Electrical Engineering - 2005 Unsolved Paper

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ELECTRICAL ENGINEERING - UNSOLVED PAPER - 2005

SECTION – I

 Single Correct Answer Type
 There are five parts in this question. Four choices are given for each part and one of them is

correct. Indicate you choice of the correct answer for each part in your answer-book by

writing the letter (a), (b), (c) or (d) whichever is appropriate

01 Problem

In the figure given below the value of R is

a. 2.5 Ω
b. 5.0 Ω
c. 7.5 Ω
d. 10.0 Ω

02 Problem

The RMS value of the voltage u(t) = 3 + 4cos (3t) is

a. √l7 V
b. 5 V
c. 7 V
d. (3 + 2√2)V

03 Problem

For the two port network shown in the figure the Z-matrix is given by

a.

b.
c.

d.

04 Problem

In the figure given below, 4 the initial capacitor voltage is zero. The switch is
closed at t = 0. The final steady-state voltage across the capacitor is

a. 20 V
b. 10 V
c. 5 V
d. 0 V

05 Problem

If Ē is the electric field intensity, ( × Ē) is equal to

a. Ē
b. I Ē l
c. null vector
d. zero

06 Problem

A system with zero initial conditions has the closed loop transfer function. T(s)
= (s2 + 4)/((s + 1) (s + 4)). 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

07 Problem

Figure shows the root locus plot (location of poles not given) of a third order system
whose open loop transfer function is

a. K/s3
b. K/(s2(s+ 1))
c. K/(s(s2 + 1))
d. K/(s(s2 - 1))

08 Problem

The gain margin of a unity feedback control system with the open
loop transfer function G (s) = (s + 1 )/s2 is

a. 0
b. 1/√2
c. √2
d.

09 Problem

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 [Pq] 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 Problem

If P and Q are two random events, then the following is TRUE

a. Independence of P and Q implies that probability (P  Q ) = 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) ≤ Probability (P)

11 Problem

If S = x 3 dx , then S has the value
1

a. (-1)/3
b. 1/4
c. 1/2
d. 1

12 Problem

The solution of the first order differential equation x(t) = -3x(t), x (0) = X0 is

a. x (t) = x0 e-3t
b. x (t) = x0 e-3
c. x (t) = x0 e-1/3
d. X (t) = X0 e-1

13 Problem

The equivalent circuit of a transformer has leakage reactances X1, X'2 and
magnetizing reactance XM. Their magnitudes satisfy

a. X1 >> X'2 >>XM
b. X1 << X'2 << XM
c. X1 ≈ X‘2>>XM
d. X1 ≈ X'2 >> XM

14 Problem

Which three-phase connection can be used in a transformer to introduce a
phase difference of 30° between its output and corresponding input time
voltages

a. Star - Star
b. Star - Delta
c. Delta - Delta
d. Delta - Zigzag

15 Problem

On the torque/speed curve of induction motor shown in the figure four points
of operation are marked 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 Problem

For an induction motor, operating at a slip s, the ratio of gross power output to
air gap power is equal to

a. (1-s)2
b. (1 - s)
c. √(1- s)
d. (1 - √s)

17 Problem

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 Problem

An 800 kV transmission line has a maximum power transfer capacity of P. If it
is operated at 400 kV with the series reactance unchanged, then new
maximum power transfer capacity is approximately

a. P
b. 2P
c. P/2
d. P/4

19 Problem

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 Problem

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 Problem

The Q - meter works on the principle of

a. mutual inductance
b. self inductance
c. series resonance
d. parallel resonance

22 Problem

A PMMC voltmeter is connected across a series combination of a DC voltage
source V1=2 V and an AC voltage source V2 (t) = 3 sin (4t) V. The meter reads

a. 2 V
b. 5 V
c. (2 + √3/2) V
d. (√17/2) V

23 Problem

Assume that D1 and D2 in figure are ideal diodes. The value of current I is

a. 0 mA
b. 0.5 mA
c. 1 mA
d. 2 mA

24 Problem

The 8085 assembly language instruction that stores the content of H and L
registers into the memory locations 2050H and 2051H, respectively, is

a. SPHL 2050H
b. SPHL 2051H
c. SHLD 2050H
d. STAX 2050H

25 Problem

Assume that the N-channel MOSFET shown in the figure is ideal, and that its
thereshold voltage is + 1.0 V. the voltage Vab between nodes a and b is

a. 5 V
b. 2 V
c. 1 V
d. 0 V

26 Problem

The digital circuit shown in the figure works as a

a. JK flip-flop
b. Clocked RS flip-flop
c. T flip-flop
d. Ring counter

27 Problem

A digital-to-analog converter with a full-scale output voltage of 3.5 V has a
resolution close to 14 m V. Its bit size is

a. 4
b. 8
c. 16
d. 32

28 Problem
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 Problem

A three-phase diode bridge rectifier is fed from a 400 V RMS, 50 Hz, three-
phase AC source. If the load is purely resistive, then peak instantaneous
output voltage is equal to

a. 400V
b. 400√2V
c. 400√(2/3) V
d. (400√3) V

30 Problem

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 triple harmonics

31 Problem

The RL circuit of the figure is fed from a constant magnitude, variable
frequency sinusoidal voltage source VIN- At 100 Hz, the R and L elements each
have a voltage drop URMS- IF the frequency of the source is changed to 50Hz,
then new voltage drop across R is

a. √(5/8) uRMS
b. √(2/3) uRMS
c. √(8/5) uRMS
d. √(3/2) uRMS

32 Problem

For the three-phase circuit shown in the figure the ratio of the currents IR : ly :
IB is given by

a. 1 : 1 : √3
b. 1 : 1 : 2
c. 1 : 1 : 0
d. 1 : 1 : √3/2

33 Problem

For the triangular wave form shown in the figure, the RMS value of the voltage is
equal to

a. √(1/6)
b. √(1/3)
c. 1/3
d. √(2/3)

34 Problem

The circuit shown in the figure 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

a. 0 A
b. 0.5 A
c. 1 A
d. 2 A

35 Problem

The charge distribution in a metal-dielectric semiconductor specimen is shown in
the figure. The negative charge density decreases linearly in the semiconductor
as shown. The electric field distribution is as shown in

a.

b.

c.

d.

36 Problem

In the given figure, the Thevenin's equivalent pair (voltage, impedance), as
seen at the

a. (2V, 5 Ω)
b. (2 V, 7.5 Ω)
c. (4V, 5 Ω)
d. (4 V, 7.5 Ω)

37 Problem

A unity feedback system, having an open loop gain G(s)H(s) = (K(1 - s))/(1 + s),
becomes stable when

a. |K|>1
b. K > 1
c. |K|<1
d. K < - 1

38 Problem

When subjected to a unit step input, the closed loop control system shown in
the figure will have a steady state error of

a. -1.0
b. -0.5
c. 0
d. 0.5

39 Problem

In the GH(s) plane, the Nyquist plot of the loop transfer function G(s)H(s)π=e(
-0.25)/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 Problem

If the compensated system shown in the figure has a phase margin of 60° at
the crossover frequency of 1 rad/sec, then value of the gain K is

a. 0.366
b. 0.732
c. 1.366
d. 2.738

41 Problem

For the matrix P = one of the eigen values is equal to -2. Which

of the following is an eigen vector?

a.

b.

c.

d.

42 Problem

If R = , then top row of R-1 is

a. [5 6 4]
b. [5 -3 1]
c. [2 0 -1]
d. [2 -1 1/2]

43 Problem

A fair coin is tossed three times in succession. If the first toss poduces 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 Problem

For the function f(x) = x2 e-x, the maximum occurs when x is equal to

a. 2
b. 1
c. 0
d. -1

45 Problem

For the scalar field u = (x2/2) + (y2/3), magnitude of the gradient at the point (1,
3) is

a. √(13/9)
b. √(9/2)
c. √5
d. 9/2

46 Problem

For the equation (t) +3 (t) + 2x(t) = 5, the solution x (t) approaches which of
the following values as t → ∞?

a. 0
b. 5/2
c. 5
d. 10

47 Problem

The Laplace transform of a function f(t) is F(s) = (5s2 + 23s + 6)/(s(s2 + 2s + 2)).
As t → ∞, f(t) approaches ?

a. 3
b. 5
c. 17/2
d. ∞

48 Problem

The Fourier series for the function f(x) = sin2 x is

a. sin x + sin 2x
b. 1 - cos 2x
c. sin 2x + cos 2x
d. 0.5 - 0.5 cos 2x

49 Problem

If u(t) is the unit step and δ (t) is the unit impulse function, the inverse z-
transform of F(z) = (1/(z + 1)) for k > 0 is

a. (-1)k δ(k)
b. δ(k) - (-1)k
c. (-1)k u(k)
d. u(k) - (-1)k

50 Problem

Two magnetic poles revolve around a stationary armature carrying two coil (c1 –
c1’, c2 – c2’) as shown in the figure. 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 coilsides c1 and c2.

a. in c1, no emf in c2
b. in c1, no emf in c2
c. in c2, no emf in c1
d. in c2, no emf in c1

51 Problem

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 Problem

In relation to DC machines, match the following and choose the correct

combination
Group -1 Group – 2
Performance Variables Proportional to
P Armature emf (E) 1 Flux (Ф), speed (ω) and
armatrue current (la)
Q Developed torque (T) 2 Ф and ω only
R Developed power (P) 3 Ф and la only
4 la and ω only
5 la 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 Problem

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 Problem

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 Problem

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%, then 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 Problem

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. uick acceleration
c. high efficiency
d. reduced size

57 Problem

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-synchrbnous 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 Problem

The parameters of a transposed overhead transmission line are given as : Self
reactance xs = 0.4 Ω /km and Mutual reactance xm = 0.1 Ω /km
The positive sequence reactance X1 and zero sequence reactance X0,
respectively, in Ω /km are

a. 0.3, 0.2
b. 0.5, 0.2
c. 0.5, 0.6
d. 0.3, 0.6

59 Problem

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
b. 1.00
c. 0.80 lag
d. 0.90 lag

60 Problem

The network shown in the given figure has impedances in p.u. as indicated. The
diagonal element Y22 of the bus admittance matrix YBUS of the network is

a. -j 19.8
b. + j 20.0
c. +j 0.2
d. - j 19.95

61 Problem

A load centre is at an equidistant from the two thermal generating stations G1
and G2 as shown in the figure. The fuel cost characteristics of the generating
stations are given by
F1 = a + bP1 + cP12 Rs/hour
F1 = a + bP2 + 2CP22 Rs/hour
where P1 and P2 are the generation in MW of G1 and G2, respectively.
For most economic generation to meet 300 MW of load, P1 and P2, respectively,
are

a. 150, 150
b. 100, 200
c. 200, 100
d. 175, 125

62 Problem

Two networks are connected in cascade as shown in the figure. With the usual
notations the equivalent A, B, C and D constants are obtained. Given that, C =
0.025 45°, the value of Z2 is

a. 10 300 Ω
b. 40 -450 Ω
c. 1 Ω
d. 0 Ω

63 Problem

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 bar as shown in the figure. 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, then 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 Problem

The simultaneous application of signals x(t) and y(t) to the horizontal and
vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-8
display. If P and Q are constants, and x(t) = P sin (4t + 30), then y(t) is equal to

a. Q sin (4t - 30)
b. Q sin (2t+ 15)
c. Q sin (8t + 60)
d. Q sin (4t + 30)

65 Problem

A DC ammeter has a resistance of 0.1 Ω and its current range is 0-100A. If the
range is to be extended to 0-500A, then meter requires the following shunt
resistance

a. 0.010 Ω
b. 0.011 Ω
c. 0.025 Ω
d. 1.0 Ω

66 Problem

The set-up in the figure is used to measure resistance R. The ammeter and
voltmeter resistances are 0.01 Ω and 2000Ω, respectively. Their readings are 2 A
and 180 V, respectively, giving a measured resistance Ω 90. The percentage
error in the measurement is

a. 2.25 %
b. 2.35 %
c. 4.5 %
d. 4.71 %

67 Problem

A 1000 V DC supply has two 1-core cables as its positive and negative leads:
their insulation resistances to earth are 4 MΩ and 6 MΩ, respectively, as shown
in the figure. A voltmeter with resistance 50 Ω is used to measure the insulation
of the cable. When connected between the positive core and earth, then
voltmeter reads

a. 8 V
b. 16 V
c. 24 V
d. 40 V

68 Problem

Two wattmeters, which are connected to measure the total power on a three -
phase system supplying a balanced load, read 10.5 kW and - 2.5 kW,
respectively. The total powere 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 Problem

The common emitter amplifier shown in the figure is biased using a 1 mA ideal
current source. The approximate base current value is

a. 0 μA
b. 10 μA
c. 100 μA
d. 1000 μA

70 Problem

Consider the inverting amplifier, using an ideal operational amplifier shown in
the figure. The designer wishes to realize the input resistance seen by the small-
signal source to be as large as possible, while keepiong the voltage gain
between -10 and -25. The upper limit on RF is 1 MΩ. The value of R1 should be

a. Infinity
b. 1 MΩ
c. 100 kΩ
d. 40 kΩ

71 Problem

The typical frequency response of a two-stage direct coupled voltage amplifier
is as shown in

a.

b.

c.

d.

72 Problem

In the given figure, if the input is a sinusoidal signal, the output will appear as
shown in

a.

b.

c.

d.

73 Problem

Select the circuit which will produce the given output Q for the input signals X1
and X2 given in the figure

a.

b.

c.

d.

74 Problem

If X1 and X2 are the inputs to the circuit shown in the figure, the output Q is

a.
b.

c.

d.

75 Problem

In the figure, as long as X1 =1 and X2 = 1, the output Q remains

a. at 1
b. at 0
c. at its initial value
d. unstable

76 Problem

The figure shows the voltage across a power semiconductor device and the
current through the device during a switching transitions. It the transition a turn
ON transition or a turn OFF transition? What is the energy lost during the
transition?

a. Turn ON, VI/2 (t1 + t2)
b. Turn OFF, VI (t1 + t2)
c. Turn ON, VI (t1+ t2)
d. Turn OFF, VI/2 (t1 + t2)

77 Problem

An electronic switch S is required to block voltages of either polarity during its
OFF state as shown in the fig. (a). This switch is required to conduct in only one
direction during its ON state as shown in the figure (b)

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 Problem

The given figure shows a step-down chopper switched at 1kHz 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 Problem

An electric motor, developing a starting torque of 15 Nm, starts with a load
torque of 7Nm on its shaft. If the acceleration at start is 2 rad/sec2, the moment
of inertia of the systems must be (neglecting viscous and Coulomb friction)

a. 0.25 kg m2
b. 0.25 Nm2
c. 4 kg m2
d. 4 Nm2

80 Problem

Consider a phase-controlled converter shown in the figure. The thyristor is fired
at an angle a in every postive half cycle of the input voltage. If the peak value of
the instantaneous output voltage equals 230 V, the firing angle α is close to

a. 45°
b. 135°
c. 90°
d. 83.6°

81a Problem

If, at t = 0+, the voltage across the coil is 120 V, the value of resistance R is

a. 0 Ω
b. 20 Ω
c. 40 Ω
d. 60 Ω

81b Problem

For the value of obtained in (a), the time taken for 95% of the stored energy to
be dissipated is close to

a. 0.10 sec
b. 0.15 sec
c. 0.50 sec
d. 1.0 sec

82a Problem

The state transition matrix

1
1 (1 e 3t )
3
a. 0 e 3t )

1 t
1 (e e 3t )
3
b.
0 e t)

1 t
1 (e e 3t )
c. 3
0 e 3t )

1 (1 e t )
d. 0 e t)

82b Problem

The state transition equation

t
t e
a. X(t) = e t

t
t e
b. X(t) = 3e 3t

3t
c. X(t) = t e
3t
3e

3t
t e
d. X(t) = e t

83a Problem

The induced emf (line-to-line) is close to

a. 5.5 kV
b. 7.2 kV
c. 9.6 kV
d. 12.5 kV

83b Problem

The power (or torque) angle is close to

a. 13.9°
b. 18.3°
c. 24.6°
d. 33.0°

84a Problem

the positive sequence driving point reactance at the bus is

a. 2.5 Ω
b. 4.033 Ω
c. 5.5 Ω
d. 12.1 Ω

84b Problem

and the zero sequence driving point reactance at the bus is

a. 2.2 Ω
b. 4.84 Ω
c. 18.18 Ω
d. 22.72 Ω

85a Problem

The transconductance of the MOSFET is

a. 0.75 ms
b. 1 ms
c. 2 ms
d. 10 ms

85b Problem

The voltage gain of the amplifier is

a. +5
b. -7.5
c. +10
d. -10

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Electrical Engineering - 2005 Unsolved Paper

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