SECTION A 1. This question consists of TWENTYFIVE subquestions (1.1 1.5) of ONE mark each. For each of these subquestions, 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 9 out of phase with the input voltage (d) can be greater than the input voltage, and is in phase with the input voltage. 1. Two incandescent light bulbs of 4 W and 6 W rating are connected in series across the mains. Then (a) the bulbs together consume 1 W (b) the bulbs together consume 5W (c) the 6 W bulb glows brighter (d) the 4 W bulb glows brighter 1.3 A unit step voltage is applied at t = 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 = is zero. (c) The energy stored in the inductor in the steady state is zero. (d) The resistor current eventually falls to zero. 1.4 Given two coupled inductors L 1 and L, their mutual inductance M satisfies (a) 1 M = L L (b) M > ( L L ) 1 (c) M > LL 1 (d) M LL 1 1.5 A passive port network is in a steadystate. Compared to its input, the steady state output can never offer (a) higher voltage (c) greater power (b) lower impedance (d) better regulation
1.6 A singlephase transformer is to be switched to the supply to have minimum inrush current. The switch should be closed at (a) maximum supply voltage (c) (b) zero supply voltage 1 maximum supply voltage (d) 1 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 shortpitched by an electrical angle of (a) 3 (b) 36 (c) 7 (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,.8 power factor leading is given by No load Rated armature current unit pf A B C D Exciting current (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 1.1 X, X and X are steady state daxis synchronous reactance, transient daxis d d d reactance and subtransient daxis reactance of a synchronous machine respectively. Which of the following statements is true? (a) X > X > X (b) X > X > X d d d (c) d d d d d d X > X > X (d) Xd > Xd > Xd 1.11 A 5 Hz balanced threephase, Yconnected supply is connected to a balanced three phase Yconnected load. If the instantaneous phaseα of the supply voltage is Vcos(ωt) and the phaseα of the load current is Icos(ωtφ), the instantaneous threephase power is (a) a constant with a magnitude of VIcosφ
(b) a constant with a magnitude of (3/)VIcosφ (c) timevarying with an average value of (3/) VIcosφ and a frequency of 1 Hz. (d) timevarying with an average value of VIcosφ and a frequency of 5 Hz. 1.1 In the protection of transformers, harmonic restraint is used to guard aainst (a) magnetizing inrush current (b) unbalanced operation (c) lightning (d) switching overvoltages 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 type1, 3pole, openloop system is shown in Fig.P1.14. the closed loop system is GH plane 1.4 w= o w= (a) always stable (b) marginally stable (c) unstable with one pole on the right half splane (d) unstable with two poles on the right half splane 1.15 Given the homogeneous statespace equaion 3 1 x& = x the steady state value x x ( t ) 1] T, is (a) x ss = (b) ss = lim, given the initial state value of x() = [1 x ss t 3 = (c) x ss 1 = 1 (d) xss =
1.16 If an energy meter disc makes 1 revolutions in 1 seconds when a load of 45 W is connected to it, the meter constant (in rev/kwh) is (a) 1 (b) 5 (c) 16 (d) 8 1.17 The minimum number of wattmeter (s) required to measure 3phase, 3wire balanced or unbalanced power is (a) 1 (b) (c) 3 (d) 4 1.18 In the singlestage transistor amplifier circuit shown in Fig.P1.18, the capacitor C E is removed. Then, the ac smallsignal midband voltage gain of the amplifier 1V Input C E Output (a) increases (c) is unaffected (b) decreases (d) drops to zero 1.19. Among the following four, the slowest ADC (analogtodigital converter) is (a) parallel comparator (i.e., flash) type (b) successive approximation type (c) integrating type (d) counting type 1.. The output of a logic gate is 1 when all its inputs are at logic. The gate is either (a) a NAND or an EXOR gate (c) an AND or an EXNOR gate (b) a NOR or an EXOR gate (d) a NOR or an EXNOR gate 1.1. The output f of the 4to1 MUX shown in Fig.P1.1 is V CC 1 MUX S 1 S X Y (a) xy x (b) xy (c) x y (d) xyx
1.. An opamp has an openloop gain of 1 5 and an openloop upper cutoff frequency of 1 Hz. If this opamp is connected as an amplifier with a closedloop gain of 1, then the new upper cutoff frequency is (a) 1 Hz (b) 1 Hz (c) 1 khz (d) 1 khz 1.3. 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 1.4. ACtoDC circulating current dual converters are operated with the following relationship between their triggering angles (α 1 and α ). (a) α 1 α = 18 (b) α 1 α = 36 (c) α 1 α = 18 (d) α 1 α = 9 1.5 In case of an armature controlled separately excited dc motor drive with closedloop 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. This question consists of TWENTYFIVE subquestions (.1.5) of TWO marks each. For each of these subquestions, 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 The electric field E ur (in volts/metre) at the point (1,1,) due to a point charge of 1µC located at (1,1,1) (coordinates in metres)is 1 6 (a) ( i k ) (b) ( i k ) 5πε 1 6 6 1 πε (c) ( i k ) (d) ( i k ) 5πε 6 1 πε.. A connected network of N> 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.3. Consider the star network shown in Fig.P.3. The resistance between terminals A and B with C open is 6Ω, between terminals B and C with A open is 11Ω, and between terminals C and A with B open is 9Ω. Then A R A R B R C (a) R = 4 Ω, R = Ω, R = 5Ω (b) R = Ω, R = 4 Ω, R = 7Ω A B C A B C (c) R = 3 Ω, R = 3 Ω, R = 4Ω (d) R = 5 Ω, R = 1 Ω, R = 1Ω A B C B C A B C.4. Given the potential function in free space to be V(x) = ( 5x 5y 5z ) volts, 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) 1; (i j k) (b) 1 3 ;(i j k) (c) 1 3 ;[(i j k)/ 3 ] (d) 1 3 ;[(i j k)/ 3 ].5. The hysteresis loop of a magnetic material has an area of 5 cm with the scales given as 1 cm = AT and 1 cm = 5 mwb. At 5 Hz, the total hysteresis loss is (a) 15 W (b) W (c) 5 W (d) 5 W.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.7. A 3phase transformer has rating of MVA, kv (star) 33 kv (delta) with leakage reactance of 1%. The transformer reactance (in ohms) referred to each phase of the L.V. deltaconnected side is (a) 3.5 (b) 19.6 (c) 18.5 (d) 8.7
.8. A 75 NVA, 1 kv synchronous generator has X d =.4 p.u. The X d value (in p.u.) is a base of 1 MVA, 11 kv is (a).578 (b).79 (c).41 (d).44.9. A starconnected 44 V, 5 Hz alternators has per phase synchronous reactance of 1Ω. It supplies a balanced capacitive load current of A, as shown in the per phase equivalent circuit of Fig..9. It is desirable to have zero voltage regulation. The load power factor should be J1Ω A ~ Eph = 44 V 3 Load (a).8 (b).47 (c).39 (d).9.1. A 4 V singlephase ac source is connected to a load with an impedance of 1 6 Ω. A capacitor is connected in parallel with the load. If the capacitor supplies 15 VAR, the real power supplied by the source is (a) 36 W (b) 88 W (c) 4 W (d) 1 W.11. A 5 Hz alternator is rated 5 MVA, kv, with X d = 1. per unit and X =. per unit. It supplies a purely resistive load of 4 MW at kv. The load d 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. (b) 6.4 (c) 3. (d)..1. Consider the model shown in Fig.P.1 of a transmission line with a series capacitor at its midpoint. The maximum voltage on the line is at the location P 1 j.1pu j.1pu Vs = 1pu j.1pu P P 3 P 4 I=1pu pf=1 V r (a) P 1 (b) P (c) P 3 (d) P 4
.13. A power system has two synchronous generators. The Governorturbine characteristics corresponding to the generators are P 1 = 5(5 f), P = 1(51 f) Where f denotes the system frequency in Hz, and P 1 and P are, respectively, the power outputs (in MW) of turbines 1 and. assuming the generators and transmission network to be lossless, the system frequency for a total load of 4 MW is (a) 47.5 Hz (b) 48. Hz (c) 48.5 Hz (d) 49. Hz.14. The conductors of a 1 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) 5. mh (b) 45.3 mh (c) 3.8 mh (d) 19.6 mh.15. Given the relationship between the input u(t) and the output y(t) to be t 3 ( t τ t τ e ) u τ dτ, ( ) = ( ) y t ( ) the transfer function Y(s)/U(s) is (a) s e s 3 s (b) ( ) s 3 (c) s 5 s 3 s 7 (d) ( ) s 3.16. The asymptotic approximation of the logmagnitude versus frequency plot of a minimum phase system with real poles and one zero is shown in Fig.P.16. Its transfer functions is db ( s 5) (a) s ( s ) ( s 5) 4dB/dec 54 6dB/dec 1 ( s 5) (b) s 4dB/dec s 5 (c) (d) ( ) ( ) ( s 5) ( ) ( 5) s s s 5 ( s 5) ( ) ( 5) s s s.1 5 5 6dB/dec rad/s.17. A 1µA ammeter has an internal resistance of 1Ω. For extending its range to measure 5µA, the shunt required is of resistance (in Ω) (a). (b). (c) 5. (d) 5.
.18. Resistances R 1 and R have, respectively, nominal values of 1Ω and 5Ω, and tolerances of ±5% and ±1%. The range of values for the parallel combination of R 1 and R is (a) 3.77 Ω to 3.636 Ω (c) 3.37 Ω to 3.678 Ω (b).85 Ω to 3.371 Ω (d) 3.19 Ω to 3.435 Ω.19. For the oscillator circuit shown in Fig.P.19, the expression for the time period of oscillation can be given by (where τ=rc) R (a) τ ln 3 (b) τ ln 3 C (c) τ ln (d) τ ln R R v o.. An Intel 885 processor is executing the program given below. MVI A, 1H MVI B, 1H 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) (c) 3 (d) 4.1. A sampleandhold (S/H) circuit, having a holding capacitor of.1 nf, is used at the input of an ADC (analogtodigital converter). The conversion time of the ADC is 1µsec, and during this time, the capacitor should not lose more than.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).5 ma (b).5 ma (c) 5. µa (d).5 µa.. An opamp, having a slew rate of 6.8 V/µsec, is connected in a voltage follower configuration. If the maximum amplitude of the input sinusoid is 1V, then the minimum frequency at which the slew rate limited distortion would set in at the output is (a) 1. MHz (b) 6.8 MHz (c) 1. MHz (d) 6.8 MHz
.3. An nchannel JFET, having a pinchoff voltage (V p ) of 5 V, shows a transconductance (g m ) of 1 ma/v when the applied gatetosource voltage (V GS ) is 3V. Its maximum transconductance (in ma/v) is (a) 1.5 (b). (c).5 (d) 3..4. A halfwave thyristor converter supplies a purely inductive load, as shown in Fig..4. If the triggering angle of the thyristor is 1, the extinction angle will be (a) 4 (b) 18 (c) (d) 1 ~ V msinωt L.5. A singlephase fullbridge voltage source inverter feeds a purely inductive load, a shown in Fig.P.5, where T 1, T, T 3, T 4 are power transistors and D 1, D, D 3, D 4 are feedback diodes. The inverter is operated in squarewave mode with a frequency of 5 Hz. If the average load current is zero, what is the time duration of conduction of each feedback diode in a cycle? T 1 T 4 D 1 D 3 L D 4 D T 3 T (a) 5 msec (b) 1 msec (c) msec (d).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 Qfactor of the circuit shown in Fig.P3. Data: R = 1Ω, C= 3µF, L 1 = 4 mh, L = 1 mh and M = 1 mh M ~ R C L 1 L
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: i 1 3 5 7 t(s) (a) the core flux φ oc with the secondary of the transformer open (b) the opencircuited secondary terminal voltage v (t) (c) the shortcircuited secondary current i (t), and (d) the core flux φ sc with the secondary of the transformer shortcircuited. 5. Consider the voltage waveform ν, shown in Fig.P5. Find. ν (a) the dc component of ν, 1V (b) the amplitude of the fundamental component of ν, and (c) the rms value of the ac part of ν. 1V 3 5 8 1 13 t(ms) 6. In a dc motor running at rpm, the hysteresis and eddy current losses are 5W and W respectively. If the flux remains constant, calculate the speed at which the total iron losses are halved. 7. A dc series motor is rated 3V, 1 rpm, 8 A (refer to Fig.P7). the series field resistance is.11ω, and the armature resistance is.14ω. If the flux at an armature current of A is.4 times of that under rated condition, calculate the speed at this reduced armature current of A. R 1=.11Ω R =.14Ω 3V
8. A 5 kw synchronous motor is tested by driving it by another motor. When the excitation is not switched on, the driving motor takes 8W. When the armature is shortcircuited and the rated armature current of 1 A is passed through it, the driving motor requires 5 W. On opencircuiting the armature with rated excitation, the driving motor takes 18W. Calculate the efficiency of the synchronous motor at 5% load. Neglect the losses in the driving motor. 9. Two identical synchronous generators, each of 1 MVA, are working in parallel supplying 1 MVA at.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 d = X q =.8 p.u., no field saturation and rated voltage across load. Reasonable approximations may be made. 1. A 13 kv transmission line AB is connected to a cable BC. The characteristic impedances of the overhead line and the cable are 4Ω and 8Ω respectively. Assume that these are purely resistive. A 5 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 Ybus matrix given in per unit values, where the first, second, third and fourth row refers to bus 1,, 3 and 4 respectively, draw the reactance diagram. 6.5 1.5 4 Ybus = j.5.5 9 4 4 4 8 1. A synchronous generator is connected to an infinite bus through a lossless double circuit transmission line. The generator is delivering 1. per unit power at a load angle of 3 when a sudden fault reduces the peak power that can be transmitted to.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 linetoground fault occurs on an unloaded generator in phase a positive, negative, and zero sequence impedances of the generator are j.5 p.u., j.5p.u., and j.15 p.u. respectively. The generator neutral is grounded through a reactance of j.5 p.u. The prefault generator terminal voltage is 1. 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 1 (P G1 ) =.6P G1 8P G1 35 (Thousand Rupees/Hour) Generator : C (P G ) =.9P G 7P G1 4 (Thousand Rupees/Hour) The generator limits are 1 MW P G1 65 MW 5 MW P G 5 MW A load demand of 6 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 openloop transfer function of ( ) G s = 1 ( 1) s s (a) Determine the magnitude of G(jω) in db at an angular frequency of ω= 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 3 s s Ks K =. Sketch the root locus as K varies from zero to infinity. Find the angle and real axis intercept of the asymptotes, breakaway/breakin 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 111 (i.e., Q 3,Q,Q 1,Q =111). Determine the MOD number of the counter. D Q 3 D Q D Q 1 D Q Clock
18. For the opamp circuit shown in Fig.P18, determine the output voltage ν. Assume that the opamps are ideal. 1V 1kΩ kω 4kΩ 8kΩ kω 3kΩ 1V V O 1kΩ 19. The transistor in the amplifier circuit shown in Fig.P19 is biased at I C = 1mA. Use V = = kt / q = 6 mv, β =, r =, and r. T ( ) b (a) Determine the ac small signal midband voltage gain ν /ν I of the circuit. (b) Determine the required value of C E for the circuit to have a lower cutoff frequency of 1 Hz. V CC R C 1kΩ ν o R B ν i 5kΩ C E R E 1Ω. A simple active filter is shown in Fig.P. Assume ideal opamp. Derive the transfer function ν /ν 1 of the circuit, and state the type of the filter (i.e., highpass, lowpass, bandpass, or bandreject). Determine the required values of R 1, R and C in order for the filter to have a 3dB frequency of 1 khz, a highfrequency input resistance of 1 kω, and a high frequency gain magnitude of 1. R ν i R 1 C ν
1. A voltage commutated thyristor chopper circuit is shown in Fig.P1. The chopper is operated at 5 Hz with 5% duty ratio. The load takes a constant current of A. (a) Evaluate the circuit turn off time for the main thyristor Th i. (b) Calculate the value of inductor L, if the peak current through the main thyristor Th i is limited to 18% of the load current. (c) Calculate the maximum instantaneous output voltage of the chopper. Th 1 I L=A C 6µF Th D V dc L D 1 Load 1V. A separately excited dc motor is controlled by varying its armature voltage using a single phase fullconverter bridge as shown in Fig.P. the field current is kept constant at the rated value. The motor has an armature resistance of.ω, and the motor voltage constant is.5 V/(rad/sec). The motor is driving a mechanical load having a constant torque of 14 Nm. The triggering angle of the converter is 6. 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. I 5V(rms) 5Hz R =.Ω ~ I f constant