A 50 kW synchronous motor is tested by driving it by another motor. When the excitation is not switched on, the driving motor takes 800W. When the armature is short-circuited and the rated armature current of 10 A is passed through it, the driving motor requires 2500 W. On open-circuiting the armature with rated excitation, the driving motor takes 1800W. Calculate the efficiency of the
synchronous motor at 50% load. Neglect the losses in the driving motor.
9. Two identical synchronous generators, each of 100 MVA, are working in parallel supplying 100 MVA at 0.8 lagging p.f. at rated voltage. Initially the machines are sharing load equally. If the field current of first generator is reduced by 5% and of the second generator increased by 5%, find the sharing of load (MW and MVAR) between the generators. Assume X = X = 0.8 p.u., no field saturation and rated voltage across load. Reasonable approximations may be made.
10. A 132 kV transmission line AB is connected to a cable BC. The characteristic impedances of the overhead line and the cable are 400 and 80 respectively. Assume that these are purely resistive. A 250 kV switching surge travels from A to B.
(a) Calculate the value of this voltage surge when it first reaches C.
(b) Calculate the value of the reflected component of this surge when the first reflection reaches A.
(c) Calculate the surge current in the cable BC.
11. For the Y-bus matrix given in per unit values, where the first, second, third and fourth row refers to bus 1, 2, 3 and 4 respectively, draw the reactance diagram.
» ÿ – 6 2 2.5 0
… Ÿ
2 10 2.5 4 -
… Ÿ Y j =
… Ÿ bus 2.5 2.5 9 4 -
… Ÿ
… Ÿ 0 4 4 8 – /
12. A synchronous generator is connected to an infinite bus through a lossless double circuit transmission line. The generator is delivering 1.0 per unit power at a load angle of 30° when a sudden fault reduces the peak power that can be transmitted to 0.5 per unit. After clearance of fault, the peak power that can be transmitted becomes 1.5 per unit. Find the critical clearing angle.
13. A single line-to-ground fault occurs on an unloaded generator in phase a positive, negative, and zero sequence impedances of the generator are j0.25 p.u., j0.25p.u., and j0.15 p.u. respectively. The generator neutral is grounded through
a reactance of j0.05 p.u. The prefault generator terminal voltage is 1.0 p.u.
(a) Draw the positive, negative, and zero sequence networks for the fault given.
(b) Draw the interconnection of the sequence networks for the fault analysis.
(c) Determine the fault current.
14. A power system has two generators with the following cost curves:
Generator 1: C (P ) = 0.006P + 8P + 350 (Thousand Rupees/Hour) 2
Generator 2: C (P ) = 0.009P + 7P + 400 (Thousand Rupees/Hour) 2
The generator limits are
100 MW = P = 650 MW
50 MW = P = 500 MW
A load demand of 600 MW is supplied by the generators in an optimal manner. Neglecting losses in the transmission network, determine the optimal generation of each generator.
15. A unity feedback system has an open-loop transfer function of
(a) Determine the magnitude of G(j ) in dB at an angular frequency of =20
rad/sec.
(b) Determine the phase margin in degrees.
(c) Determine the gain margin in dB.
(d) Is the system stable or unstable?
16. Given the characteristic equation
Sketch the root locus as K varies from zero to infinity. Find the angle and real axis intercept of the asymptotes, break-away/break-in points, and imaginary axis crossing points, if any.
17. For the ring counter shown in Fig.P17, find the steady state sequence if the initial state of the counters is 1110 (i.e., Q ,number of the counter.
18. For the op-amp circuit shown in Fig.P18, determine the output voltage .
Assume that the op-amps are ideal.
19. The transistor in the amplifier circuit shown in Fig.P19 is biased at I = 1mA. Use
(a) Determine the ac small signal midband voltage gain / of the circuit.
(b) Determine the required value of C for the circuit to have a lower cutoff
frequency of 10 Hz.
20. A simple active filter is shown in Fig.P20. Assume ideal op-amp. Derive the transfer function / of the circuit, and state the type of the filter (i.e., high-pass, low-pass, band-pass, or band-reject). Determine the required values of R , R and C in order for the filter to have a 3-dB frequency of 1 kHz, a high- frequency input resistance of 100 k , and a high frequency gain magnitude of
21. A voltage commutated thyristor chopper circuit is shown in Fig.P21. The chopper is operated at 500 Hz with 50% duty ratio. The load takes a constant current of 20A.
(a) Evaluate the circuit turn off time for the main thyristor Th .
(b) Calculate the value of inductor L, if the peak current through the main
thyristor Th is limited to 180% of the load current.
(c) Calculate the maximum instantaneous output voltage of the chopper.
22. A separately excited dc motor is controlled by varying its armature voltage using a single phase full-converter bridge as shown in Fig.P22. the field current is kept constant at the rated value. The motor has an armature resistance of 0.2 , and the motor voltage constant is 2.5 V/(rad/sec). The motor is driving a mechanical load having a constant torque of 140 Nm. The triggering angle of the converter is 60°. The armature current can be assumed to be continuous and ripple free.
(a) Calculate the motor armature current
(b) Evaluate the motor speed in rad/sec.
(c) Calculate the rms value of the fundamental component of the input current to the bridge.
1. This question consists of TWENTY-FIVE sub-questions (1.1 œ 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 and L , their mutual inductance M satisfies
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
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) maximum supply voltage (d) 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 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?
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 VIcos f
(b) a constant with a magnitude of (3/2)VIcos f
(c) time-varying with an average value of (3/2) VIcos f and a frequency of 100 Hz.
(d) time-varying with an average value of VIcos f 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
the steady state value x x t = lim , given the initial state value of x(0) = [10
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 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
1.22. An op-amp has an open-loop gain of 10 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 and a ).
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 œ 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 (in volts/metre) at the point (1,1,0) due to a point charge of +1 C located at (-1,1,1) (coordinates in metres)is
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 exist
(b) can have an unlimited number of branches
(c) can only have at most N branches
(d) can have a minimum number of branches not decided by N
2.3. Consider the star network shown in Fig.P2.3. The resistance between terminals A and B with C open is 6 , between terminals B and C with A open is 11 , and between terminals C and A with B open is 9 . Then
(a) 4 , 2 , 5 R R R = = = (b) 2 , 4 , 7 R R R = = =
(c) 3 , 3 , 4 R R R = = = (d) 5 , 1 , 10 R R R = = =
2.4. Given the potential function in free space to be V(x) =
the magnitude (in volts/metre) and the direction of the electric field at a point (1,-1,1), where the dimensions are in metres, are
(a) 100; (i + j + k) (b) 100
3 ;(i - j + k)
(c) 100
3 ;[(-i œ j œ k)/ 3 ] (d) 100 3 ;[(i œ j œ k)/ 3 ]
2.5. The hysteresis loop of a magnetic material has an area of 5 cm with the scales given as 1 cm = 2 AT and 1 cm = 50 mWb. At 50 Hz, the total hysteresis loss is
(a) 15 W (b) 20 W (c) 25 W (d) 50 W
2.6. An electric motor with ”constant output power‘ will have a torque speed
characteristic in the form of a
(a) straight line through the origin
(b) straight line parallel to the speed axis
(c) circle about the origin (d) rectangular hyperbola
2.7. A 3-phase transformer has rating of 20 MVA, 220 kV (star) œ 33 kV (delta) with leakage reactance of 12%. The transformer reactance (in ohms) referred to each phase of the L.V. delta-connected side is
(a) 23.5 (b) 19.6 (c) 18.5 (d) 8.7
2.8. A 75 NVA, 10 kV synchronous generator has X = 0.4 p.u. The X value (in p.u.)
is a base of 100 MVA, 11 kV is
(a) 0.578 (b) 0.279 (c) 0.412 (d) 0.44
2.9. A star-connected 440 V, 50 Hz alternators has per phase synchronous reactance of 10 . It supplies a balanced capacitive load current of 20 A, as shown in the per phase equivalent circuit of Fig.2.9. It is desirable to have zero voltage regulation. The load power factor should be
(a) 0.82 (b) 0.47 (c) 0.39 (d) 0.92
2.10. A 240 V single-phase ac source is connected to a load with an impedance of 10 60° . A capacitor is connected in parallel with the load. If the capacitor supplies 1250 VAR, the real power supplied by the source is
(a) 3600 W (b) 2880 W (c) 2400 W (d) 1200 W
2.11. A 50 Hz alternator is rated 500 MVA, 20 kV, with X = 1.0 per unit and
” = X 0.2 per unit. It supplies a purely resistive load of 400 MW at 20 kV. The load is connected directly across the generator terminals when a symmetrical fault occurs at the load terminals. The initial rms current in the generator in per unit is
(a) 7.22 (b) 6.4 (c) 3.22 (d) 2.2
2.12. Consider the model shown in Fig.P2.12 of a transmission line with a series capacitor at its mid-point. The maximum voltage on the line is at the location
2.13. A power system has two synchronous generators. The Governor-turbine characteristics corresponding to the generators are
P = 50(50 œ f), P = 100(51 œ f)
Where f denotes the system frequency in Hz, and P and P are, respectively, the power outputs (in MW) of turbines 1 and 2. assuming the generators and
transmission network to be lossless, the system frequency for a total load of 400 MW is
(a) 47.5 Hz (b) 48.0 Hz (c) 48.5 Hz (d) 49.0 Hz
2.14. The conductors of a 10 km long, single phase, two wire line are separated by a distance of 1.5m. The diameter of each conductor is 1 cm. If the conductors are of copper, the inductance of the circuit is
(a) 50.0 mH (b) 45.3 mH (c) 23.8 mH (d) 19.6 mH
2.15. Given the relationship between the input u(t) and the output y(t) to be
2.16. The asymptotic approximation of the log-magnitude versus frequency plot of a minimum phase system with real poles and one zero is shown in Fig.P2.16. Its transfer functions is
2.17. A 100 A ammeter has an internal resistance of 100 . For extending its range to measure 500 A, the shunt required is of resistance (in )
(a) 20.0 (b) 22.22 (c) 25.0 (d) 50.0
2.18. Resistances R and R have, respectively, nominal values of 10 and 5 , and tolerances of ±5% and ±10%. The range of values for the parallel combination of R and R is
(a) 3.077 to 3.636 (b) 2.805 to 3.371
(c) 3.237 to 3.678 (d) 3.192 to 3.435
2.19. For the oscillator circuit shown in Fig.P2.19, the expression for the time period of oscillation can be given by (where t =RC)
(a) t ln 3
(b) 2 t ln 3 -
(c) t ln 2
(d) 2 t ln 2
2.20. An Intel 8085 processor is executing the program given below.
MVI A, 10H
MVI B, 10H
BACK: NOP
ADD B
RLC
JNC BACK
HLT
The number of times that the operation NOP will be executed is equal to
(a) 1 (b) 2 (c) 3 (d) 4
2.21. A sample-and-hold (S/H) circuit, having a holding capacitor of 0.1 nF, is used at the input of an ADC (analog-to-digital converter). The conversion time of the ADC is 1 sec, and during this time, the capacitor should not lose more than 0.5% of the charge put across it during the sampling time. The maximum value of the input signal to the S/H circuit is 5V. The leakage current of the S/H circuit should be less than
(a) 2.5 mA (b) 0.25 mA (c) 25.0 A (d) 2.5 A
2.22. An op-amp, having a slew rate of 62.8 V/ sec, is connected in a voltage follower configuration. If the maximum amplitude of the input sinusoid is 10V, then the minimum frequency at which the slew rate limited distortion would set in at the output is
(a) 1.0 MHz (b) 6.28 MHz (c) 10.0 MHz (d) 62.8 MHz
2.23. An n-channel JFET, having a pinch-off voltage (V ) of œ5 V, shows a trans-p conductance (g ) of 1 mA/V when the applied gate-to-source voltage (V ) is m GS
3V. Its maximum transconductance (in mA/V) is
(a) 1.5 (b) 2.0 (c) 2.5 (d) 3.0
2.24. A half-wave thyristor converter supplies a purely inductive load, as shown in Fig.2.24. If the triggering angle of the thyristor is 120°, the extinction angle will be
(a) 240°
(b) 180°
(c) 200°
(d) 120°
2.25. A single-phase full-bridge voltage source inverter feeds a purely inductive load, as shown in Fig.P2.25, where T , T , T , T are 3
power transistors and D , D , D , D are L feedback diodes. The inverter is operated in square-wave mode with a frequency of 50 Hz. If the average load current is zero, what -
T D is the time duration of conduction of each D
T feedback diode in a cycle?
(a) 5 msec (b) 10 msec
(c) 20 msec (d) 2.5 msec
SECTION – B
This section consists of TWENTY questions of FIVE marks each. ANY FIFTEEN out of them have to be answered. If more number of questions are attempted, score off the answers not be evaluated, else, only the first fifteen unscored answers will be considered.
3. Determine the resonance frequency and the Q-factor of the circuit shown in Fig.P3. Data: R = 10 , C= 3 F, L = 40 mH, L = 10 mH and M = 10 mH
4. An ideal transformer has a linear B/H characteristic with a finite slope and a turns ratio of 1:1. The primary of the transformer is energized with an ideal current source, producing the signal i as shown in Fig.P4. Sketch the shape (neglecting the scale factor) of the following signals, labeling the time axis clearly:
(a) the core flux f with the secondary of the transformer open
(b) the open-circuited secondary terminal voltage v (t)
(c) the short-circuited secondary current i (t), and
(d) the core flux f with the secondary of the transformer short-circuited.
5. Consider the voltage waveform , shown
in Fig.P5. Find.
(a) the dc component of ,
(b) the amplitude of the fundamental
component of , and 0 3 t(ms) 5 8 10 13
(c) the rms value of the ac part of .
6. In a dc motor running at 2000 rpm, the hysteresis and eddy current losses are 500W and 200W respectively. If the flux remains constant, calculate the speed at which the total iron losses are halved.
7. A dc series motor is rated 230V, 1000 rpm, 80 A (refer to Fig.P7). the series field resistance is 0.11 , and the armature resistance is 0.14 . If the flux at an armature current of 20A is 0.4 times of that under rated condition, calculate the speed at this reduced armature current of 20A.
8. A 50 kW synchronous motor is tested by driving it by another motor. When the excitation is not switched on, the driving motor takes 800W. When the armature is short-circuited and the rated armature current of 10 A is passed through it, the driving motor requires 2500 W. On open-circuiting the armature with rated excitation, the driving motor takes 1800W. Calculate the efficiency of the
synchronous motor at 50% load. Neglect the losses in the driving motor.
9. Two identical synchronous generators, each of 100 MVA, are working in parallel supplying 100 MVA at 0.8 lagging p.f. at rated voltage. Initially the machines are sharing load equally. If the field current of first generator is reduced by 5% and of the second generator increased by 5%, find the sharing of load (MW and MVAR) between the generators. Assume X = X = 0.8 p.u., no field saturation and rated voltage across load. Reasonable approximations may be made.
10. A 132 kV transmission line AB is connected to a cable BC. The characteristic impedances of the overhead line and the cable are 400 and 80 respectively. Assume that these are purely resistive. A 250 kV switching surge travels from A to B.
(a) Calculate the value of this voltage surge when it first reaches C.
(b) Calculate the value of the reflected component of this surge when the first reflection reaches A.
(c) Calculate the surge current in the cable BC.
11. For the Y-bus matrix given in per unit values, where the first, second, third and fourth row refers to bus 1, 2, 3 and 4 respectively, draw the reactance diagram.
» ÿ – 6 2 2.5 0
… Ÿ
2 10 2.5 4 -
… Ÿ Y j =
… Ÿ bus 2.5 2.5 9 4 -
… Ÿ
… Ÿ 0 4 4 8 – /
12. A synchronous generator is connected to an infinite bus through a lossless double circuit transmission line. The generator is delivering 1.0 per unit power at a load angle of 30° when a sudden fault reduces the peak power that can be transmitted to 0.5 per unit. After clearance of fault, the peak power that can be transmitted becomes 1.5 per unit. Find the critical clearing angle.
13. A single line-to-ground fault occurs on an unloaded generator in phase a positive, negative, and zero sequence impedances of the generator are j0.25 p.u., j0.25p.u., and j0.15 p.u. respectively. The generator neutral is grounded through
a reactance of j0.05 p.u. The prefault generator terminal voltage is 1.0 p.u.
(a) Draw the positive, negative, and zero sequence networks for the fault given.
(b) Draw the interconnection of the sequence networks for the fault analysis.
(c) Determine the fault current.
14. A power system has two generators with the following cost curves:
Generator 1: C (P ) = 0.006P + 8P + 350 (Thousand Rupees/Hour) 2
Generator 2: C (P ) = 0.009P + 7P + 400 (Thousand Rupees/Hour) 2
The generator limits are
100 MW = P = 650 MW
50 MW = P = 500 MW
A load demand of 600 MW is supplied by the generators in an optimal manner. Neglecting losses in the transmission network, determine the optimal generation of each generator.
15. A unity feedback system has an open-loop transfer function of
(a) Determine the magnitude of G(j ) in dB at an angular frequency of =20
rad/sec.
(b) Determine the phase margin in degrees.
(c) Determine the gain margin in dB.
(d) Is the system stable or unstable?
16. Given the characteristic equation
Sketch the root locus as K varies from zero to infinity. Find the angle and real axis intercept of the asymptotes, break-away/break-in points, and imaginary axis crossing points, if any.
17. For the ring counter shown in Fig.P17, find the steady state sequence if the initial state of the counters is 1110 (i.e., Q ,number of the counter.
18. For the op-amp circuit shown in Fig.P18, determine the output voltage .
Assume that the op-amps are ideal.
19. The transistor in the amplifier circuit shown in Fig.P19 is biased at I = 1mA. Use
(a) Determine the ac small signal midband voltage gain / of the circuit.
(b) Determine the required value of C for the circuit to have a lower cutoff
frequency of 10 Hz.
20. A simple active filter is shown in Fig.P20. Assume ideal op-amp. Derive the transfer function / of the circuit, and state the type of the filter (i.e., high-pass, low-pass, band-pass, or band-reject). Determine the required values of R , R and C in order for the filter to have a 3-dB frequency of 1 kHz, a high- frequency input resistance of 100 k , and a high frequency gain magnitude of
21. A voltage commutated thyristor chopper circuit is shown in Fig.P21. The chopper is operated at 500 Hz with 50% duty ratio. The load takes a constant current of 20A.
(a) Evaluate the circuit turn off time for the main thyristor Th .
(b) Calculate the value of inductor L, if the peak current through the main
thyristor Th is limited to 180% of the load current.
(c) Calculate the maximum instantaneous output voltage of the chopper.
22. A separately excited dc motor is controlled by varying its armature voltage using a single phase full-converter bridge as shown in Fig.P22. the field current is kept constant at the rated value. The motor has an armature resistance of 0.2 , and the motor voltage constant is 2.5 V/(rad/sec). The motor is driving a mechanical load having a constant torque of 140 Nm. The triggering angle of the converter is 60°. The armature current can be assumed to be continuous and ripple free.
(a) Calculate the motor armature current
(b) Evaluate the motor speed in rad/sec.
(c) Calculate the rms value of the fundamental component of the input current to the bridge.
GATE EE – 2005 Electrical Engineering Question Paper
Q.1 – Q.30 carry one mark each.
1. In Fig.Q1, the value of R is
(a) 2.5
(b) 5.0
(c) 7.5
(d) 10.0
2. The RMS value of the voltage
(a) 17V
(b) 5V
(c) 7V
(d) 3 2 2 V +
3. For the two-port network shown in Fig.Q3, the Z-matrix is given by
4. In Fig.Q4, the initial capacitor voltage is zero. The switch is closed at t = 0. the final steady-state voltage across the capacitor is:
(a) 20V
(b) 10V
(c) 5V
(d) 0V
5. If is the electric field intensity, . is equal to E × E
(a) (b) E E
(c) null vector (d) zero
6. A system with zero initial conditions has the closed loop transfer function
( ) ( )( ) 2 s + 4 .
T s s s = + + The system output is zero at the frequency
(a) 0.5 rad/sec. (b) 1 rad/sec. (c) 2 rad/sec. (d) 4 rad/sec.
7. Fig.Q7 shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is:
8. The gain margin of a unity feedback control system with the open loop transfer function G s = is:
9. 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:
(a) Augmented matrix [P q] must have the same rank as matrix P
(b) Vector q must have only non-zero elements
(c) Matrix P must be singular
(d) Matrix P must be square
10. If P and Q are two random events, then the following is TRUE:
(a) Independence of P and Q implies that probability P Q n = 0
(b) Probability P Q = Probability (P) + Probability (Q)
(c) If P and Q are mutually exclusive, then they must be independent
(d) Probability P Q n = Probability (P)
11. If S x dx = , then S has the value – 3
(a) 1 (b) 1
3 4 (c) 1 2 (d) 1
12. The solution of the first order differential equation x t x t x x = – = 3 , 0 is:
13. The equivalent circuit of a transformer has leakage reactance X X , and ‘
magnetizing reactance . X Their magnitudes satisfy
14. Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and corresponding input line voltages
(a) Star – Star (b) Star – Delta (c) Delta – Delta (d) Delta – Zigzag
15. On the torque/speed curve of induction motor shown in Fig.Q15, four points of operation are market as W, X, Y and Z. Which one of them represents the operation at a slip greater than 1?
(a) W (b) X (c) Y (d) Z
16. For an induction motor, operating at a slip s, the ratio of gross power output to air gap power is equal to:
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
(a) 4, 0.4 (b) 100, 10 (c) 4, 10 (d) 100, 0.4
18. An 800 kV transmission line has a maximum power transfer capacity on the operated at 400 kV with the series reactance unchanged, the new maximum power transfer capacity is approximately
P (d) 4 P
(a) P (b) 2P (c) 2
19. The insulation strength of an EHV transmission line is mainly governed by
(a) load power factor (b) switching over-voltages
(c) harmonics (d) corona
20. High Voltage DC (HVDC) transmission is mainly used for
(a) bulk power transmission over very long distances
(b) inter-connecting two systems with the same nominal frequency
(c) eliminating reactive power requirement in the operation
(d) minimizing harmonics at the converter stations
21. The Q-meter works on the principle of
(a) mutual inductance (b) self inductance
(c) series resonance (d) parallel resonance
22. A PMMC voltmeter is connected across a series combination of a DC voltage source V V = 2 and an AC voltage source t t V = 3 sin 4 . The meter reads
(a) 2V (b) 5V (c) 3 2 2 V + (d) 17
23. Assume that D D in Fig.Q23 are ideal diodes. The value of current I is: and
(a) 0 mA
(b) 0.5 mA
(c) 1 mA
(d) 2 mA
24. The 8085 assembly language instruction that stores the contents of H and L registers into the memory locations 2050 and 2051 , respectively, is:
H H
(a) SPHL 2050 (b) SPHL 2051 (c) SHLD 2050 (d) STAX 2050
25. Assume that the N-channel MOSFET shown in Fig.Q25 is ideal, and that its threshold voltage is +1.0V. The voltage V between nodes a and b is:
(a) 5V
(b) 2V
(c) 1V
(d) 0V
26. The digital circuit shown in Fig.Q26 works as a
(a) JK flip-flop
(b) Clocked RS flip-flop
(c) T flip-flop
(d) Ring counter
27. A digital-to-analog converter with a full-scale output voltage of 3.5V has a resolution close to 14 mV. Its bit size is:
(a) 4 (b) 8 (c) 16 (d) 32
28. The conduction loss versus device current characteristic of a power MOSFET is best approximated by
(a) a parabola (b) a straight line
(c) a rectangular hyperbola
(d) an exponentially decaying function
29. A three-phase diode bridge rectifier is fed from a 400V RMS, 50 Hz, three-phase AC source. If the load is purely resistive, the peak instantaneous output voltage is equal to
(a) 400 V (b) 400 2 V (c) 2 400 V
3 V (d) 400 3
30. The output voltage waveform of a three-phase square-wave inverter contains
(a) only even harmonics (b) both odd and even harmonics
(c) only odd harmonics (d) only triplen harmonics
Q.31 – Q.80 carry two m arks each
31. The RL circuit of Fig.Q31 is fed from a constant magnitude, variable frequency sinusoidal voltage source . At 100 Hz, the R and L elements each have a I N voltage drop . u If the frequency of the source is changed to 50 Hz, the new R M S voltage drop across R is:
32. For the three-phase circuit shown in Fig.Q32, the ratio of the current : : I I I is given by (a) 1 : 1: 3 (b) 1:1:2
(c) 1:1:0 (d) 1:1: 3
33. For the triangular waveform shown in Fig.Q33, the RMS value of the voltage is equal to
(a) 1
6 (b) 1 3 (c) 1 3 (d) 2 3
34. The circuit shown in Fig.Q34 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
10
(a) 0 A
(b) 0.5 A
(c) 1 A
(d) 2 A
35. The charge distribution in a metal-dielectric-semiconductor specimen is shown in Fig.Q35. The negative charge density decreases linearly in the semiconductor as shown. The electric field distribution is as shown in
Metal Semiconductor Dielectric
36. In Fig.Q36, the Thevenin‘s equivalent pair (voltage, impedance), as seen at the terminals P-Q, is given by
(a) (2V, 5 )
(b) (2V, 7.5 )
(c) (4V, 5 )
(d) (4V, 7.5 )
37. A unity feedback system, having an open loop gain
K s 1 , – ( ) ( ) ( )
G s H s s = + becomes stable when ( )
1
(a) 1 K > (b) K >1 (c) 1 K < (d) K < -1
38. When subjected to a unit step input, the closed loop control system shown in Fig.Q38 will have a steady state error of
(a) -1.0 (b) -0.5 (c) 0 (d) 0.5
39. In the GH(s) plane, the Nyquist plot of the loop transfer function
G s H s s = passes through the negative real axis at the point
(a) (-0.25,j0) (b) (-0.5,j0) (c) (-1,j0) (d) (-2,j0)
40. If the compensated system shown in Fig.Q40 has a phase margin of 60° at the crossover frequency of 1 rad/sec, the value of the gain K is:
(a) 0.366
(b) 0.732
(c) 1.366
(d) 2.738
41. For the matrix
42. If
» ÿ 1 0 1 -
… Ÿ
R = – 2 1 1 , the top row of R is: – 1
… Ÿ
… Ÿ 2 3 2 /
» ÿ
(a) 5 6 4 » ÿ » ÿ – » ÿ – 2 1 2 – / (b) 5 3 1 / (c) 2 0 1 / (d) 1 … Ÿ
/
43. A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is:
(a) 1
8 (b) 1 2 (c) 3 8 (d) 3 4
44. For the function fx x e = x , the maximum occurs when x is equal to: 2 -
(a) 2 (b) 1 (c) 0 (d) -1
45. For the scalar field, the magnitude of the gradient at the point (1,3) is:
(a) 13
9 (b) 9 2 (c) 5 (d) 9
solution approaches the following values at
(a) 0 (b) 5
2 (c) 5 (d) 10
47. The Laplace transform of a function f(t) is
48. The Fourier series for the function fx x = sin is: 2
(a) x x + – x sin sin2 (b) 1 cos2
x x + – x (c) sin2 cos2 (d) 0.5 0.5 cos2
49. If is the unit step and is the unit impulse function, the inverse z-
F z z = + k = transform of for 0 is:
(a) 1 (b) 1 (c) 1 (d) 1
50. Two magnetic poles revolve around a stationary armature carrying two coils as shown in Fig.Q50. 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 coil sides and .
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
(a) 25 kW in (i) and 75 kW in (ii) (b) 25 kW in (i) and 50 kW in (ii)
(c) 50 kW in (i) and 75 kW in (ii) (d) 50 kW in (i) and 50 kW in (ii)
52. In relation to DC machines, match the following and choose the correct
combination.
Group œ1 Group œ 2
Performance Variables Proportional to
(P) Armature emf (E) (1) Flux ( ), speed ( ) and armature current ( )
(Q) Developed torque (T) (2) and only
(R) Developed power (P) (3) and only
(4) and only(A) P – 3 Q – 3 R – 1
(B) P – 2 Q – 5 R – 4
(C) P – 3 Q – 5 R – 4
(D) P – 2 Q – 3 R – 1
53. In relation to the synchronous machines, which one of the following statements is false?
(a) In salient pole machines, the direct-axis synchronous reactance is greater than the quadrature-axis synchronous reactance
(b) The damper bars help the synchronous motor self-start
(c) Short circuit ratio is the ratio of the field current required to produce the
rated voltage on open circuit to the rated armature current
(d) The V-curve of a synchronous motor represents the variation in the armature current with field excitation, at a given output power
54. Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value,
(a) the speed decreases and the stator current increases
(b) both the speed and the stator current decrease
(c) the speed and the stator current remain practically constant
(d) there is negligible change in the speed but the stator current decreases
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%, the ratio of the starting developed torque to the full load torque is approximately equal to
(a) 0.24 (b) 1.44 (c) 2.40 (d) 6.00
56. In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve
(a) low starting torque (b) quick acceleration
(c) high efficiency (d) reduced size
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-
synchronous 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.
(a) Both [a] and [r] are true and [r] is the correct reason for [a]
(b) Both [a] and [r] are true but [r] is not the correct reason for [a]
(c) Both [a] and [r] are false
(d) [a] is true but [r] is false
58. The parameters of a transposed overhead transmission line are given as:
x km km = = Self reactance 0.5 / and Mutual reactance x 0.1 /
The positive sequence reactance and zero sequence reactance ,
respectively, in /km are
(a) 0.3, 0.2 (b) 0.5, 0.2 (c) 0.5, 0.6 (d) 0.3, 0.6
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
(a) 0.85 lag (b) 1.00 lag (c) 0.80 lag (d) 0.90 lag
60. The network shown in Fig.Q60 has impedances in p.u. as indicated. The diagonal element of the bus admittance matrix of the network is:
(a) -j19.8 (b) +j20.0 (c) +j0.2 (d) -j19.95
61. A load centre is at an equidistant from the two thermal generating stations G and G as shown in Fig.Q61. The fuel cost characteristics of the generating stations are given by
Load F a bP cP = + + 2 2 Rs/hour
where and are the generation in MW of and , respectively. For most
economic generation to meet 300 MW of load, and , respectively, are
(a) 150, 150 (b) 100, 200 (c) 200, 100 (d) 175, 125
62. Two networks are connected in cascade as shown in Fig.Q62. With the usual notations the equivalent A, B, C and D constants are obtained. Given that
Z C = ° 0.025 45 , the value of is:
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 bas as shown in Fig.Q63. 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, the resulting steady state stability power limit in p.u. will be
(a) 12.5 p.u.
(b) 3.125 p.u.
(c) 10.0 p.u.
(d) 5.0 p.u.
64. The simultaneous application of signals and to the horizontal and
vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-8 display. If P and Q are constants, and sin 4 30 , then is equal to
(a) sin 4 30 (b) sin 2 15 (c) sin 8 60 (d) sin 4 30
65. A DC ammeter has a resistance of 0.1 and its current range is 0 œ 100A. If the range is to be extended to 0 œ 500A, the meter requires the following shunt resistance:
(a) 0.010 (b) 0.011 (c) 0.025 (d) 1.0
66. The set-up in Fig.Q66 is used to measure resistance R. The ammeter and voltmeter resistances are 0.01 and 2000 , respectively. Their readings are 2A and 180V, respectively, giving a measured resistance of 90 . The percentage error in the measurement is:
(a) 2.25% (b) 2.35%
(c) 4.5% (d) 4.71%
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 and 6 M , respectively, as shown in Fig.Q67. A voltmeter with resistance 50 K is used to measure the insulation of the cable. When connected between the positive core and earth, the voltmeter reads
(a) 8 V (b) 16 V (c) 24 V (d) 40 V
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 œ2.5 kW,
respectively. The total power and the power factor, respectively, are
(a) 13.0 kW, 0.334 (b) 13.0 kW, 0.684
(c) 8.0 kW, 0.52 (d) 8.0 kW, 0.334
69. The common emitter amplifier shown in Fig.Q69 is R =1k biased using a 1 mA ideal current source. The approximate base current value is:
(a) 0 A
(b) 10 A
(c) 100 A
(d) 1000 A
70. Consider the inverting amplifier, using an ideal operational amplifier shown in Fig.Q70. The designer wishes to realize the input resistance seen by the small-signal source to be as large as possible, while keeping the voltage gain between the upper limit on is 1 M . The value of should be
71. The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in
72. In Fig.Q72, if the input is a sinusoidal signal, the output will appear as shown in
73. Select the circuit, which will produce the given output Q for the input signals and given in Fig.Q73.
74. If and are the inputs to the circuit shown in Fig.Q74, the output Q is:
75. In Fig.Q75, as long as 1 and 1, the output Q remains
(a) at 1
(b) at 0
(c) at its initial value
(d) unstable
76. Fig.Q76 shows the voltage across a power semiconductor device and the current through the device during a switching transition. Is the transition a turn ON transition or a turn OFF transition? What is the energy lost during the transition?
(a) Turn ON,
(b) Turn OFF,
(c) Turn ON,
(d) Turn OFF,
77. An electronic switch S is required to block voltages of either polarity during its OFF state as shown in Fig.Q.77a. This switch is required to conduct in only one direction during its ON state as shown in Fig.Q77b.
Fig.Q77a Fig.Q77b
Which of the following are valid realizations of the switch S?
(a) Only P (b) P and Q (c) P and R (d) R and S
78. Fig.Q78 shows a step-down chopper switched at 1 KHz with a duty ratio D = 0.5.
The peak-peak ripple in the load current is close to
(a) 10 A
(b) 0.5 A
(c) 0.125 A
(d) 0.25 A
79. An electric motor, developing a starting torque of 15 Nm, starts with a load torque of 7 Nm on its shaft. If the acceleration at start is 2 rad/sec , the moment of inertia of the systems must be (neglecting viscous and Coulomb/friction).
(a) 0.25 kg m (b) 0.25 Nm (c) 4 kg m (d) 4 Nm
80. Consider a phase controlled converter shown in Fig.Q.80. The thyristor is fired at an angle in every positive half cycle of the input voltage. If the peak value of the instantaneous output voltage equals 230 V, the firing angle is close to
(a) 45°
(b) 135°
(c) 90°
(d) 83.6°
-
Linked Answer Questions: 81a to Q85b carry two marks each
Statement for Linked Answer Questions 81a & 81b: A coil of inductance 10 H
resistance 40 is connected as shown in Fig.Q81. After the switch S has been in connection with point 1 for a very long time, it is moved to point 2 at t = 0. + 81. (A) If, at t = 0 , the voltage across the coil is 120V, the value of resistance R is:
(a) 0
(b) 20
(c) 40
(d) 60
(B) For the value of R obtained in (a), the time taken for 95% of the stored
energy dissipated is close to
(a) 0.10 sec (b) 0.15 sec (c) 0.50 sec (d) 1.0 sec
Statement for Linked Answer Questions 82a & 82b:
A state variable system
83. The induced emf (line-to-line) is close to (A)
(a) 5.5 kV (b) 7.2 kV (c) 9.6 kV (d) 12.5 kV
The power (or torque) angle is close to (B)
(a) 13.9° (b) 18.3° (c) 24.6° (d) 33.0°
At a 220 kV substation of a Statem ent for Linked Answer Questions 84a & 84b:
power system, it is given that the three-phase fault level is 4000 MVA and single-line to ground fault level is 5000 MVA. Neglecting the resistance and the shunt susceptances of the system,
84. the positive sequence driving point reactance at the bus is: (A)
(a) 2.5 (b) 4.033 (c) 5.5 (d) 12.1
and the zero sequence driving point reactance at the bus is: (B)
(a) 2.2 (b) 4.84 (c) 18.18 (d) 22.72
Assume that the threshold Statem ent for Linked Answer Questions 85a & 85b: voltage of the N-channel MOSFET shown in Fig. Q85 is +0.75V. The output characteristics of the MOSFET are also shown.
85. The transconductance of the MOSFET is: (A)
(a) 0.75 mS (b) 1 mS (c) 2 mS (d) 10 mS
The voltage gain of the amplifier is: (B)
(a) +5 (b) -7.5 (c) +10 (d) -10
1. In Fig.Q1, the value of R is
(a) 2.5
(b) 5.0
(c) 7.5
(d) 10.0
2. The RMS value of the voltage
(a) 17V
(b) 5V
(c) 7V
(d) 3 2 2 V +
3. For the two-port network shown in Fig.Q3, the Z-matrix is given by
4. In Fig.Q4, the initial capacitor voltage is zero. The switch is closed at t = 0. the final steady-state voltage across the capacitor is:
(a) 20V
(b) 10V
(c) 5V
(d) 0V
5. If is the electric field intensity, . is equal to E × E
(a) (b) E E
(c) null vector (d) zero
6. A system with zero initial conditions has the closed loop transfer function
( ) ( )( ) 2 s + 4 .
T s s s = + + The system output is zero at the frequency
(a) 0.5 rad/sec. (b) 1 rad/sec. (c) 2 rad/sec. (d) 4 rad/sec.
7. Fig.Q7 shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is:
8. The gain margin of a unity feedback control system with the open loop transfer function G s = is:
9. 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:
(a) Augmented matrix [P q] must have the same rank as matrix P
(b) Vector q must have only non-zero elements
(c) Matrix P must be singular
(d) Matrix P must be square
10. If P and Q are two random events, then the following is TRUE:
(a) Independence of P and Q implies that probability P Q n = 0
(b) Probability P Q = Probability (P) + Probability (Q)
(c) If P and Q are mutually exclusive, then they must be independent
(d) Probability P Q n = Probability (P)
11. If S x dx = , then S has the value – 3
(a) 1 (b) 1
3 4 (c) 1 2 (d) 1
12. The solution of the first order differential equation x t x t x x = – = 3 , 0 is:
13. The equivalent circuit of a transformer has leakage reactance X X , and ‘
magnetizing reactance . X Their magnitudes satisfy
14. Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and corresponding input line voltages
(a) Star – Star (b) Star – Delta (c) Delta – Delta (d) Delta – Zigzag
15. On the torque/speed curve of induction motor shown in Fig.Q15, four points of operation are market as W, X, Y and Z. Which one of them represents the operation at a slip greater than 1?
(a) W (b) X (c) Y (d) Z
16. For an induction motor, operating at a slip s, the ratio of gross power output to air gap power is equal to:
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
(a) 4, 0.4 (b) 100, 10 (c) 4, 10 (d) 100, 0.4
18. An 800 kV transmission line has a maximum power transfer capacity on the operated at 400 kV with the series reactance unchanged, the new maximum power transfer capacity is approximately
P (d) 4 P
(a) P (b) 2P (c) 2
19. The insulation strength of an EHV transmission line is mainly governed by
(a) load power factor (b) switching over-voltages
(c) harmonics (d) corona
20. High Voltage DC (HVDC) transmission is mainly used for
(a) bulk power transmission over very long distances
(b) inter-connecting two systems with the same nominal frequency
(c) eliminating reactive power requirement in the operation
(d) minimizing harmonics at the converter stations
21. The Q-meter works on the principle of
(a) mutual inductance (b) self inductance
(c) series resonance (d) parallel resonance
22. A PMMC voltmeter is connected across a series combination of a DC voltage source V V = 2 and an AC voltage source t t V = 3 sin 4 . The meter reads
(a) 2V (b) 5V (c) 3 2 2 V + (d) 17
23. Assume that D D in Fig.Q23 are ideal diodes. The value of current I is: and
(a) 0 mA
(b) 0.5 mA
(c) 1 mA
(d) 2 mA
24. The 8085 assembly language instruction that stores the contents of H and L registers into the memory locations 2050 and 2051 , respectively, is:
H H
(a) SPHL 2050 (b) SPHL 2051 (c) SHLD 2050 (d) STAX 2050
25. Assume that the N-channel MOSFET shown in Fig.Q25 is ideal, and that its threshold voltage is +1.0V. The voltage V between nodes a and b is:
(a) 5V
(b) 2V
(c) 1V
(d) 0V
26. The digital circuit shown in Fig.Q26 works as a
(a) JK flip-flop
(b) Clocked RS flip-flop
(c) T flip-flop
(d) Ring counter
27. A digital-to-analog converter with a full-scale output voltage of 3.5V has a resolution close to 14 mV. Its bit size is:
(a) 4 (b) 8 (c) 16 (d) 32
28. The conduction loss versus device current characteristic of a power MOSFET is best approximated by
(a) a parabola (b) a straight line
(c) a rectangular hyperbola
(d) an exponentially decaying function
29. A three-phase diode bridge rectifier is fed from a 400V RMS, 50 Hz, three-phase AC source. If the load is purely resistive, the peak instantaneous output voltage is equal to
(a) 400 V (b) 400 2 V (c) 2 400 V
3 V (d) 400 3
30. The output voltage waveform of a three-phase square-wave inverter contains
(a) only even harmonics (b) both odd and even harmonics
(c) only odd harmonics (d) only triplen harmonics
Q.31 – Q.80 carry two m arks each
31. The RL circuit of Fig.Q31 is fed from a constant magnitude, variable frequency sinusoidal voltage source . At 100 Hz, the R and L elements each have a I N voltage drop . u If the frequency of the source is changed to 50 Hz, the new R M S voltage drop across R is:
32. For the three-phase circuit shown in Fig.Q32, the ratio of the current : : I I I is given by (a) 1 : 1: 3 (b) 1:1:2
(c) 1:1:0 (d) 1:1: 3
33. For the triangular waveform shown in Fig.Q33, the RMS value of the voltage is equal to
(a) 1
6 (b) 1 3 (c) 1 3 (d) 2 3
34. The circuit shown in Fig.Q34 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
10
(a) 0 A
(b) 0.5 A
(c) 1 A
(d) 2 A
35. The charge distribution in a metal-dielectric-semiconductor specimen is shown in Fig.Q35. The negative charge density decreases linearly in the semiconductor as shown. The electric field distribution is as shown in
Metal Semiconductor Dielectric
36. In Fig.Q36, the Thevenin‘s equivalent pair (voltage, impedance), as seen at the terminals P-Q, is given by
(a) (2V, 5 )
(b) (2V, 7.5 )
(c) (4V, 5 )
(d) (4V, 7.5 )
37. A unity feedback system, having an open loop gain
K s 1 , – ( ) ( ) ( )
G s H s s = + becomes stable when ( )
1
(a) 1 K > (b) K >1 (c) 1 K < (d) K < -1
38. When subjected to a unit step input, the closed loop control system shown in Fig.Q38 will have a steady state error of
(a) -1.0 (b) -0.5 (c) 0 (d) 0.5
39. In the GH(s) plane, the Nyquist plot of the loop transfer function
G s H s s = passes through the negative real axis at the point
(a) (-0.25,j0) (b) (-0.5,j0) (c) (-1,j0) (d) (-2,j0)
40. If the compensated system shown in Fig.Q40 has a phase margin of 60° at the crossover frequency of 1 rad/sec, the value of the gain K is:
(a) 0.366
(b) 0.732
(c) 1.366
(d) 2.738
41. For the matrix
42. If
» ÿ 1 0 1 -
… Ÿ
R = – 2 1 1 , the top row of R is: – 1
… Ÿ
… Ÿ 2 3 2 /
» ÿ
(a) 5 6 4 » ÿ » ÿ – » ÿ – 2 1 2 – / (b) 5 3 1 / (c) 2 0 1 / (d) 1 … Ÿ
/
43. A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is:
(a) 1
8 (b) 1 2 (c) 3 8 (d) 3 4
44. For the function fx x e = x , the maximum occurs when x is equal to: 2 -
(a) 2 (b) 1 (c) 0 (d) -1
45. For the scalar field, the magnitude of the gradient at the point (1,3) is:
(a) 13
9 (b) 9 2 (c) 5 (d) 9
solution approaches the following values at
(a) 0 (b) 5
2 (c) 5 (d) 10
47. The Laplace transform of a function f(t) is
48. The Fourier series for the function fx x = sin is: 2
(a) x x + – x sin sin2 (b) 1 cos2
x x + – x (c) sin2 cos2 (d) 0.5 0.5 cos2
49. If is the unit step and is the unit impulse function, the inverse z-
F z z = + k = transform of for 0 is:
(a) 1 (b) 1 (c) 1 (d) 1
50. Two magnetic poles revolve around a stationary armature carrying two coils as shown in Fig.Q50. 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 coil sides and .
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
(a) 25 kW in (i) and 75 kW in (ii) (b) 25 kW in (i) and 50 kW in (ii)
(c) 50 kW in (i) and 75 kW in (ii) (d) 50 kW in (i) and 50 kW in (ii)
52. In relation to DC machines, match the following and choose the correct
combination.
Group œ1 Group œ 2
Performance Variables Proportional to
(P) Armature emf (E) (1) Flux ( ), speed ( ) and armature current ( )
(Q) Developed torque (T) (2) and only
(R) Developed power (P) (3) and only
(4) and only(A) P – 3 Q – 3 R – 1
(B) P – 2 Q – 5 R – 4
(C) P – 3 Q – 5 R – 4
(D) P – 2 Q – 3 R – 1
53. In relation to the synchronous machines, which one of the following statements is false?
(a) In salient pole machines, the direct-axis synchronous reactance is greater than the quadrature-axis synchronous reactance
(b) The damper bars help the synchronous motor self-start
(c) Short circuit ratio is the ratio of the field current required to produce the
rated voltage on open circuit to the rated armature current
(d) The V-curve of a synchronous motor represents the variation in the armature current with field excitation, at a given output power
54. Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value,
(a) the speed decreases and the stator current increases
(b) both the speed and the stator current decrease
(c) the speed and the stator current remain practically constant
(d) there is negligible change in the speed but the stator current decreases
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%, the ratio of the starting developed torque to the full load torque is approximately equal to
(a) 0.24 (b) 1.44 (c) 2.40 (d) 6.00
56. In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve
(a) low starting torque (b) quick acceleration
(c) high efficiency (d) reduced size
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-
synchronous 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.
(a) Both [a] and [r] are true and [r] is the correct reason for [a]
(b) Both [a] and [r] are true but [r] is not the correct reason for [a]
(c) Both [a] and [r] are false
(d) [a] is true but [r] is false
58. The parameters of a transposed overhead transmission line are given as:
x km km = = Self reactance 0.5 / and Mutual reactance x 0.1 /
The positive sequence reactance and zero sequence reactance ,
respectively, in /km are
(a) 0.3, 0.2 (b) 0.5, 0.2 (c) 0.5, 0.6 (d) 0.3, 0.6
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
(a) 0.85 lag (b) 1.00 lag (c) 0.80 lag (d) 0.90 lag
60. The network shown in Fig.Q60 has impedances in p.u. as indicated. The diagonal element of the bus admittance matrix of the network is:
(a) -j19.8 (b) +j20.0 (c) +j0.2 (d) -j19.95
61. A load centre is at an equidistant from the two thermal generating stations G and G as shown in Fig.Q61. The fuel cost characteristics of the generating stations are given by
Load F a bP cP = + + 2 2 Rs/hour
where and are the generation in MW of and , respectively. For most
economic generation to meet 300 MW of load, and , respectively, are
(a) 150, 150 (b) 100, 200 (c) 200, 100 (d) 175, 125
62. Two networks are connected in cascade as shown in Fig.Q62. With the usual notations the equivalent A, B, C and D constants are obtained. Given that
Z C = ° 0.025 45 , the value of is:
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 bas as shown in Fig.Q63. 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, the resulting steady state stability power limit in p.u. will be
(a) 12.5 p.u.
(b) 3.125 p.u.
(c) 10.0 p.u.
(d) 5.0 p.u.
64. The simultaneous application of signals and to the horizontal and
vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-8 display. If P and Q are constants, and sin 4 30 , then is equal to
(a) sin 4 30 (b) sin 2 15 (c) sin 8 60 (d) sin 4 30
65. A DC ammeter has a resistance of 0.1 and its current range is 0 œ 100A. If the range is to be extended to 0 œ 500A, the meter requires the following shunt resistance:
(a) 0.010 (b) 0.011 (c) 0.025 (d) 1.0
66. The set-up in Fig.Q66 is used to measure resistance R. The ammeter and voltmeter resistances are 0.01 and 2000 , respectively. Their readings are 2A and 180V, respectively, giving a measured resistance of 90 . The percentage error in the measurement is:
(a) 2.25% (b) 2.35%
(c) 4.5% (d) 4.71%
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 and 6 M , respectively, as shown in Fig.Q67. A voltmeter with resistance 50 K is used to measure the insulation of the cable. When connected between the positive core and earth, the voltmeter reads
(a) 8 V (b) 16 V (c) 24 V (d) 40 V
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 œ2.5 kW,
respectively. The total power and the power factor, respectively, are
(a) 13.0 kW, 0.334 (b) 13.0 kW, 0.684
(c) 8.0 kW, 0.52 (d) 8.0 kW, 0.334
69. The common emitter amplifier shown in Fig.Q69 is R =1k biased using a 1 mA ideal current source. The approximate base current value is:
(a) 0 A
(b) 10 A
(c) 100 A
(d) 1000 A
70. Consider the inverting amplifier, using an ideal operational amplifier shown in Fig.Q70. The designer wishes to realize the input resistance seen by the small-signal source to be as large as possible, while keeping the voltage gain between the upper limit on is 1 M . The value of should be
71. The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in
72. In Fig.Q72, if the input is a sinusoidal signal, the output will appear as shown in
73. Select the circuit, which will produce the given output Q for the input signals and given in Fig.Q73.
74. If and are the inputs to the circuit shown in Fig.Q74, the output Q is:
75. In Fig.Q75, as long as 1 and 1, the output Q remains
(a) at 1
(b) at 0
(c) at its initial value
(d) unstable
76. Fig.Q76 shows the voltage across a power semiconductor device and the current through the device during a switching transition. Is the transition a turn ON transition or a turn OFF transition? What is the energy lost during the transition?
(a) Turn ON,
(b) Turn OFF,
(c) Turn ON,
(d) Turn OFF,
77. An electronic switch S is required to block voltages of either polarity during its OFF state as shown in Fig.Q.77a. This switch is required to conduct in only one direction during its ON state as shown in Fig.Q77b.
Fig.Q77a Fig.Q77b
Which of the following are valid realizations of the switch S?
(a) Only P (b) P and Q (c) P and R (d) R and S
78. Fig.Q78 shows a step-down chopper switched at 1 KHz with a duty ratio D = 0.5.
The peak-peak ripple in the load current is close to
(a) 10 A
(b) 0.5 A
(c) 0.125 A
(d) 0.25 A
79. An electric motor, developing a starting torque of 15 Nm, starts with a load torque of 7 Nm on its shaft. If the acceleration at start is 2 rad/sec , the moment of inertia of the systems must be (neglecting viscous and Coulomb/friction).
(a) 0.25 kg m (b) 0.25 Nm (c) 4 kg m (d) 4 Nm
80. Consider a phase controlled converter shown in Fig.Q.80. The thyristor is fired at an angle in every positive half cycle of the input voltage. If the peak value of the instantaneous output voltage equals 230 V, the firing angle is close to
(a) 45°
(b) 135°
(c) 90°
(d) 83.6°
-
Linked Answer Questions: 81a to Q85b carry two marks each
Statement for Linked Answer Questions 81a & 81b: A coil of inductance 10 H
resistance 40 is connected as shown in Fig.Q81. After the switch S has been in connection with point 1 for a very long time, it is moved to point 2 at t = 0. + 81. (A) If, at t = 0 , the voltage across the coil is 120V, the value of resistance R is:
(a) 0
(b) 20
(c) 40
(d) 60
(B) For the value of R obtained in (a), the time taken for 95% of the stored
energy dissipated is close to
(a) 0.10 sec (b) 0.15 sec (c) 0.50 sec (d) 1.0 sec
Statement for Linked Answer Questions 82a & 82b:
A state variable system
83. The induced emf (line-to-line) is close to (A)
(a) 5.5 kV (b) 7.2 kV (c) 9.6 kV (d) 12.5 kV
The power (or torque) angle is close to (B)
(a) 13.9° (b) 18.3° (c) 24.6° (d) 33.0°
At a 220 kV substation of a Statem ent for Linked Answer Questions 84a & 84b:
power system, it is given that the three-phase fault level is 4000 MVA and single-line to ground fault level is 5000 MVA. Neglecting the resistance and the shunt susceptances of the system,
84. the positive sequence driving point reactance at the bus is: (A)
(a) 2.5 (b) 4.033 (c) 5.5 (d) 12.1
and the zero sequence driving point reactance at the bus is: (B)
(a) 2.2 (b) 4.84 (c) 18.18 (d) 22.72
Assume that the threshold Statem ent for Linked Answer Questions 85a & 85b: voltage of the N-channel MOSFET shown in Fig. Q85 is +0.75V. The output characteristics of the MOSFET are also shown.
85. The transconductance of the MOSFET is: (A)
(a) 0.75 mS (b) 1 mS (c) 2 mS (d) 10 mS
The voltage gain of the amplifier is: (B)
(a) +5 (b) -7.5 (c) +10 (d) -10
GATE EE – 2004 Electrical Engineering Question Paper
Q.1 – Q.30 Carry One Mark Each
1. The value of Z in Figure.Q.1, which is most appropriate to cause parallel
resonance at 500 Hz, is
(a) 125.00 mH
(b) 304.20 F
(c) 2.0 F
(d) 0.05 F
2. A parallel plate capacitor is shown in figure Q.2. It is made of two square metal plates of 400 mm side. The 14 mm space between the plates is filled with two layers od dielectrics of 4,6 = mm thick and 2,8 = mm thick. Neglecting fringing of fields at the edges the capacitance is
(a) 1298 pF
(b) 944 pF
(c) 354 pF
(d) 257 pF
3. The inductance of a long solenoid of length 1000 mm wound uniformly with 3000 turns on a cylindrical paper tube of 60mm diameter is
(a) 3.2 H (b) 3.2 mH (c) 32.0 mH (d) 3.2 H
4. Total instantaneous power supplied by a 3-phase ac supply to a balanced R-L load is
(a) zero (b) constant
(c) pulsating with zero average (d) pulsating with non-zero average
5. A 500 kVA, 3-phase transformer has iron loses of 300 W and full load copper losses of 600 W. The percentage load at which the transformer is expected to have maximum efficiency is
(a) 50.0% (b) 70.7% (c) 141.4% (d) 200.0%
6. For a given stepper motor, the following torque has the highest numerical value.
(a) Detent torque (b) Pull-in torque
(c) Pull-out torque (d) Holding torque
7. The following motor definitely has a permanent magnet rotor
(a) DC commutator motor (b) Brushless dc motor
(c) Stepper motor (d) Reluctance motor
8. The type of single-phase induction motor having the highest power factor at full load is
(a) shaded pole type (b) split-phase type
(c) capacitor-start type (d) capacitor-run type
9. The direction of rotation of a 3-phase induction motor is clockwise when it is supplied with 3-phase sinusoidal voltage having phase sequence A-B-C. For counter clockwise rotation of the motor, the phase sequence of the power supply should be
(a) B-C-A (b) C-A-B
(c) A-C-B (d) B-C-A or C-A-B
10. For a linear electromagnetic circuit, the following statement is true.
(a) Field energy is equal to the co-energy
(b) Field energy is greater than the co-energy
(c) Field energy is lesser than the co-energy
(d) Co-energy is zero
11. The rated voltage of a 3-phase power system is given as
(a) rms phase voltage (b) peak phase voltage
(c) rms line to line voltage (d) peak line to line voltage
12. The phase sequence of the 3-phase system shown in Figure is
(a) RYB (b) RBY (c) BRY (d) YBR
13. In thermal power plants, the pressure in the working fluid cycle is developed by
(a) condenser (b) super heater
(c) feed water pump (d) turbine
14. For harnessing low variable water heads, the suitable hydraulic turbine with high percentage of reaction and runner adjustable vanes is
(a) Kaplan (b) Francis (c) Pelton (d) Impeller
15. The transmission line distance protection relay having the property of being inherently directional is
(a) impedance relay (b) MHO relay
(c) OHM relay (d) reactance relay
16. The current through the Zener diode in figure is
(a) 33 mA (b) 3.3 mA (c) 2 mA (d) 0 mA
17. Two perfectly matched silicon transistors are connected as shown in figure. The value of the current I is
(a) 0 mA (b) 2.3 mA (c) 4.3 mA (d) 7.3 mA
18. The feedback used in the circuit shown in figure can be classified as
(a) shunt-series feedback (b) shunt-shunt feedback
(c) series-shunt feedback (d) series-series feedback
19. The digital circuit using two inverters shown in figure will act as
(a) a bistable multi-vibrator
(b) an astable mutli-vibrator
(c) a monostable multi-vibrator
(d) an oscillator
20. The voltage comparator shown in figure can be used in the analog-to-digital conversion as
(a) a 1-bit quantizer
(b) a 2-bit quantizer
(c) a 4-bit quantizer 2
(d) a 8-bit quantizer
21. The Nyquist plot of loop transfer function G(s) H(s) of a closed loop control system passes through the point (-1,j0) in the G(s) H(s) plane. The phase margin of the system is
(a) 0° (b) 45° (c) 90° (d) 180°
22. Consider the function F s = , where F(s) is the Laplace transform
of the function f(t). the initial value of f(t) is equal to
(a) 5 (b) 5
2 (c) 5 3 (d) 0
23. For a tachometer if (t) is the rotor displacement is radians, e(t) is the output voltage and K is the tachometer constant in V/rad/sec, then the transfer
24. A dc potentiometer is designed to measure up to about 2V with a slide wire of 300 mm. A standard cell of emf 1.18 V obtains balance at 600 mm. A test cell is seen to obtain balance at 680 mm. The emf of the test cell is
(a) 1.00 V (b) 1.34 V (c) 1.50 V (d) 1.70 V
25. The circuit in figure is used to measure the power consumed by the load. The current coil and the voltage coil of the wattmeter have 0.02 and 1000
resistances respectively. The measured power compared to the load power will be
(a) 0.4% less
(b) 0.2% less
(c) 0.2% more
(d) 0.4% more
26. A galvanometer with a full-scale current of 10mA has a resistance of 1000 . The multiplying power (the ratio of measured current to galvanometer current) of a 100 shunt with this galvanometer is
(a) 110 (b) 100 (c) 11 (d) 10
27. A bipolar junction transistor (BJT) is used as a power control switch by biasing it in the cut-off region (OFF state) or in the saturation region (ON state). In the ON state, for the BJT
(a) both the base-emitter and base-collector junctions are reverse biased
(b) the base-emitter junctions is reverse biased, and the base-collector junction is forward biased
(c) the base-emitter junction is forward biased, and the base-collector junction is reverse biased
(d) both the base-emitter and base-collector junctions are forward biased
28. The circuit in figure shows a full-wave rectifier. The input voltage is 230V (rms) single-phase ac. The peak reverse voltage across the diodes D1 and D2 is
(a) 100 2 V
(b) 100 V
(c) 50 2 V
(d) 50 V
29. The triggering circuit of a thyristor is shown in figure. The thyristor requires a gate current of 10 mA, for guaranteed turn-on. The value of R required for the thyristor to turn on reliably under all conditions of Vb variation is
(a) 10000
(b) 1600
(c) 1200
(d) 800
30. The circuit in figure shows a 3-phase half-wave rectifier. The source is a
symmetrical, 3-phase four-wire system. The line-to-line voltage of the source is 100 V. The supply frequency is 400 Hz. The ripple frequency at the output is
(a) 400 Hz (b) 800 Hz (c) 1200 Hz (d) 2400 Hz
Question No.31 to 90 Carry 2 Marks Each.
31. The rms value of the periodic waveform given in figure is
32. In figure, the value of the source voltage is
(a) 12 V
(b) 24 V
(c) 30 V
(d) 44 V
33. In figure, Ra, Rb and Rc are 20 , 10 and 10 respectively. The resistance R1, R2 and R3 in of an equivalent star-connection are
(a) 2.5, 5, 5 (b) 5, 2.5, 5 (c) 5, 5, 2.5 (d) 2.5, 5, 2.5
34. In figure, the admittance values of the elements in Siemens are
Y j = + 0.5 0. Y j Y j = – = + 0 1.5. 0 0.3 respectively. The value of I as a phasor R 1 C
when the voltage E across the elements is 10 0 V is o
(a) 1.5 + j0.5
(b) 5 œ j18
(c) 0.5+j1.8
(d) 5 œ j12
35. In figure, the value of resistance R in is
(a) 10 (b) 20
(c) 30 (d) 40
36. In figure, the capacitor initially has a charge of 10 Coulomb. The current in the circuit one second after the switch S is closed will be
37. The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal alternating current of peak value 20 A is
(a) 14.1 A (b) 17.3 A (c) 22.4 A (d) 30.0 A
38. The Z matrix of a 2-port network as given by
» ÿ
0.9 0.2 … Ÿ
0.2 0.6 /
The element Y of the corresponding Y matrix of the same network is given by
(a) 1.2 (b) 0.4 (c) -0.4 (d) 1.8
39. The synchronous speed for the seventh space harmonic mmf wave of a 3-phase, 8 pole, 50 Hz induction machine is
(a) 107.14 rpm in forward direction (b) 107.14 rpm in reverse direction
(c) 5250 rpm in forward direction (d) 5250 rpm in reverse direction
40. A rotating electrical machine having its self-inductances of both the stator and the rotor windings, independent of the rotor position will be definitely not develop
(a) starting torque (b) synchronizing torque
(c) hysteresis torque (d) reluctance torque
41. The armature resistance of a permanent magnet dc motr is 0.8 . At no load, the motor draws 1.5 A from a supply voltage of 25 V and runs at 1500 rpm. The efficiency of the motor while it is operating on load at 1500 rpm drawing a current of 3.5 A form the same source will be
(a) 48.0% (b) 57.1% (c) 59.2% (d) 88.8%
42. A 50 kVA, 3300/230V single-phase transformers is connected as an
autotransformer shown in figure. The nominal rating of the autotransformer will be
(a) 50.0 kVA
N2
(b) 53.5 kVA
V (c) 717.4 kVA out
(d) 767.4 kVA
V =3300V N1
in
43. The resistance and reactance of a 100 kVA 11000|400V, Í -Y distribution transformer are 0.02 and 0.07 pu respectively. The phase impedance of the transformer referred to the primary is
(a) (0.02 + j0.07) (b) (0.55 + j1.925)
(c) (15.125 + j52.94) (d) (72.6 + j254.1)
44. A single-phase, 230 V, 50 Hz, 4 pole, capacitor-start induction motor has the following stand still impedances
Main winding Z =6.0 + j4.0
Auxiliary winding Z = 8.0 + j6.0
The value of the starting capacitor required to produce 90° phase difference
between the currents in the main and auxiliary windings will be
(a) 176.84 F (b) 187.24 F (c) 265.26 F (d) 280.86 F
45. Two 3-phase, Y-connected alternators are to be paralleled to a set of common bus bars. The armature has a per phase synchronous reactance of 1.7 and negligible armature resistance. The line voltage of the first machines is adjusted to 3300 V and that of the second machine is adjusted to 3200 V. the machine voltages are in phase at the instant they are paralleled. Under this condition, the synchronizing current per phase will be
(a) 16.98 A (b) 29.41 A (c) 33.96 A (d) 58.82 A
46. A 400V, 15 kW, 4 pole, 50 Hz, Y-connected induction motor has full load slip of 4% . The output torque of the machine at full load is
(a) 1.66 Nm (b) 95.50 Nm (c) 99.47 Nm (d) 624.73 Nm
47. For a 1.8°, 2-phase bipolar stepper motor, the stepping rate is 100 steps/second. The rotational speed of the motor in rpm is
(a) 15 (b) 30 (c) 60 (d) 90
48. A 8 pole, DC generator has a simplex wave-wound armature containing 32 coils of 6 turns each. Its flux per pole is 0.06 Wb. The machine is running at 250 rpm. The induced armature voltage is
(a) 96V (b) 192V (c) 384V (d) 768V
49. A 400V, 50 kVA, 0.8 pf leading Í-connected, 50 Hz synchronous machine has a synchronous reactance of 2 and negligible armature resistance. The friction and windage losses are 2kW and the core loss is 0.8 kW. The shaft is supplying 9kW load at a power factor of 0.8 leading. The line current drawn is
(a) 12.29 A (b) 16.24 A (c) 21.29 A (d) 36.88 A
50. A 500 MW 3-phase Y-connected synchronous generator has a rated voltage of 21.5 kV at 0.85 pf. The line current when operating at full load rated conditions will be
(a) 13.43 kA (b) 15.79 kA (c) 23.25 kA (d) 27.36 kA
51. A 800 kV transmission line is having per phase line inductance of 1.1 mH/km and per phase line capacitance of 11.68 nF/km. Ignoring the length of the line, its ideal power transfer capability in MW is
(a) 1204 MW (b) 1504 MW (c) 2085 MW (d) 2606 MW
52. A 110 kV, single core coaxial, XLPE insulated power cable delivering power at 50 Hz, has a capacitance of 125 nF/km. If the dielectric loss tangent of XLPE is
× – 4 2 10 , the dielectric power loss in this cable in W/km is
(a) 5.0 (b) 31.7 (c) 37.8 (d) 189.0
53. A lightning stroke discharges impulse current of 10 kA (peak) on a 400 kV transmission line having surge impedance of 250 . The magnitude of transient over-voltage traveling waves in either direction assuming equal distribution form the point of lightning strike will be
(a) 1250kV (b) 1650 kV (c) 2500 kV (d) 2900kV
54. The generalized circuit constants of a 3-phase, 220 kV rated voltage, medium length transmission line are
o A = D = 0.936 + j0.016 = 0.936 0.98
o B = 33.5 +j138=142.0 76.4
× – 6 C=(-5.18+j914) 10
If the load at the receiving end is 50 MW at 220 kV with a power factor of 0.9
lagging, the magnitude of line to lien sending end voltage should be
(a) 133.23 kV (b) 220.00 kV (c) 230.78 kV (d) 246.30 kV
55. A new generator having E = 1.4 30 pu [equivalent to (1.212+j0.70)pu] and synchronous reactance ”X ‘ of 1.0 pu on the system base, is to be connected to a bus having voltage V in the existing power system. This existing power system = can be represented by Thevenin‘s voltage 0.90 E pu in series with Thevenin‘s = impedance 0.25 90 Z pu. The magnitude of the bus voltage V of the system
in pu will be
(a) 0.990 (b) 0.973 (c) 0.963 (d) 0.900
56. A 3-phase generator rated at 110MVA, 11 kV is connected through circuit breakers to a transformer. The generator is having direct axis sub-transient = reactance 19% X , transient reactance 26% X and synchronous reactance =130% . The generator is operating at no load and rated voltage when a three-phase short circuit fault occurs between the breakers and the transformer. The magnitude of initial symmetrical rims current in the breakers will be
(a) 4.44 kA (b) 22.20 kA (c) 30.39 kA (d) 38.45 kA
57. A 3-phase transmission line supplies Í-connected load Z. The conductor ”c‘ I A = 10 0 o a a of the line develops an open circuit fault as shown in figure. The currents in the lines are as shown on the diagram.
The positive sequence current component in line ”a‘ will be
58. A 500 MVA, 50 Hz, 3-phase turbo-generator produces power at 22 kV. Generator is Y-connected and its neutral is solidly grounded. Their sequence reactances are = = = X X X pu 0.15 and 0.05 . it is operating at rated voltage and disconnected from the rest of the system (no load). The magnitude of the sub-transient line current for single line ground fault at the generator terminal in pu will be
(a) 2.851 (b) 3.333 (c) 6.667 (d) 8.553
59. A 50 Hz, 4-pole, 500 MVA, 22 kV turbo-generator is delivering rated megavolt-amperes at 0.8 power factor. Suddenly a fault occurs reducing is electric power output by 40% . Neglect losses and assume constant power input to the shaft. The accelerating torque in the generator in MNm at the time of the fault will be
(a) 1.528 (b) 1.018 (c) 0.848 (d) 0.509
60. A hydraulic turbine having rated speed of 250 rpm is connected to a synchronous generator. In order to produce power at 50 Hz, the number of poles required in the generator are
(a) 6 (b) 12 (c) 16 (d) 24
61. Assuming that he diodes are ideal in figure, the current in D is
(a) 8 mA
(b) 5 mA
(c) 0 mA
(d) -3 mA
62. The transconductance g of the transistor shown in figure is 10 mS. The value of the input resistance R is
(a) 10.0 k
(b) 8.3 k
(c) 5.0 k
(d) 2.5 k
63. The value of R for which the PMOS transistor in figure will be biased in linear region is
(a) 220 (b) 470 (c) 680 (d) 1200
64. In the active filter circuit shown in figure, if Q=1, a pair of poles will be realized with equal to
(a) 1000 rad/s (b) 100 rad/s (c) 10 rad/s (d) 1 rad/s
65. The input resistance R i of the circuit
in figure is
(a) +100k
(b) -100k
(c) +1 M
(d) – 1 M
67. A digital circuit, which compares two numbers, , , , , is shown in
figure. To get output Y=0, choose one pair of correct input numbers.
(a) 1010, 1010 (b) 0101, 0101 (c) 0010, 0010 (d) 0010, 1011
68. The digital circuit shown in figure generates a modified clock pulse at the output. Choose the correct output waveform form the options given below.
69. In the Schmitt trigger circuit shown in
figure, if V =0.1V, the output logic low
level (V ) is
(a) 1.25 V
(b) 1.35 V
(c) 2.50 V
(d) 5.00 V
70. If the following program is executed in a microprocessor, the number of
instruction cycles it will take from START TO HALT is
START MV1A, 14 H : Move 14 H to register A
SHIFT RLC : Rotate left without carry
JNZ SHIFT : Jump on non-zero to SHIFT
HALT
(a) 4 (b) 8 (c) 13 (d) 16
71. For the equation, s s s 4 6 0 , the number of roots in the left half of s- – + + = 3 2
plane will be
(a) zero (b) one (c) two (d) three
72. For the block diagram shown in figure, the transfer function R s is equal to
73. The state variable description of a linear autonomous system is X = AX,
where X is the two dimensional state vector and A is the system matrix given by
0 2 . A = The roots of the characteristic equation are
(a) -2 and +2 (b) -j2 and +j2 (c) -2 and -2 (d) +2 and -2
74. The block diagram of a closed loop control system is given by figure. The values of K and P such that the system has a damping ratio of 0.7 and an undamped natural frequency of 5 rad/sec, are respectively equal to
(a) 20 and 0.3
(b) 20 and 0.2
(c) 25 and 0.3
(d) 25 and 0.2
75. The unit impulse response of a second order under-damped system starting from rest is given by
The steady-state value of the unit step response of the system is equal to
(a) 0 (b) 0.25 (c) 0.5 (d) 1.0
76. In the system shown in figure, the input x(t)=sin t. In the steady-state, the response y(t) will be
77. The open loop transfer function of a unity feedback control system is given as The value of ”a‘ to give a phase margin of 45° is equal to
(a) 0.141 (b) 0.441 (c) 0.841 (d) 1.141
78. A CRO probe has an impedance of 500 k in parallel with a capacitance of 10 pF. The probe is used to measure the voltage between P and Q as shown in figure. The measured voltage will be
(a) 3.53 V
(b) 4.37 V
(c) 4.54 V
(d) 5.00 V
79. A moving coil of a meter has 100 turns, and a length and depth of 10 mm and 20 mm respectively. It is positioned in a uniform radial flux density of 200 mT. The coil carries a current of 50 mA. The torque on the coil is
(a) 200 Nm (b) 100 Nm (c) 1000 Nm (d) 1 Nm
80. A dc A-h meter is rated for 15 A, 250V. The meter constant is 14.4 A-sec/rev. The meter constant at rated voltage may be expressed as
(a) 3750 rev/kWh (b) 3600 rev/kWh (c) 1000 rev/kWh (d) 960 rev/kWh
81. A moving iron ammeter produces a full-scale torque of 240 Nm with a deflection of 120° at a current of 10 A. The rate of change of self inductance ( H/radian) of the instrument at full scale is
(a) 2.0 H/radian (b) 4.8 H/radian
(c) 12.0 H/radian (d) 114.6 H/radian
82. A single-phase load is connected between R and Y terminals of a 415 V, symmetrical, 3-phase, 4-wire system with phase sequence RYB. A wattmeter is connected in the system as shown in figure. The power factor of the load is 0.8 lagging. The wattmeter will read
(a) -795 W
(b) -597 W
(c) +597 W
(d) +795 W
83. A 50 Hz, bar primary CT has a secondary with 500 turns. The secondary supplies 5A current into a purely resistive burden of 1 . The magnetizing ampere-turns is 200. The phase angle between the primary and secondary current is
(a) 4.6° (b) 85.4° (c) 94.6° (d) 175.4°
84. The core flux in the CT of problem 83, under the given operating condition is
(a) 0 (b) 45.0 Wb (c) 22.5 mWb (d) 100.0 mWb
85. A MOSFET rated for 15 A, carries a periodic current as shown in figure. The ON state resistance of the MOSFET is 0.15 . The average ON state loss in the MOSFET is
(a) 33.8 W
(b) 15.0 W
(c) 7.5 W
(d) 3.8 W
86. The triac circuit shown in figure controls the ac output power to the resistive load. The peak power dissipation in the load is
(a) 3968 W
(b) 5290 W
(c) 7935 W
(d) 10580 W
87. Figure shows a chopper operating from a 100 V dc input. The duty ratio of the main switch S is 0.8. The load is sufficiently inductive so that the load current is ripple free. The average current through the diode D under steady state is
(a) 1.6 A (b) 6.4 A (c) 8.0 A (d) 10.0 A
88. Figure shows a chopper. The device S1 is the main switching device. S2 is the auxiliary commutation device. S1 is rated for 400V, 60A. S2 is rated for 400V, 30 A. the load current is 20 A. The main device operates with a duty ratio of 0.5. The peak current through S1 is
(a) 10 A (b) 20 A (c) 30 A (d) 40 A
89. A single-phase half-controlled rectifier is driving a separately excited dc motor.
The dc motor has a back emf constant of 0.5 V/rpm. The armature current is 5A without any ripple. The armature resistance is 2 . The converter is working from a 230 V, single-phase ac source with a firing angle of 30°. Under this operating condition, the speed of the motor will be
(a) 339 rpm (b) 359 rpm (c) 366 rpm (d) 386 rpm
90. A variable speed drive rated for 1500 rpm, 40 Nm is reversing under no load. Figure shows the reversing torque and the speed during the transient. The moment of inertia of the drive is
(a) 0.048 kg m (b) 0.064 kg m
(c) 0.096 kg m (d) 0.128 kg m
1. The value of Z in Figure.Q.1, which is most appropriate to cause parallel
resonance at 500 Hz, is
(a) 125.00 mH
(b) 304.20 F
(c) 2.0 F
(d) 0.05 F
2. A parallel plate capacitor is shown in figure Q.2. It is made of two square metal plates of 400 mm side. The 14 mm space between the plates is filled with two layers od dielectrics of 4,6 = mm thick and 2,8 = mm thick. Neglecting fringing of fields at the edges the capacitance is
(a) 1298 pF
(b) 944 pF
(c) 354 pF
(d) 257 pF
3. The inductance of a long solenoid of length 1000 mm wound uniformly with 3000 turns on a cylindrical paper tube of 60mm diameter is
(a) 3.2 H (b) 3.2 mH (c) 32.0 mH (d) 3.2 H
4. Total instantaneous power supplied by a 3-phase ac supply to a balanced R-L load is
(a) zero (b) constant
(c) pulsating with zero average (d) pulsating with non-zero average
5. A 500 kVA, 3-phase transformer has iron loses of 300 W and full load copper losses of 600 W. The percentage load at which the transformer is expected to have maximum efficiency is
(a) 50.0% (b) 70.7% (c) 141.4% (d) 200.0%
6. For a given stepper motor, the following torque has the highest numerical value.
(a) Detent torque (b) Pull-in torque
(c) Pull-out torque (d) Holding torque
7. The following motor definitely has a permanent magnet rotor
(a) DC commutator motor (b) Brushless dc motor
(c) Stepper motor (d) Reluctance motor
8. The type of single-phase induction motor having the highest power factor at full load is
(a) shaded pole type (b) split-phase type
(c) capacitor-start type (d) capacitor-run type
9. The direction of rotation of a 3-phase induction motor is clockwise when it is supplied with 3-phase sinusoidal voltage having phase sequence A-B-C. For counter clockwise rotation of the motor, the phase sequence of the power supply should be
(a) B-C-A (b) C-A-B
(c) A-C-B (d) B-C-A or C-A-B
10. For a linear electromagnetic circuit, the following statement is true.
(a) Field energy is equal to the co-energy
(b) Field energy is greater than the co-energy
(c) Field energy is lesser than the co-energy
(d) Co-energy is zero
11. The rated voltage of a 3-phase power system is given as
(a) rms phase voltage (b) peak phase voltage
(c) rms line to line voltage (d) peak line to line voltage
12. The phase sequence of the 3-phase system shown in Figure is
(a) RYB (b) RBY (c) BRY (d) YBR
13. In thermal power plants, the pressure in the working fluid cycle is developed by
(a) condenser (b) super heater
(c) feed water pump (d) turbine
14. For harnessing low variable water heads, the suitable hydraulic turbine with high percentage of reaction and runner adjustable vanes is
(a) Kaplan (b) Francis (c) Pelton (d) Impeller
15. The transmission line distance protection relay having the property of being inherently directional is
(a) impedance relay (b) MHO relay
(c) OHM relay (d) reactance relay
16. The current through the Zener diode in figure is
(a) 33 mA (b) 3.3 mA (c) 2 mA (d) 0 mA
17. Two perfectly matched silicon transistors are connected as shown in figure. The value of the current I is
(a) 0 mA (b) 2.3 mA (c) 4.3 mA (d) 7.3 mA
18. The feedback used in the circuit shown in figure can be classified as
(a) shunt-series feedback (b) shunt-shunt feedback
(c) series-shunt feedback (d) series-series feedback
19. The digital circuit using two inverters shown in figure will act as
(a) a bistable multi-vibrator
(b) an astable mutli-vibrator
(c) a monostable multi-vibrator
(d) an oscillator
20. The voltage comparator shown in figure can be used in the analog-to-digital conversion as
(a) a 1-bit quantizer
(b) a 2-bit quantizer
(c) a 4-bit quantizer 2
(d) a 8-bit quantizer
21. The Nyquist plot of loop transfer function G(s) H(s) of a closed loop control system passes through the point (-1,j0) in the G(s) H(s) plane. The phase margin of the system is
(a) 0° (b) 45° (c) 90° (d) 180°
22. Consider the function F s = , where F(s) is the Laplace transform
of the function f(t). the initial value of f(t) is equal to
(a) 5 (b) 5
2 (c) 5 3 (d) 0
23. For a tachometer if (t) is the rotor displacement is radians, e(t) is the output voltage and K is the tachometer constant in V/rad/sec, then the transfer
24. A dc potentiometer is designed to measure up to about 2V with a slide wire of 300 mm. A standard cell of emf 1.18 V obtains balance at 600 mm. A test cell is seen to obtain balance at 680 mm. The emf of the test cell is
(a) 1.00 V (b) 1.34 V (c) 1.50 V (d) 1.70 V
25. The circuit in figure is used to measure the power consumed by the load. The current coil and the voltage coil of the wattmeter have 0.02 and 1000
resistances respectively. The measured power compared to the load power will be
(a) 0.4% less
(b) 0.2% less
(c) 0.2% more
(d) 0.4% more
26. A galvanometer with a full-scale current of 10mA has a resistance of 1000 . The multiplying power (the ratio of measured current to galvanometer current) of a 100 shunt with this galvanometer is
(a) 110 (b) 100 (c) 11 (d) 10
27. A bipolar junction transistor (BJT) is used as a power control switch by biasing it in the cut-off region (OFF state) or in the saturation region (ON state). In the ON state, for the BJT
(a) both the base-emitter and base-collector junctions are reverse biased
(b) the base-emitter junctions is reverse biased, and the base-collector junction is forward biased
(c) the base-emitter junction is forward biased, and the base-collector junction is reverse biased
(d) both the base-emitter and base-collector junctions are forward biased
28. The circuit in figure shows a full-wave rectifier. The input voltage is 230V (rms) single-phase ac. The peak reverse voltage across the diodes D1 and D2 is
(a) 100 2 V
(b) 100 V
(c) 50 2 V
(d) 50 V
29. The triggering circuit of a thyristor is shown in figure. The thyristor requires a gate current of 10 mA, for guaranteed turn-on. The value of R required for the thyristor to turn on reliably under all conditions of Vb variation is
(a) 10000
(b) 1600
(c) 1200
(d) 800
30. The circuit in figure shows a 3-phase half-wave rectifier. The source is a
symmetrical, 3-phase four-wire system. The line-to-line voltage of the source is 100 V. The supply frequency is 400 Hz. The ripple frequency at the output is
(a) 400 Hz (b) 800 Hz (c) 1200 Hz (d) 2400 Hz
Question No.31 to 90 Carry 2 Marks Each.
31. The rms value of the periodic waveform given in figure is
32. In figure, the value of the source voltage is
(a) 12 V
(b) 24 V
(c) 30 V
(d) 44 V
33. In figure, Ra, Rb and Rc are 20 , 10 and 10 respectively. The resistance R1, R2 and R3 in of an equivalent star-connection are
(a) 2.5, 5, 5 (b) 5, 2.5, 5 (c) 5, 5, 2.5 (d) 2.5, 5, 2.5
34. In figure, the admittance values of the elements in Siemens are
Y j = + 0.5 0. Y j Y j = – = + 0 1.5. 0 0.3 respectively. The value of I as a phasor R 1 C
when the voltage E across the elements is 10 0 V is o
(a) 1.5 + j0.5
(b) 5 œ j18
(c) 0.5+j1.8
(d) 5 œ j12
35. In figure, the value of resistance R in is
(a) 10 (b) 20
(c) 30 (d) 40
36. In figure, the capacitor initially has a charge of 10 Coulomb. The current in the circuit one second after the switch S is closed will be
37. The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal alternating current of peak value 20 A is
(a) 14.1 A (b) 17.3 A (c) 22.4 A (d) 30.0 A
38. The Z matrix of a 2-port network as given by
» ÿ
0.9 0.2 … Ÿ
0.2 0.6 /
The element Y of the corresponding Y matrix of the same network is given by
(a) 1.2 (b) 0.4 (c) -0.4 (d) 1.8
39. The synchronous speed for the seventh space harmonic mmf wave of a 3-phase, 8 pole, 50 Hz induction machine is
(a) 107.14 rpm in forward direction (b) 107.14 rpm in reverse direction
(c) 5250 rpm in forward direction (d) 5250 rpm in reverse direction
40. A rotating electrical machine having its self-inductances of both the stator and the rotor windings, independent of the rotor position will be definitely not develop
(a) starting torque (b) synchronizing torque
(c) hysteresis torque (d) reluctance torque
41. The armature resistance of a permanent magnet dc motr is 0.8 . At no load, the motor draws 1.5 A from a supply voltage of 25 V and runs at 1500 rpm. The efficiency of the motor while it is operating on load at 1500 rpm drawing a current of 3.5 A form the same source will be
(a) 48.0% (b) 57.1% (c) 59.2% (d) 88.8%
42. A 50 kVA, 3300/230V single-phase transformers is connected as an
autotransformer shown in figure. The nominal rating of the autotransformer will be
(a) 50.0 kVA
N2
(b) 53.5 kVA
V (c) 717.4 kVA out
(d) 767.4 kVA
V =3300V N1
in
43. The resistance and reactance of a 100 kVA 11000|400V, Í -Y distribution transformer are 0.02 and 0.07 pu respectively. The phase impedance of the transformer referred to the primary is
(a) (0.02 + j0.07) (b) (0.55 + j1.925)
(c) (15.125 + j52.94) (d) (72.6 + j254.1)
44. A single-phase, 230 V, 50 Hz, 4 pole, capacitor-start induction motor has the following stand still impedances
Main winding Z =6.0 + j4.0
Auxiliary winding Z = 8.0 + j6.0
The value of the starting capacitor required to produce 90° phase difference
between the currents in the main and auxiliary windings will be
(a) 176.84 F (b) 187.24 F (c) 265.26 F (d) 280.86 F
45. Two 3-phase, Y-connected alternators are to be paralleled to a set of common bus bars. The armature has a per phase synchronous reactance of 1.7 and negligible armature resistance. The line voltage of the first machines is adjusted to 3300 V and that of the second machine is adjusted to 3200 V. the machine voltages are in phase at the instant they are paralleled. Under this condition, the synchronizing current per phase will be
(a) 16.98 A (b) 29.41 A (c) 33.96 A (d) 58.82 A
46. A 400V, 15 kW, 4 pole, 50 Hz, Y-connected induction motor has full load slip of 4% . The output torque of the machine at full load is
(a) 1.66 Nm (b) 95.50 Nm (c) 99.47 Nm (d) 624.73 Nm
47. For a 1.8°, 2-phase bipolar stepper motor, the stepping rate is 100 steps/second. The rotational speed of the motor in rpm is
(a) 15 (b) 30 (c) 60 (d) 90
48. A 8 pole, DC generator has a simplex wave-wound armature containing 32 coils of 6 turns each. Its flux per pole is 0.06 Wb. The machine is running at 250 rpm. The induced armature voltage is
(a) 96V (b) 192V (c) 384V (d) 768V
49. A 400V, 50 kVA, 0.8 pf leading Í-connected, 50 Hz synchronous machine has a synchronous reactance of 2 and negligible armature resistance. The friction and windage losses are 2kW and the core loss is 0.8 kW. The shaft is supplying 9kW load at a power factor of 0.8 leading. The line current drawn is
(a) 12.29 A (b) 16.24 A (c) 21.29 A (d) 36.88 A
50. A 500 MW 3-phase Y-connected synchronous generator has a rated voltage of 21.5 kV at 0.85 pf. The line current when operating at full load rated conditions will be
(a) 13.43 kA (b) 15.79 kA (c) 23.25 kA (d) 27.36 kA
51. A 800 kV transmission line is having per phase line inductance of 1.1 mH/km and per phase line capacitance of 11.68 nF/km. Ignoring the length of the line, its ideal power transfer capability in MW is
(a) 1204 MW (b) 1504 MW (c) 2085 MW (d) 2606 MW
52. A 110 kV, single core coaxial, XLPE insulated power cable delivering power at 50 Hz, has a capacitance of 125 nF/km. If the dielectric loss tangent of XLPE is
× – 4 2 10 , the dielectric power loss in this cable in W/km is
(a) 5.0 (b) 31.7 (c) 37.8 (d) 189.0
53. A lightning stroke discharges impulse current of 10 kA (peak) on a 400 kV transmission line having surge impedance of 250 . The magnitude of transient over-voltage traveling waves in either direction assuming equal distribution form the point of lightning strike will be
(a) 1250kV (b) 1650 kV (c) 2500 kV (d) 2900kV
54. The generalized circuit constants of a 3-phase, 220 kV rated voltage, medium length transmission line are
o A = D = 0.936 + j0.016 = 0.936 0.98
o B = 33.5 +j138=142.0 76.4
× – 6 C=(-5.18+j914) 10
If the load at the receiving end is 50 MW at 220 kV with a power factor of 0.9
lagging, the magnitude of line to lien sending end voltage should be
(a) 133.23 kV (b) 220.00 kV (c) 230.78 kV (d) 246.30 kV
55. A new generator having E = 1.4 30 pu [equivalent to (1.212+j0.70)pu] and synchronous reactance ”X ‘ of 1.0 pu on the system base, is to be connected to a bus having voltage V in the existing power system. This existing power system = can be represented by Thevenin‘s voltage 0.90 E pu in series with Thevenin‘s = impedance 0.25 90 Z pu. The magnitude of the bus voltage V of the system
in pu will be
(a) 0.990 (b) 0.973 (c) 0.963 (d) 0.900
56. A 3-phase generator rated at 110MVA, 11 kV is connected through circuit breakers to a transformer. The generator is having direct axis sub-transient = reactance 19% X , transient reactance 26% X and synchronous reactance =130% . The generator is operating at no load and rated voltage when a three-phase short circuit fault occurs between the breakers and the transformer. The magnitude of initial symmetrical rims current in the breakers will be
(a) 4.44 kA (b) 22.20 kA (c) 30.39 kA (d) 38.45 kA
57. A 3-phase transmission line supplies Í-connected load Z. The conductor ”c‘ I A = 10 0 o a a of the line develops an open circuit fault as shown in figure. The currents in the lines are as shown on the diagram.
The positive sequence current component in line ”a‘ will be
58. A 500 MVA, 50 Hz, 3-phase turbo-generator produces power at 22 kV. Generator is Y-connected and its neutral is solidly grounded. Their sequence reactances are = = = X X X pu 0.15 and 0.05 . it is operating at rated voltage and disconnected from the rest of the system (no load). The magnitude of the sub-transient line current for single line ground fault at the generator terminal in pu will be
(a) 2.851 (b) 3.333 (c) 6.667 (d) 8.553
59. A 50 Hz, 4-pole, 500 MVA, 22 kV turbo-generator is delivering rated megavolt-amperes at 0.8 power factor. Suddenly a fault occurs reducing is electric power output by 40% . Neglect losses and assume constant power input to the shaft. The accelerating torque in the generator in MNm at the time of the fault will be
(a) 1.528 (b) 1.018 (c) 0.848 (d) 0.509
60. A hydraulic turbine having rated speed of 250 rpm is connected to a synchronous generator. In order to produce power at 50 Hz, the number of poles required in the generator are
(a) 6 (b) 12 (c) 16 (d) 24
61. Assuming that he diodes are ideal in figure, the current in D is
(a) 8 mA
(b) 5 mA
(c) 0 mA
(d) -3 mA
62. The transconductance g of the transistor shown in figure is 10 mS. The value of the input resistance R is
(a) 10.0 k
(b) 8.3 k
(c) 5.0 k
(d) 2.5 k
63. The value of R for which the PMOS transistor in figure will be biased in linear region is
(a) 220 (b) 470 (c) 680 (d) 1200
64. In the active filter circuit shown in figure, if Q=1, a pair of poles will be realized with equal to
(a) 1000 rad/s (b) 100 rad/s (c) 10 rad/s (d) 1 rad/s
65. The input resistance R i of the circuit
in figure is
(a) +100k
(b) -100k
(c) +1 M
(d) – 1 M
67. A digital circuit, which compares two numbers, , , , , is shown in
figure. To get output Y=0, choose one pair of correct input numbers.
(a) 1010, 1010 (b) 0101, 0101 (c) 0010, 0010 (d) 0010, 1011
68. The digital circuit shown in figure generates a modified clock pulse at the output. Choose the correct output waveform form the options given below.
69. In the Schmitt trigger circuit shown in
figure, if V =0.1V, the output logic low
level (V ) is
(a) 1.25 V
(b) 1.35 V
(c) 2.50 V
(d) 5.00 V
70. If the following program is executed in a microprocessor, the number of
instruction cycles it will take from START TO HALT is
START MV1A, 14 H : Move 14 H to register A
SHIFT RLC : Rotate left without carry
JNZ SHIFT : Jump on non-zero to SHIFT
HALT
(a) 4 (b) 8 (c) 13 (d) 16
71. For the equation, s s s 4 6 0 , the number of roots in the left half of s- – + + = 3 2
plane will be
(a) zero (b) one (c) two (d) three
72. For the block diagram shown in figure, the transfer function R s is equal to
73. The state variable description of a linear autonomous system is X = AX,
where X is the two dimensional state vector and A is the system matrix given by
0 2 . A = The roots of the characteristic equation are
(a) -2 and +2 (b) -j2 and +j2 (c) -2 and -2 (d) +2 and -2
74. The block diagram of a closed loop control system is given by figure. The values of K and P such that the system has a damping ratio of 0.7 and an undamped natural frequency of 5 rad/sec, are respectively equal to
(a) 20 and 0.3
(b) 20 and 0.2
(c) 25 and 0.3
(d) 25 and 0.2
75. The unit impulse response of a second order under-damped system starting from rest is given by
The steady-state value of the unit step response of the system is equal to
(a) 0 (b) 0.25 (c) 0.5 (d) 1.0
76. In the system shown in figure, the input x(t)=sin t. In the steady-state, the response y(t) will be
77. The open loop transfer function of a unity feedback control system is given as The value of ”a‘ to give a phase margin of 45° is equal to
(a) 0.141 (b) 0.441 (c) 0.841 (d) 1.141
78. A CRO probe has an impedance of 500 k in parallel with a capacitance of 10 pF. The probe is used to measure the voltage between P and Q as shown in figure. The measured voltage will be
(a) 3.53 V
(b) 4.37 V
(c) 4.54 V
(d) 5.00 V
79. A moving coil of a meter has 100 turns, and a length and depth of 10 mm and 20 mm respectively. It is positioned in a uniform radial flux density of 200 mT. The coil carries a current of 50 mA. The torque on the coil is
(a) 200 Nm (b) 100 Nm (c) 1000 Nm (d) 1 Nm
80. A dc A-h meter is rated for 15 A, 250V. The meter constant is 14.4 A-sec/rev. The meter constant at rated voltage may be expressed as
(a) 3750 rev/kWh (b) 3600 rev/kWh (c) 1000 rev/kWh (d) 960 rev/kWh
81. A moving iron ammeter produces a full-scale torque of 240 Nm with a deflection of 120° at a current of 10 A. The rate of change of self inductance ( H/radian) of the instrument at full scale is
(a) 2.0 H/radian (b) 4.8 H/radian
(c) 12.0 H/radian (d) 114.6 H/radian
82. A single-phase load is connected between R and Y terminals of a 415 V, symmetrical, 3-phase, 4-wire system with phase sequence RYB. A wattmeter is connected in the system as shown in figure. The power factor of the load is 0.8 lagging. The wattmeter will read
(a) -795 W
(b) -597 W
(c) +597 W
(d) +795 W
83. A 50 Hz, bar primary CT has a secondary with 500 turns. The secondary supplies 5A current into a purely resistive burden of 1 . The magnetizing ampere-turns is 200. The phase angle between the primary and secondary current is
(a) 4.6° (b) 85.4° (c) 94.6° (d) 175.4°
84. The core flux in the CT of problem 83, under the given operating condition is
(a) 0 (b) 45.0 Wb (c) 22.5 mWb (d) 100.0 mWb
85. A MOSFET rated for 15 A, carries a periodic current as shown in figure. The ON state resistance of the MOSFET is 0.15 . The average ON state loss in the MOSFET is
(a) 33.8 W
(b) 15.0 W
(c) 7.5 W
(d) 3.8 W
86. The triac circuit shown in figure controls the ac output power to the resistive load. The peak power dissipation in the load is
(a) 3968 W
(b) 5290 W
(c) 7935 W
(d) 10580 W
87. Figure shows a chopper operating from a 100 V dc input. The duty ratio of the main switch S is 0.8. The load is sufficiently inductive so that the load current is ripple free. The average current through the diode D under steady state is
(a) 1.6 A (b) 6.4 A (c) 8.0 A (d) 10.0 A
88. Figure shows a chopper. The device S1 is the main switching device. S2 is the auxiliary commutation device. S1 is rated for 400V, 60A. S2 is rated for 400V, 30 A. the load current is 20 A. The main device operates with a duty ratio of 0.5. The peak current through S1 is
(a) 10 A (b) 20 A (c) 30 A (d) 40 A
89. A single-phase half-controlled rectifier is driving a separately excited dc motor.
The dc motor has a back emf constant of 0.5 V/rpm. The armature current is 5A without any ripple. The armature resistance is 2 . The converter is working from a 230 V, single-phase ac source with a firing angle of 30°. Under this operating condition, the speed of the motor will be
(a) 339 rpm (b) 359 rpm (c) 366 rpm (d) 386 rpm
90. A variable speed drive rated for 1500 rpm, 40 Nm is reversing under no load. Figure shows the reversing torque and the speed during the transient. The moment of inertia of the drive is
(a) 0.048 kg m (b) 0.064 kg m
(c) 0.096 kg m (d) 0.128 kg m
GATE EE – 1993 Electrical Engineering Question Paper
1. In the following circuit (figure) under steady state is:
(a) zero
(b) 5
(c) 7.07 sint
6.2 The following circuit (figure) resonates at
(a) all frequencies
(b) 0.5 rad/sec
(c) 5 rad/sec
(d) 1 rad/sec
6.3 Consider a second order system whose state space representation is of the form
(a) controllable (b) uncontrollable
(c) observable (d) unstable
6.4 is step response and is impulse response of a system. Its response
6.5 The transfer function for the state variable representation
X Ax Bu y CX du = + = + , is given by
(a) D C sI A B + – (b) B sI A C D – + -
(c) D sI A B C – + (d) C sI A D B – + -
6.6 Signal flow graph is used to obtain the
(a) stability of a system (b) transfer function of a system
(c) controllability of a system (d) observability of a system
6.7 A Wien bridge oscillator is shown in figure. Which of the following statements are true, if f is the frequency of oscillation?
(a) For R = 1 K, 1 , 1 C F f kHz = =
(b) For R = 3 K, 1 , 3 C F f kHz = =
(c) The gain of the op-amp state should be less than two for proper operation.
(d) The gain of the op-amp stage should be three for proper operation
6.8 A 10 bit A/D converter is used to digitize an analog signal in the 0 to 5 V range.
The maximum pea k to peak ripple voltage that can be allowed in the D.C. supply voltage is:
(a) nearly 100 mV (b) nearly 50 mV
(c) nearly 25 mV (d) nearly 5.0 mV
6.9 Three devices A, B and C have to be connected to a 8085 microprocessor. Device A has highest priority and device C has the lowest priority. In this context which of the following is correct assignment of interrupt inputs?
(a) A uses TRAP, B uses RST 5.5 and C uses RST 6.5
(b) A uses RST 7.5, B uses RST 6.5 and C uses RST 5.5
(c) A uses RST 5.5, B uses RST 6.5 and C uses RST 7.5
(d) A uses RST 5.5, B uses RST 6.5 and C uses TRAP
6.10 , and V V V are the instantaneous line to neutral voltages and , and i i i
are instantaneous line current sin a balanced three-phase circuit, the
computation, V i i V V i – - – will yield a quantity proportional to
(a) the active power (b) the power factor
(c) the reactive power (d) the complex power
6.11 A CRO screen has ten divisions on the horizontal scale. If a voltage signal 5 sin 314 45 t + ° is examined with a line base settings of 5 msec/div, the number of cycles of signal displayed on the screen will be
(a) 0.5 cycles (b) 2.5 cycles (c) 5 cycles (d) 10 cycles
6.12 A metal strain gauge has factor of two. Its nominal resistance is 120 ohms. If it undergoes a strain of 10 , the value of change of resistance in response to the – 5 strain is:
(a) 240 ohms (b) 2 10 × ohms – 5
(c) 2.5 10 × ohms (d) 1.2 10 × ohms – 5 – 3
6.13 The line integral of the vector potential A around the boundary of a surface S represents
(a) flux through in the surface S (b) flux density in the surface S
(c) magnetic density (d) current density
6.14 A 220/440 V, 50 Hz, 5 kVA single phase transformer operates on 220 V, 40 Hz supply with secondary winding. Then
(a) the eddy current loss and hysteresis loss of the transformer decrease
(b) the eddy current loss and hysteresis loss of the transformer increase
(c) the hysteresis loss of the transformer increases while eddy current loss
remains the same
(d) the hysteresis loss remain the same whereas eddy current loss decreases
6.15 A cumulative compounded long shunt motor is driving a load at a rated torque and rated speed. If the series field is shunted by a resistance equal to the resistance of the series field, keeping the torque constant,
(a) the armature current increases (b) the motor speed increases
(c) the armature current decreases (d) the motor speed decreases
6.16 A three phase alternator has negligible stator resistance. A short circuit test is conducted on this alternator. At a particular speed a field current of I is required to drive the rated armature current. If the speed of the alternator is reduced to half, the field current required to maintain rated armature current
(a) would be equal to I (b) would be equal to
(c) would be equal to
(d) cannot be predicated due to insufficient data
6.17 A synchronous motor operates at 0.8 p.f. lagging. If the field current of the motor is continuously increased
(a) the power fa ctor decreases upto a certain value of field current and
thereafter it increases
(b) the armature current increases upto a certain value of field current and
thereafter it decreases
(c) the power factor increases upto a certain value of field current and thereafter it decreases
(d) the armature current decreases upto a certain value of field current and
thereafter it increases
6.18 A three phase slip ring induction motor is fed from the rotor side with stator winding short circuited. The frequency of the currents flowing in the short circuited stator is:
(a) slip frequency (b) supply frequency
(c) frequency corresponding to rotor speed (d) zero
6.19. A three phase overhead transmission line has its conductors horizontally spaced with spacing between adjacent conductors equal to ”d‘. if now the conductors of the line are rearranged to form an equilateral triangle of sides equal to ”d‘ then
(a) average capacitance and inductance will increase
(b) average capacitance will increase and inductance will increase
(c) average capacitance will increase and inductance will decrease
(d) surge impedance loading of the line increases
6.20. The distribution system shown in figure is to be protected by over current system of protection.
For proper fault discrimination directional over current relays will be required at locations
(a) 1 and 4 (b) 2 and 3 (c) 1, 4 and 5 (d) 2, 3 and 5
6.21. The transient stability of the power system can be effectively improved by
(a) excitation control (b) phase shifting transformer
(c) single pole switching of circuit breakers
(d) increasing the turbine valve opening
6.22. In load flow analysis, the load connected at a bus is represented as
(a) constant current drawn from the bus
(b) constant impedance connected at the bus
(c) voltage and frequency dependent source at the bus
(d) constant real and reactive drawn from the bus6.23. The thermal resistance between the body of a power semiconductor device and the ambient is expressed as
(a) voltage across the device divided by current through the device
(b) average power dissipated in the device divided by the square of the RMS
current in the device
(c) average power dissipated in the device divided by the temperature difference from body to ambient.
(d) temperature difference from body to ambient divided by average power
dissipated in the device.
6.24. When a line commutated converter operates in the inverter mode
(a) it draws both real and reactive power from the A.C. supply
(b) it delivers both real and reactive power to the A.C. supply
(c) it delivers real power to the A.C. supply
(d) it draws reactive power from the A.C. supply
6.25 a chopper operating at a fixed frequency is feeding an R-L load. As the duty ratio of the chopper is increased from 25% to 75% , the ripple in the load current
(a) remains constant
(b) decreases, reaches a minimum at 50% duty ratio and then increases
(c) increases, reaches a minimum at 50% duty ratio and then decreases
(d) keeps on increasing as the duty ratio is increased
SECTION – B
7.1 Determine the voltage V and V in the following circuit(figure below) using cutest analysis. Choose circuit elements marked 1 2 3 in the three for this purpose.
7.2. Consider circuit shown in figure. Determine t in terms of i t Evaluate. .
7.3. A control system is described by the differential equation
Where, y t is the output and u t is the input. The realization of the system is
shown in figure with ß as unknown.
7.4. A unity feedback system has the open loop transfer function
(i) Calculate the Break awa y point and the imaginary axis crossing points
(ii) Sketch the root loci as K varies from 0 to 8 .
(iii) Give the procedure for finding closed loop transfer function directly from the root locus diagram for a given damping ratio of dominant root pair.
7.5. A Schmitt trigger is shown in figure (a) and its characteristic is shown in figure
(b). Here 10 , 10 , 5, 5 . V V V V V V V = = – = = -
(i) If the input is V t = + 1 7 sin volts, where, = 200 p radians/sec, calculate
the time duration in each cycle for which the output of the Schmitt trigger
remains at -10V level.
(ii) Draw the circuit diagram of an astable multi-vibrator using the Schmitt
trigger in figure (a), a resistor () and a capacitor (C). if the period of this
astable multi-vibrats is now to be doubled, what should be the new value of
resistance.
7.6. The output V of an N-bit D/A converter is given by
Where, K is a proportionality factor determined by the system parameters and where the coefficients a represent the binary word and a = 1 0 if the j bit is
(i) A 6-bit D/A converter gives V V = 3.6 for the word 100100. find the value of V for the word 110011.
(ii) For the R-2R ladder D/A converter (shown in figure) find the value of the
output voltage V where 6 V = Volts. Clearly show the steps in the
calculations.
7.7. A bridge circuit is shown in figure.
(a) The output signal of the bridge is V Looking into this part find an .
expression for the Thevenin equivalent resistance of the bridge.
(b) If R R x R R x R R = – = + = 1 , 1 and , find an expression for the output
voltage V in terms of E and x. take 0 R = in this case.
7.8. A pair of long parallel wires carry a current of I amp in opposite direction in the plane of a closed rectangular loop of wire of dimensions l and b as shown in figure. Determine an expression for the induced electromotive force in the loop using Faraday‘s law of induction.
7.9. A 10 kW, 240V dc shunt motor draws a line current of 5.2A while running at no load speed of 1200 rpm from a240V dc supply. It has an armature resistance of 0.25 ohm and a field resistance of 160 ohm. Estimate the efficiency of the mtoro when it delivers rated load.
7.10. A 40 kW, 3-phase slip ring induction motor of negligible stator impedance runs at a speed of 0.96 times synchronous speed at rated torque. The slip at maximum torque is 4 times the full load value. If the rotor resistance of the motor is increased by 5 times, determine:
(a) the speed, power output and rotor copper loss at rated torque,
(b) the speed corresponding to maximum torque.
Neglect mechanical losses.
7.11. A 10 kVA, 380V, 50 Hz, 3-phase, star connected salient pole alternator has direct
axis and quadrature axis reactances of 12 ohm and 8 ohm respectively. The
armature has a resistance of 1 per phase. The generator delivers rated load at 0.8 p.f. lagging with the terminal voltage being maintained at rated value. If the load angle is 16.15°, determine
(a) the direct and quadrature axis components of armature current.
(b) excitation voltage of the generator.
7.12. A 33 kV single circuit, 3-phase transmission line has the ABCD parameters A D B = = ° = ° 1 0 , 11.1863.43 ohm.
The line is to deliver 7.5 MVA at 0.85 pf lagging at the load end. The receiving end voltage is 32 kV (line to line). How much active and reactive power is to be dispatched from the sending end?
7.13. A 3-phase, star connected generator supplies a star connected inductive load through a transmission line. The star point of the load is grounded and the generator neutral is ungrounded. The load reactance is j 0.5 p.u per phase and the line reactance is j 0.1 p.u. per phase. The positive, negative and zero sequence reactances of the generator are j 0.5, j0.5 and j0.05 p.u respectively.
7.14. A 3-phase fully controlled thyristor bridge converter is operated from an a.c. supply of 400 V rms line to line. When the converter is operated in the rectifier mode at a control angle a = 30°, the overlap angle due to the line reactance is 15°. Calculate the reduction in d.c. output voltage due to the overlap. If the converter operates in the inverter mode with a a = 120° and without any change in the d.c. load current, what will be the overlap angle
7.15. A separately excited d.c. motor has the following name plate data:
220 V, 100 A, 2200 rpm
The armature resistance is 0.1 ohm and inductance is 5 mH. The motor is fed by a chopper which is operating from a d.c. supply of 250 V. Due to restrictions in the power circuit, the chopper can be operated over a duty cycle range from 20% to 80% . Determine the range of speeds over which the motor can be operated at rated torque.
(a) zero
(b) 5
(c) 7.07 sint
6.2 The following circuit (figure) resonates at
(a) all frequencies
(b) 0.5 rad/sec
(c) 5 rad/sec
(d) 1 rad/sec
6.3 Consider a second order system whose state space representation is of the form
(a) controllable (b) uncontrollable
(c) observable (d) unstable
6.4 is step response and is impulse response of a system. Its response
6.5 The transfer function for the state variable representation
X Ax Bu y CX du = + = + , is given by
(a) D C sI A B + – (b) B sI A C D – + -
(c) D sI A B C – + (d) C sI A D B – + -
6.6 Signal flow graph is used to obtain the
(a) stability of a system (b) transfer function of a system
(c) controllability of a system (d) observability of a system
6.7 A Wien bridge oscillator is shown in figure. Which of the following statements are true, if f is the frequency of oscillation?
(a) For R = 1 K, 1 , 1 C F f kHz = =
(b) For R = 3 K, 1 , 3 C F f kHz = =
(c) The gain of the op-amp state should be less than two for proper operation.
(d) The gain of the op-amp stage should be three for proper operation
6.8 A 10 bit A/D converter is used to digitize an analog signal in the 0 to 5 V range.
The maximum pea k to peak ripple voltage that can be allowed in the D.C. supply voltage is:
(a) nearly 100 mV (b) nearly 50 mV
(c) nearly 25 mV (d) nearly 5.0 mV
6.9 Three devices A, B and C have to be connected to a 8085 microprocessor. Device A has highest priority and device C has the lowest priority. In this context which of the following is correct assignment of interrupt inputs?
(a) A uses TRAP, B uses RST 5.5 and C uses RST 6.5
(b) A uses RST 7.5, B uses RST 6.5 and C uses RST 5.5
(c) A uses RST 5.5, B uses RST 6.5 and C uses RST 7.5
(d) A uses RST 5.5, B uses RST 6.5 and C uses TRAP
6.10 , and V V V are the instantaneous line to neutral voltages and , and i i i
are instantaneous line current sin a balanced three-phase circuit, the
computation, V i i V V i – - – will yield a quantity proportional to
(a) the active power (b) the power factor
(c) the reactive power (d) the complex power
6.11 A CRO screen has ten divisions on the horizontal scale. If a voltage signal 5 sin 314 45 t + ° is examined with a line base settings of 5 msec/div, the number of cycles of signal displayed on the screen will be
(a) 0.5 cycles (b) 2.5 cycles (c) 5 cycles (d) 10 cycles
6.12 A metal strain gauge has factor of two. Its nominal resistance is 120 ohms. If it undergoes a strain of 10 , the value of change of resistance in response to the – 5 strain is:
(a) 240 ohms (b) 2 10 × ohms – 5
(c) 2.5 10 × ohms (d) 1.2 10 × ohms – 5 – 3
6.13 The line integral of the vector potential A around the boundary of a surface S represents
(a) flux through in the surface S (b) flux density in the surface S
(c) magnetic density (d) current density
6.14 A 220/440 V, 50 Hz, 5 kVA single phase transformer operates on 220 V, 40 Hz supply with secondary winding. Then
(a) the eddy current loss and hysteresis loss of the transformer decrease
(b) the eddy current loss and hysteresis loss of the transformer increase
(c) the hysteresis loss of the transformer increases while eddy current loss
remains the same
(d) the hysteresis loss remain the same whereas eddy current loss decreases
6.15 A cumulative compounded long shunt motor is driving a load at a rated torque and rated speed. If the series field is shunted by a resistance equal to the resistance of the series field, keeping the torque constant,
(a) the armature current increases (b) the motor speed increases
(c) the armature current decreases (d) the motor speed decreases
6.16 A three phase alternator has negligible stator resistance. A short circuit test is conducted on this alternator. At a particular speed a field current of I is required to drive the rated armature current. If the speed of the alternator is reduced to half, the field current required to maintain rated armature current
(a) would be equal to I (b) would be equal to
(c) would be equal to
(d) cannot be predicated due to insufficient data
6.17 A synchronous motor operates at 0.8 p.f. lagging. If the field current of the motor is continuously increased
(a) the power fa ctor decreases upto a certain value of field current and
thereafter it increases
(b) the armature current increases upto a certain value of field current and
thereafter it decreases
(c) the power factor increases upto a certain value of field current and thereafter it decreases
(d) the armature current decreases upto a certain value of field current and
thereafter it increases
6.18 A three phase slip ring induction motor is fed from the rotor side with stator winding short circuited. The frequency of the currents flowing in the short circuited stator is:
(a) slip frequency (b) supply frequency
(c) frequency corresponding to rotor speed (d) zero
6.19. A three phase overhead transmission line has its conductors horizontally spaced with spacing between adjacent conductors equal to ”d‘. if now the conductors of the line are rearranged to form an equilateral triangle of sides equal to ”d‘ then
(a) average capacitance and inductance will increase
(b) average capacitance will increase and inductance will increase
(c) average capacitance will increase and inductance will decrease
(d) surge impedance loading of the line increases
6.20. The distribution system shown in figure is to be protected by over current system of protection.
For proper fault discrimination directional over current relays will be required at locations
(a) 1 and 4 (b) 2 and 3 (c) 1, 4 and 5 (d) 2, 3 and 5
6.21. The transient stability of the power system can be effectively improved by
(a) excitation control (b) phase shifting transformer
(c) single pole switching of circuit breakers
(d) increasing the turbine valve opening
6.22. In load flow analysis, the load connected at a bus is represented as
(a) constant current drawn from the bus
(b) constant impedance connected at the bus
(c) voltage and frequency dependent source at the bus
(d) constant real and reactive drawn from the bus6.23. The thermal resistance between the body of a power semiconductor device and the ambient is expressed as
(a) voltage across the device divided by current through the device
(b) average power dissipated in the device divided by the square of the RMS
current in the device
(c) average power dissipated in the device divided by the temperature difference from body to ambient.
(d) temperature difference from body to ambient divided by average power
dissipated in the device.
6.24. When a line commutated converter operates in the inverter mode
(a) it draws both real and reactive power from the A.C. supply
(b) it delivers both real and reactive power to the A.C. supply
(c) it delivers real power to the A.C. supply
(d) it draws reactive power from the A.C. supply
6.25 a chopper operating at a fixed frequency is feeding an R-L load. As the duty ratio of the chopper is increased from 25% to 75% , the ripple in the load current
(a) remains constant
(b) decreases, reaches a minimum at 50% duty ratio and then increases
(c) increases, reaches a minimum at 50% duty ratio and then decreases
(d) keeps on increasing as the duty ratio is increased
SECTION – B
7.1 Determine the voltage V and V in the following circuit(figure below) using cutest analysis. Choose circuit elements marked 1 2 3 in the three for this purpose.
7.2. Consider circuit shown in figure. Determine t in terms of i t Evaluate. .
7.3. A control system is described by the differential equation
Where, y t is the output and u t is the input. The realization of the system is
shown in figure with ß as unknown.
7.4. A unity feedback system has the open loop transfer function
(i) Calculate the Break awa y point and the imaginary axis crossing points
(ii) Sketch the root loci as K varies from 0 to 8 .
(iii) Give the procedure for finding closed loop transfer function directly from the root locus diagram for a given damping ratio of dominant root pair.
7.5. A Schmitt trigger is shown in figure (a) and its characteristic is shown in figure
(b). Here 10 , 10 , 5, 5 . V V V V V V V = = – = = -
(i) If the input is V t = + 1 7 sin volts, where, = 200 p radians/sec, calculate
the time duration in each cycle for which the output of the Schmitt trigger
remains at -10V level.
(ii) Draw the circuit diagram of an astable multi-vibrator using the Schmitt
trigger in figure (a), a resistor () and a capacitor (C). if the period of this
astable multi-vibrats is now to be doubled, what should be the new value of
resistance.
7.6. The output V of an N-bit D/A converter is given by
Where, K is a proportionality factor determined by the system parameters and where the coefficients a represent the binary word and a = 1 0 if the j bit is
(i) A 6-bit D/A converter gives V V = 3.6 for the word 100100. find the value of V for the word 110011.
(ii) For the R-2R ladder D/A converter (shown in figure) find the value of the
output voltage V where 6 V = Volts. Clearly show the steps in the
calculations.
7.7. A bridge circuit is shown in figure.
(a) The output signal of the bridge is V Looking into this part find an .
expression for the Thevenin equivalent resistance of the bridge.
(b) If R R x R R x R R = – = + = 1 , 1 and , find an expression for the output
voltage V in terms of E and x. take 0 R = in this case.
7.8. A pair of long parallel wires carry a current of I amp in opposite direction in the plane of a closed rectangular loop of wire of dimensions l and b as shown in figure. Determine an expression for the induced electromotive force in the loop using Faraday‘s law of induction.
7.9. A 10 kW, 240V dc shunt motor draws a line current of 5.2A while running at no load speed of 1200 rpm from a240V dc supply. It has an armature resistance of 0.25 ohm and a field resistance of 160 ohm. Estimate the efficiency of the mtoro when it delivers rated load.
7.10. A 40 kW, 3-phase slip ring induction motor of negligible stator impedance runs at a speed of 0.96 times synchronous speed at rated torque. The slip at maximum torque is 4 times the full load value. If the rotor resistance of the motor is increased by 5 times, determine:
(a) the speed, power output and rotor copper loss at rated torque,
(b) the speed corresponding to maximum torque.
Neglect mechanical losses.
7.11. A 10 kVA, 380V, 50 Hz, 3-phase, star connected salient pole alternator has direct
axis and quadrature axis reactances of 12 ohm and 8 ohm respectively. The
armature has a resistance of 1 per phase. The generator delivers rated load at 0.8 p.f. lagging with the terminal voltage being maintained at rated value. If the load angle is 16.15°, determine
(a) the direct and quadrature axis components of armature current.
(b) excitation voltage of the generator.
7.12. A 33 kV single circuit, 3-phase transmission line has the ABCD parameters A D B = = ° = ° 1 0 , 11.1863.43 ohm.
The line is to deliver 7.5 MVA at 0.85 pf lagging at the load end. The receiving end voltage is 32 kV (line to line). How much active and reactive power is to be dispatched from the sending end?
7.13. A 3-phase, star connected generator supplies a star connected inductive load through a transmission line. The star point of the load is grounded and the generator neutral is ungrounded. The load reactance is j 0.5 p.u per phase and the line reactance is j 0.1 p.u. per phase. The positive, negative and zero sequence reactances of the generator are j 0.5, j0.5 and j0.05 p.u respectively.
7.14. A 3-phase fully controlled thyristor bridge converter is operated from an a.c. supply of 400 V rms line to line. When the converter is operated in the rectifier mode at a control angle a = 30°, the overlap angle due to the line reactance is 15°. Calculate the reduction in d.c. output voltage due to the overlap. If the converter operates in the inverter mode with a a = 120° and without any change in the d.c. load current, what will be the overlap angle
7.15. A separately excited d.c. motor has the following name plate data:
220 V, 100 A, 2200 rpm
The armature resistance is 0.1 ohm and inductance is 5 mH. The motor is fed by a chopper which is operating from a d.c. supply of 250 V. Due to restrictions in the power circuit, the chopper can be operated over a duty cycle range from 20% to 80% . Determine the range of speeds over which the motor can be operated at rated torque.
Subscribe to:
Posts (Atom)
