Page 1
GATE EE  2002
SECTION  A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V
c
(t),
across the capacitor is given by
(a) 5t (b) 5u(t)  C (c)
5
t
C
(d)
( ) 5u t
C
1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is
(a) ( ) ( ) ( )
2
8 1 1
sin sin 3 sin 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(b) ( ) ( ) ( )
2
8 1 1
sin cos 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
(c) ( ) ( ) ( )
2
8 1 1
cos cos 3 cos 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(d) ( ) ( ) ( )
2
8 1 1
cos sin 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
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 – N + 1 (b) B + N
(c) N – B + 1 (d) N – 2B 1
1.4 Two inphase, 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 XY mode?
(a) A circle of unit radius (b) An ellipse
(c) A parabola
(d) A straight line inclined at 45° with respect to the xaxis
1
0
f(t)
1 2 3
1
1
Page 2
GATE EE  2002
SECTION  A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V
c
(t),
across the capacitor is given by
(a) 5t (b) 5u(t)  C (c)
5
t
C
(d)
( ) 5u t
C
1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is
(a) ( ) ( ) ( )
2
8 1 1
sin sin 3 sin 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(b) ( ) ( ) ( )
2
8 1 1
sin cos 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
(c) ( ) ( ) ( )
2
8 1 1
cos cos 3 cos 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(d) ( ) ( ) ( )
2
8 1 1
cos sin 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
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 – N + 1 (b) B + N
(c) N – B + 1 (d) N – 2B 1
1.4 Two inphase, 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 XY mode?
(a) A circle of unit radius (b) An ellipse
(c) A parabola
(d) A straight line inclined at 45° with respect to the xaxis
1
0
f(t)
1 2 3
1
1
GATE EE  2002
1.5 Given a vector field , F
r
the divergence theorem states that
(a) . .
s v
F dS FdV = ?
? ?
r r ur r
(b) .
s v
F dS FdV = ?×
? ?
r r ur r
(c) .
s v
F dS FdV × = ?
? ?
r r ur r
(d) .
s v
F dS FdV × = ?
? ?
r r ur r
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 torquespeed
characteristic of this motor will be
approximately represented by which curve
of Fig.1.7?
(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
Fig.1.9. The reading of the voltmeter, V,
will be
(a) 0 V (b) 400 V
(c) 600 V (d) 800 V
C
B
A
D
Torque
Speed
400V
400:200:200
~
V
50 Hz
Page 3
GATE EE  2002
SECTION  A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V
c
(t),
across the capacitor is given by
(a) 5t (b) 5u(t)  C (c)
5
t
C
(d)
( ) 5u t
C
1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is
(a) ( ) ( ) ( )
2
8 1 1
sin sin 3 sin 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(b) ( ) ( ) ( )
2
8 1 1
sin cos 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
(c) ( ) ( ) ( )
2
8 1 1
cos cos 3 cos 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(d) ( ) ( ) ( )
2
8 1 1
cos sin 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
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 – N + 1 (b) B + N
(c) N – B + 1 (d) N – 2B 1
1.4 Two inphase, 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 XY mode?
(a) A circle of unit radius (b) An ellipse
(c) A parabola
(d) A straight line inclined at 45° with respect to the xaxis
1
0
f(t)
1 2 3
1
1
GATE EE  2002
1.5 Given a vector field , F
r
the divergence theorem states that
(a) . .
s v
F dS FdV = ?
? ?
r r ur r
(b) .
s v
F dS FdV = ?×
? ?
r r ur r
(c) .
s v
F dS FdV × = ?
? ?
r r ur r
(d) .
s v
F dS FdV × = ?
? ?
r r ur r
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 torquespeed
characteristic of this motor will be
approximately represented by which curve
of Fig.1.7?
(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
Fig.1.9. The reading of the voltmeter, V,
will be
(a) 0 V (b) 400 V
(c) 600 V (d) 800 V
C
B
A
D
Torque
Speed
400V
400:200:200
~
V
50 Hz
GATE EE  2002
1.10 The frequency of the clock signal applied to
the rising edge triggered D flipflop 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 5O and the remaining
parameters are same as those of an ideal diode. The dc component of the source
current is
(a)
50
Vm
p
(b)
50 2
Vm
p
(c)
100 2
Vm
p
(d)
2
50
Vm
p
1.12 The cutin voltage of both Zener diode D
z
and diode D shown in Fig.1.12 is 0.7 V,
while break down voltage of D
z
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
0
) 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 linetoline input voltage to the 3
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
1
= 886 W and W
2
= 886 W
(b) W
1
= 500 W and W
2
= 500 W
(c) W
1
= 0 W and W
2
= 1000 W
(d) W
1
= 250 W and W
2
= 750 W
D Q
Q
FF0
CLK
45O
~
V msin(?t)
?=314 rad/s
1kO
~ 10sin(?t)
?=314 rad/s
D
D Z
V O
I
W 2
5?60°O
5?60°O
5?60°O
R
Y
B
W 1
Page 4
GATE EE  2002
SECTION  A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V
c
(t),
across the capacitor is given by
(a) 5t (b) 5u(t)  C (c)
5
t
C
(d)
( ) 5u t
C
1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is
(a) ( ) ( ) ( )
2
8 1 1
sin sin 3 sin 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(b) ( ) ( ) ( )
2
8 1 1
sin cos 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
(c) ( ) ( ) ( )
2
8 1 1
cos cos 3 cos 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(d) ( ) ( ) ( )
2
8 1 1
cos sin 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
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 – N + 1 (b) B + N
(c) N – B + 1 (d) N – 2B 1
1.4 Two inphase, 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 XY mode?
(a) A circle of unit radius (b) An ellipse
(c) A parabola
(d) A straight line inclined at 45° with respect to the xaxis
1
0
f(t)
1 2 3
1
1
GATE EE  2002
1.5 Given a vector field , F
r
the divergence theorem states that
(a) . .
s v
F dS FdV = ?
? ?
r r ur r
(b) .
s v
F dS FdV = ?×
? ?
r r ur r
(c) .
s v
F dS FdV × = ?
? ?
r r ur r
(d) .
s v
F dS FdV × = ?
? ?
r r ur r
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 torquespeed
characteristic of this motor will be
approximately represented by which curve
of Fig.1.7?
(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
Fig.1.9. The reading of the voltmeter, V,
will be
(a) 0 V (b) 400 V
(c) 600 V (d) 800 V
C
B
A
D
Torque
Speed
400V
400:200:200
~
V
50 Hz
GATE EE  2002
1.10 The frequency of the clock signal applied to
the rising edge triggered D flipflop 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 5O and the remaining
parameters are same as those of an ideal diode. The dc component of the source
current is
(a)
50
Vm
p
(b)
50 2
Vm
p
(c)
100 2
Vm
p
(d)
2
50
Vm
p
1.12 The cutin voltage of both Zener diode D
z
and diode D shown in Fig.1.12 is 0.7 V,
while break down voltage of D
z
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
0
) 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 linetoline input voltage to the 3
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
1
= 886 W and W
2
= 886 W
(b) W
1
= 500 W and W
2
= 500 W
(c) W
1
= 0 W and W
2
= 1000 W
(d) W
1
= 250 W and W
2
= 750 W
D Q
Q
FF0
CLK
45O
~
V msin(?t)
?=314 rad/s
1kO
~ 10sin(?t)
?=314 rad/s
D
D Z
V O
I
W 2
5?60°O
5?60°O
5?60°O
R
Y
B
W 1
GATE EE  2002
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) E000EFFF
(b) 000EFFFE
(c) 1000FFFF
(d) 0001FFF1
1.15 Consider a long, twowire 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 coordination for the distance relays R1 and R2 on
adjacent lines of a transmission system (Fig.1.18). The Zone 1 and Zone 2
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.
(a)
1 2
2 0.6 , 2 0.3
R R
TZ s TZ s = =
(b)
1 2
2 0.3 , 2 0.6
R R
TZ s TZ s = =
(c)
1 2
2 0.3 , 2 0.3
R R
TZ s TZ s = =
(d)
1 2
2 0.1 , 2 0.3
R R
TZ s TZ s = =
CS
A 15
A 14
A 13
A 12
Zone1 (R1)
Zone2 (R1)
Zone1 (R2)
Zone2 (R2)
R2
R1
Page 5
GATE EE  2002
SECTION  A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V
c
(t),
across the capacitor is given by
(a) 5t (b) 5u(t)  C (c)
5
t
C
(d)
( ) 5u t
C
1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is
(a) ( ) ( ) ( )
2
8 1 1
sin sin 3 sin 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(b) ( ) ( ) ( )
2
8 1 1
sin cos 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
(c) ( ) ( ) ( )
2
8 1 1
cos cos 3 cos 5
9 25
t t t p p p
p
? ?
+ + +
? ?
? ?
K
(d) ( ) ( ) ( )
2
8 1 1
cos sin 3 sin 5
9 25
t t t p p p
p
? ?
 + +
? ?
? ?
K
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 – N + 1 (b) B + N
(c) N – B + 1 (d) N – 2B 1
1.4 Two inphase, 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 XY mode?
(a) A circle of unit radius (b) An ellipse
(c) A parabola
(d) A straight line inclined at 45° with respect to the xaxis
1
0
f(t)
1 2 3
1
1
GATE EE  2002
1.5 Given a vector field , F
r
the divergence theorem states that
(a) . .
s v
F dS FdV = ?
? ?
r r ur r
(b) .
s v
F dS FdV = ?×
? ?
r r ur r
(c) .
s v
F dS FdV × = ?
? ?
r r ur r
(d) .
s v
F dS FdV × = ?
? ?
r r ur r
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 torquespeed
characteristic of this motor will be
approximately represented by which curve
of Fig.1.7?
(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
Fig.1.9. The reading of the voltmeter, V,
will be
(a) 0 V (b) 400 V
(c) 600 V (d) 800 V
C
B
A
D
Torque
Speed
400V
400:200:200
~
V
50 Hz
GATE EE  2002
1.10 The frequency of the clock signal applied to
the rising edge triggered D flipflop 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 5O and the remaining
parameters are same as those of an ideal diode. The dc component of the source
current is
(a)
50
Vm
p
(b)
50 2
Vm
p
(c)
100 2
Vm
p
(d)
2
50
Vm
p
1.12 The cutin voltage of both Zener diode D
z
and diode D shown in Fig.1.12 is 0.7 V,
while break down voltage of D
z
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
0
) 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 linetoline input voltage to the 3
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
1
= 886 W and W
2
= 886 W
(b) W
1
= 500 W and W
2
= 500 W
(c) W
1
= 0 W and W
2
= 1000 W
(d) W
1
= 250 W and W
2
= 750 W
D Q
Q
FF0
CLK
45O
~
V msin(?t)
?=314 rad/s
1kO
~ 10sin(?t)
?=314 rad/s
D
D Z
V O
I
W 2
5?60°O
5?60°O
5?60°O
R
Y
B
W 1
GATE EE  2002
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) E000EFFF
(b) 000EFFFE
(c) 1000FFFF
(d) 0001FFF1
1.15 Consider a long, twowire 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 coordination for the distance relays R1 and R2 on
adjacent lines of a transmission system (Fig.1.18). The Zone 1 and Zone 2
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.
(a)
1 2
2 0.6 , 2 0.3
R R
TZ s TZ s = =
(b)
1 2
2 0.3 , 2 0.6
R R
TZ s TZ s = =
(c)
1 2
2 0.3 , 2 0.3
R R
TZ s TZ s = =
(d)
1 2
2 0.1 , 2 0.3
R R
TZ s TZ s = =
CS
A 15
A 14
A 13
A 12
Zone1 (R1)
Zone2 (R1)
Zone1 (R2)
Zone2 (R2)
R2
R1
GATE EE  2002
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
(a) ( ) ( )
0
t
s t u d t t t 
?
(b) ( ) ( )
0
t
d
s t u d
dt
t t t
? ?
? ?

? ?
? ?
?
(c) ( ) ( )
1 1
0 0
t t
s t u d d t t t t
? ?
? ?

? ?
? ?
? ?
(d) ( ) ( )
2
0
t
s t u d t t t 
?
1.20. Let Y(s) be the Laplace transformation of the function y(t), then the final value of
the function is
(a) ( )
0
lim
s
Y s
?
(b) ( ) lim
s
Y s
?8
(c) ( )
0
lim
s
sY s
?
(d) ( ) lim
s
sY s
?8
1.21. The determinant of the matrix
1 0 0 0
100 1 0 0
100 200 1 0
100 200 300 1
? ?
? ?
? ?
? ?
? ?
? ?
? ?
is:
(a) 100 (b) 200 (c) 1 (d) 300
1.22. The state transition matrix for the system X AX =
&
with initial state X(0) is
(a) ( )
1
sI A

 (b) ( ) 0
At
e X (c) Laplace inverse of [( )
1
sI A

 ]
(d) Laplace inverse of [( )
1
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
p
(b)
100
V
p
(c) 200 V (d) 100 V
100V
?
p/3
100V
2p/3 4p/3 5p/3
2p
p
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