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# Electrical Engineering (EE) 2003 GATE Paper without solution (unsolved) GATE Notes | EduRev

## GATE : Electrical Engineering (EE) 2003 GATE Paper without solution (unsolved) GATE Notes | EduRev

``` Page 1

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Q.1 – Q.30 CARRY ONE MARK EACH

1. Fig.Q1 shows the waveform of the current passing through an inductor of
resistance 1O and inductance 2 H. The energy absorbed by the inductor in the
first four seconds is
(a) 144 J
(b) 98 J
(c) 132 J
(d) 168 J

2. A segment of a circuit is shown in Fig.Q2. V
R
= 5V, V
C
= 4 sin 2t. The voltage V
L

is given by
(a) 3 – 8 cos 2t
(b) 32 sin 2t
(c) 16 sin 2t
(d) 16 cos 2t

3. In the Fig.Q3. Z
1
=10?-60°, A2=10?60°, Z
3
=50?53.13°. The Venn impedance
seen from X-Y is
(a) 56.6?45°
(b) 60?30°
(c) 70?30°
(d) 34.4?65°

4. Two conductors are carrying forward and return current of +I and –I as shown in
Fig.Q4. The magnetic field intensity H at point P is

(a)
I
y
d p
(b)
I
x
d p
(c)
2
I
y
d p
(d)
2
I
x
d p

0
2S
6A
4S
t
+
-
-
- +
+
V R
2A
5O
1F
V L
V C
2H
P R
S
Q
~
Z 1
Z 3
Z 2
X
Y
+
-
100?0°
z
u r

x
ur

y
u r

P
-I +I
d d
Page 2

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Q.1 – Q.30 CARRY ONE MARK EACH

1. Fig.Q1 shows the waveform of the current passing through an inductor of
resistance 1O and inductance 2 H. The energy absorbed by the inductor in the
first four seconds is
(a) 144 J
(b) 98 J
(c) 132 J
(d) 168 J

2. A segment of a circuit is shown in Fig.Q2. V
R
= 5V, V
C
= 4 sin 2t. The voltage V
L

is given by
(a) 3 – 8 cos 2t
(b) 32 sin 2t
(c) 16 sin 2t
(d) 16 cos 2t

3. In the Fig.Q3. Z
1
=10?-60°, A2=10?60°, Z
3
=50?53.13°. The Venn impedance
seen from X-Y is
(a) 56.6?45°
(b) 60?30°
(c) 70?30°
(d) 34.4?65°

4. Two conductors are carrying forward and return current of +I and –I as shown in
Fig.Q4. The magnetic field intensity H at point P is

(a)
I
y
d p
(b)
I
x
d p
(c)
2
I
y
d p
(d)
2
I
x
d p

0
2S
6A
4S
t
+
-
-
- +
+
V R
2A
5O
1F
V L
V C
2H
P R
S
Q
~
Z 1
Z 3
Z 2
X
Y
+
-
100?0°
z
u r

x
ur

y
u r

P
-I +I
d d
GATE EE - 2003                            www.gateforum.com
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5. Two infinite strips of width w m in x direction as shown in Fig.Q5, are carrying
forward and return currents of +I and –I in the z direction. The strips are
separated by a distance of xm. The inductance per unit length of the
configuration is measured to be L H/m. If the distance of separation between the
strips is now reduced to ,
2
x
m the inductance per unit length of the configuration
is

(a) 2L H/m
(b) L/4 H/m
(c) L/2 H/m
(d) 4L H/m

6. A single phase transformer has a maximum efficiency of 90% at full load and
unity power factor. Efficiency at half load at the same power factor is
(a) 86.7% (b) 88.26% (c) 88.9% (d) 87.8%

7. Group I lists different applications and Group II lists the motors for these
applications. Match the application with the most suitable motor and choose the
right combination among the choices given thereafter

Group I Group II
P   Food mixer 1  Permanent magnet dc motor
Q  Cassette tape recorder 2  Single phase induction motor
R  Domestic water pump 3  Universal motor
S  Escalator 4  Three phase induction motor
5  DC series motor
6  Stepper motor

(a) P – 3  Q – 6  R – 4  S - 5 (b) P – 1  Q – 3  R – 2  S - 4
(c) P – 3  Q – 1  R – 2  S - 4 (d) P – 3  Q – 2  R – 1  S - 4

8. A stand-alone engine driven Synchronous generator is feeding a partly inductive
load. A capacitor is now connected across the load to completely nullify the
inductive current. For this operating condition.
(a) the field current and fuel input have to be reduced
(b) the field current and fuel input have to be increased
(c) the field current has to be increased and fuel input left unaltered
(d) the field current has to be reduced and fuel input left unaltered

z
u r

x
ur

y
u r

+I
-I
w
x
Page 3

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Q.1 – Q.30 CARRY ONE MARK EACH

1. Fig.Q1 shows the waveform of the current passing through an inductor of
resistance 1O and inductance 2 H. The energy absorbed by the inductor in the
first four seconds is
(a) 144 J
(b) 98 J
(c) 132 J
(d) 168 J

2. A segment of a circuit is shown in Fig.Q2. V
R
= 5V, V
C
= 4 sin 2t. The voltage V
L

is given by
(a) 3 – 8 cos 2t
(b) 32 sin 2t
(c) 16 sin 2t
(d) 16 cos 2t

3. In the Fig.Q3. Z
1
=10?-60°, A2=10?60°, Z
3
=50?53.13°. The Venn impedance
seen from X-Y is
(a) 56.6?45°
(b) 60?30°
(c) 70?30°
(d) 34.4?65°

4. Two conductors are carrying forward and return current of +I and –I as shown in
Fig.Q4. The magnetic field intensity H at point P is

(a)
I
y
d p
(b)
I
x
d p
(c)
2
I
y
d p
(d)
2
I
x
d p

0
2S
6A
4S
t
+
-
-
- +
+
V R
2A
5O
1F
V L
V C
2H
P R
S
Q
~
Z 1
Z 3
Z 2
X
Y
+
-
100?0°
z
u r

x
ur

y
u r

P
-I +I
d d
GATE EE - 2003                            www.gateforum.com
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Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question
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5. Two infinite strips of width w m in x direction as shown in Fig.Q5, are carrying
forward and return currents of +I and –I in the z direction. The strips are
separated by a distance of xm. The inductance per unit length of the
configuration is measured to be L H/m. If the distance of separation between the
strips is now reduced to ,
2
x
m the inductance per unit length of the configuration
is

(a) 2L H/m
(b) L/4 H/m
(c) L/2 H/m
(d) 4L H/m

6. A single phase transformer has a maximum efficiency of 90% at full load and
unity power factor. Efficiency at half load at the same power factor is
(a) 86.7% (b) 88.26% (c) 88.9% (d) 87.8%

7. Group I lists different applications and Group II lists the motors for these
applications. Match the application with the most suitable motor and choose the
right combination among the choices given thereafter

Group I Group II
P   Food mixer 1  Permanent magnet dc motor
Q  Cassette tape recorder 2  Single phase induction motor
R  Domestic water pump 3  Universal motor
S  Escalator 4  Three phase induction motor
5  DC series motor
6  Stepper motor

(a) P – 3  Q – 6  R – 4  S - 5 (b) P – 1  Q – 3  R – 2  S - 4
(c) P – 3  Q – 1  R – 2  S - 4 (d) P – 3  Q – 2  R – 1  S - 4

8. A stand-alone engine driven Synchronous generator is feeding a partly inductive
load. A capacitor is now connected across the load to completely nullify the
inductive current. For this operating condition.
(a) the field current and fuel input have to be reduced
(b) the field current and fuel input have to be increased
(c) the field current has to be increased and fuel input left unaltered
(d) the field current has to be reduced and fuel input left unaltered

z
u r

x
ur

y
u r

+I
-I
w
x
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9. Curves X and Y in Fig.Q9 denote open circuit and full-load zero power factor (zpf)
characteristics of asynchronous generator. Q is a point on the zpf characteristics
at 1.0 p.u. voltage. The vertical distance PQ in Fig.Q.9 gives the voltage drop
across
(a) Synchronous reactance
(b) Magnetizing reactance
(c) Potier reactance
(d) Leakage reactance

10. No-load test on a 3-phase induction motor was conducted at different supply
voltages and a plot of input power versus voltage was drawn. This curve was
extrapolated to intersect the y-axis. This intersection point yields
(a) Core loss   (b) Stator copper loss
(c) Stray load loss   (d) Friction and windage loss

11. Bundled conductors are mainly used in high voltage overhead transmission lines
to
(a) reduce transmission line losses
(b) increase mechanical strength of the line
(c) reduce corona   (d) reduce sag

12.  A power system consists of 300 buses out of which 20 buses are generator
buses, 25 buses are the ones with reactive power support and 15 buses are the
ones with fixed shunt capacitors. All the other buses are load buses. It is
proposed to perform a load flow analysis for the system using Newton-Raphson
method. The size of the Newton-Raphson Jacobian matrix is
(a) 553×553 (b) 540×540 (c) 555×555 (d) 554×554

13. Choose two appropriate auxiliary components of a HVDC transmission system
from the following
P D.C. line inductor
Q A.C. line inductor
R Reactive power sources
S Distance relays on D.C. line
T Series capacitance of A.C. line
(a) P and Q (b) P and R (c) Q and S (d) S and T

P
Q
X
Y
1.0
Voltage (p.u)
Field Current
Page 4

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Q.1 – Q.30 CARRY ONE MARK EACH

1. Fig.Q1 shows the waveform of the current passing through an inductor of
resistance 1O and inductance 2 H. The energy absorbed by the inductor in the
first four seconds is
(a) 144 J
(b) 98 J
(c) 132 J
(d) 168 J

2. A segment of a circuit is shown in Fig.Q2. V
R
= 5V, V
C
= 4 sin 2t. The voltage V
L

is given by
(a) 3 – 8 cos 2t
(b) 32 sin 2t
(c) 16 sin 2t
(d) 16 cos 2t

3. In the Fig.Q3. Z
1
=10?-60°, A2=10?60°, Z
3
=50?53.13°. The Venn impedance
seen from X-Y is
(a) 56.6?45°
(b) 60?30°
(c) 70?30°
(d) 34.4?65°

4. Two conductors are carrying forward and return current of +I and –I as shown in
Fig.Q4. The magnetic field intensity H at point P is

(a)
I
y
d p
(b)
I
x
d p
(c)
2
I
y
d p
(d)
2
I
x
d p

0
2S
6A
4S
t
+
-
-
- +
+
V R
2A
5O
1F
V L
V C
2H
P R
S
Q
~
Z 1
Z 3
Z 2
X
Y
+
-
100?0°
z
u r

x
ur

y
u r

P
-I +I
d d
GATE EE - 2003                            www.gateforum.com
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Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question
Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank,
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5. Two infinite strips of width w m in x direction as shown in Fig.Q5, are carrying
forward and return currents of +I and –I in the z direction. The strips are
separated by a distance of xm. The inductance per unit length of the
configuration is measured to be L H/m. If the distance of separation between the
strips is now reduced to ,
2
x
m the inductance per unit length of the configuration
is

(a) 2L H/m
(b) L/4 H/m
(c) L/2 H/m
(d) 4L H/m

6. A single phase transformer has a maximum efficiency of 90% at full load and
unity power factor. Efficiency at half load at the same power factor is
(a) 86.7% (b) 88.26% (c) 88.9% (d) 87.8%

7. Group I lists different applications and Group II lists the motors for these
applications. Match the application with the most suitable motor and choose the
right combination among the choices given thereafter

Group I Group II
P   Food mixer 1  Permanent magnet dc motor
Q  Cassette tape recorder 2  Single phase induction motor
R  Domestic water pump 3  Universal motor
S  Escalator 4  Three phase induction motor
5  DC series motor
6  Stepper motor

(a) P – 3  Q – 6  R – 4  S - 5 (b) P – 1  Q – 3  R – 2  S - 4
(c) P – 3  Q – 1  R – 2  S - 4 (d) P – 3  Q – 2  R – 1  S - 4

8. A stand-alone engine driven Synchronous generator is feeding a partly inductive
load. A capacitor is now connected across the load to completely nullify the
inductive current. For this operating condition.
(a) the field current and fuel input have to be reduced
(b) the field current and fuel input have to be increased
(c) the field current has to be increased and fuel input left unaltered
(d) the field current has to be reduced and fuel input left unaltered

z
u r

x
ur

y
u r

+I
-I
w
x
GATE EE - 2003                            www.gateforum.com
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Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question
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9. Curves X and Y in Fig.Q9 denote open circuit and full-load zero power factor (zpf)
characteristics of asynchronous generator. Q is a point on the zpf characteristics
at 1.0 p.u. voltage. The vertical distance PQ in Fig.Q.9 gives the voltage drop
across
(a) Synchronous reactance
(b) Magnetizing reactance
(c) Potier reactance
(d) Leakage reactance

10. No-load test on a 3-phase induction motor was conducted at different supply
voltages and a plot of input power versus voltage was drawn. This curve was
extrapolated to intersect the y-axis. This intersection point yields
(a) Core loss   (b) Stator copper loss
(c) Stray load loss   (d) Friction and windage loss

11. Bundled conductors are mainly used in high voltage overhead transmission lines
to
(a) reduce transmission line losses
(b) increase mechanical strength of the line
(c) reduce corona   (d) reduce sag

12.  A power system consists of 300 buses out of which 20 buses are generator
buses, 25 buses are the ones with reactive power support and 15 buses are the
ones with fixed shunt capacitors. All the other buses are load buses. It is
proposed to perform a load flow analysis for the system using Newton-Raphson
method. The size of the Newton-Raphson Jacobian matrix is
(a) 553×553 (b) 540×540 (c) 555×555 (d) 554×554

13. Choose two appropriate auxiliary components of a HVDC transmission system
from the following
P D.C. line inductor
Q A.C. line inductor
R Reactive power sources
S Distance relays on D.C. line
T Series capacitance of A.C. line
(a) P and Q (b) P and R (c) Q and S (d) S and T

P
Q
X
Y
1.0
Voltage (p.u)
Field Current
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14. A round rotor generator with internal voltage E
1
= 2.0 p.u. and X = 1.1 p.u. is
connected to a round rotor synchronous motor with internal voltage E
2
= 1.3 p.u.
and X = 1.2 p.u. The reactance of the line connecting the generator to the motor
is 0.5 p.u. when the generator supplies 0.5 p.u. power, the rotor angle difference
between the machines will be
(a) 57.42° (b) 1° (c) 32.58° (d) 122.58°

15. The interrupting time of a circuit breaker is the period between the instant of
(a) initiation of short circuit and the arc extinction on an opening operation
(b) energizing of the trip circuit and the arc extinction on an opening operation
(c) initiation of short circuit and the parting of primary arc contacts
(d) energizing of the trip circuit and the parting of primary arc contacts

16. The variation of drain current with gate-to-source voltage
( ) characteristic
D GS
I V - of a MOSFET is shown in Fig.Q.16. The MOSFET is
(a) an n-channel depletion mode device
(b) an n-channel enhancement mode device
(c) a p-channel depletion mode device
(d) a p-channel enhancement mode device

17. In the circuit of Fig.Q17, assume that the transistor has
99 and 0.7 .
FE BE
h V V = = The value of collector current I
C
of the transistor is
approximately
(a) [3.3/3.3] mA
(b) [3.3/(3.3+.33] mA
(c) [3.3/33] mA
(d) [3.3/(33+3.3] mA

18. For the circuit of Fig.Q18 with an ideal operational amplifier, the maximum phase
shift of the output V
out
with reference to the input V
in
is

(a) 0° (b) -90° (c) +90° (d) ±180°
I D
V GS 0
3.3kO
33kO
4V
3.3kO
12V
I C
+
-
R
C
R 1
R 1
v out
V in
Page 5

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Q.1 – Q.30 CARRY ONE MARK EACH

1. Fig.Q1 shows the waveform of the current passing through an inductor of
resistance 1O and inductance 2 H. The energy absorbed by the inductor in the
first four seconds is
(a) 144 J
(b) 98 J
(c) 132 J
(d) 168 J

2. A segment of a circuit is shown in Fig.Q2. V
R
= 5V, V
C
= 4 sin 2t. The voltage V
L

is given by
(a) 3 – 8 cos 2t
(b) 32 sin 2t
(c) 16 sin 2t
(d) 16 cos 2t

3. In the Fig.Q3. Z
1
=10?-60°, A2=10?60°, Z
3
=50?53.13°. The Venn impedance
seen from X-Y is
(a) 56.6?45°
(b) 60?30°
(c) 70?30°
(d) 34.4?65°

4. Two conductors are carrying forward and return current of +I and –I as shown in
Fig.Q4. The magnetic field intensity H at point P is

(a)
I
y
d p
(b)
I
x
d p
(c)
2
I
y
d p
(d)
2
I
x
d p

0
2S
6A
4S
t
+
-
-
- +
+
V R
2A
5O
1F
V L
V C
2H
P R
S
Q
~
Z 1
Z 3
Z 2
X
Y
+
-
100?0°
z
u r

x
ur

y
u r

P
-I +I
d d
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5. Two infinite strips of width w m in x direction as shown in Fig.Q5, are carrying
forward and return currents of +I and –I in the z direction. The strips are
separated by a distance of xm. The inductance per unit length of the
configuration is measured to be L H/m. If the distance of separation between the
strips is now reduced to ,
2
x
m the inductance per unit length of the configuration
is

(a) 2L H/m
(b) L/4 H/m
(c) L/2 H/m
(d) 4L H/m

6. A single phase transformer has a maximum efficiency of 90% at full load and
unity power factor. Efficiency at half load at the same power factor is
(a) 86.7% (b) 88.26% (c) 88.9% (d) 87.8%

7. Group I lists different applications and Group II lists the motors for these
applications. Match the application with the most suitable motor and choose the
right combination among the choices given thereafter

Group I Group II
P   Food mixer 1  Permanent magnet dc motor
Q  Cassette tape recorder 2  Single phase induction motor
R  Domestic water pump 3  Universal motor
S  Escalator 4  Three phase induction motor
5  DC series motor
6  Stepper motor

(a) P – 3  Q – 6  R – 4  S - 5 (b) P – 1  Q – 3  R – 2  S - 4
(c) P – 3  Q – 1  R – 2  S - 4 (d) P – 3  Q – 2  R – 1  S - 4

8. A stand-alone engine driven Synchronous generator is feeding a partly inductive
load. A capacitor is now connected across the load to completely nullify the
inductive current. For this operating condition.
(a) the field current and fuel input have to be reduced
(b) the field current and fuel input have to be increased
(c) the field current has to be increased and fuel input left unaltered
(d) the field current has to be reduced and fuel input left unaltered

z
u r

x
ur

y
u r

+I
-I
w
x
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9. Curves X and Y in Fig.Q9 denote open circuit and full-load zero power factor (zpf)
characteristics of asynchronous generator. Q is a point on the zpf characteristics
at 1.0 p.u. voltage. The vertical distance PQ in Fig.Q.9 gives the voltage drop
across
(a) Synchronous reactance
(b) Magnetizing reactance
(c) Potier reactance
(d) Leakage reactance

10. No-load test on a 3-phase induction motor was conducted at different supply
voltages and a plot of input power versus voltage was drawn. This curve was
extrapolated to intersect the y-axis. This intersection point yields
(a) Core loss   (b) Stator copper loss
(c) Stray load loss   (d) Friction and windage loss

11. Bundled conductors are mainly used in high voltage overhead transmission lines
to
(a) reduce transmission line losses
(b) increase mechanical strength of the line
(c) reduce corona   (d) reduce sag

12.  A power system consists of 300 buses out of which 20 buses are generator
buses, 25 buses are the ones with reactive power support and 15 buses are the
ones with fixed shunt capacitors. All the other buses are load buses. It is
proposed to perform a load flow analysis for the system using Newton-Raphson
method. The size of the Newton-Raphson Jacobian matrix is
(a) 553×553 (b) 540×540 (c) 555×555 (d) 554×554

13. Choose two appropriate auxiliary components of a HVDC transmission system
from the following
P D.C. line inductor
Q A.C. line inductor
R Reactive power sources
S Distance relays on D.C. line
T Series capacitance of A.C. line
(a) P and Q (b) P and R (c) Q and S (d) S and T

P
Q
X
Y
1.0
Voltage (p.u)
Field Current
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14. A round rotor generator with internal voltage E
1
= 2.0 p.u. and X = 1.1 p.u. is
connected to a round rotor synchronous motor with internal voltage E
2
= 1.3 p.u.
and X = 1.2 p.u. The reactance of the line connecting the generator to the motor
is 0.5 p.u. when the generator supplies 0.5 p.u. power, the rotor angle difference
between the machines will be
(a) 57.42° (b) 1° (c) 32.58° (d) 122.58°

15. The interrupting time of a circuit breaker is the period between the instant of
(a) initiation of short circuit and the arc extinction on an opening operation
(b) energizing of the trip circuit and the arc extinction on an opening operation
(c) initiation of short circuit and the parting of primary arc contacts
(d) energizing of the trip circuit and the parting of primary arc contacts

16. The variation of drain current with gate-to-source voltage
( ) characteristic
D GS
I V - of a MOSFET is shown in Fig.Q.16. The MOSFET is
(a) an n-channel depletion mode device
(b) an n-channel enhancement mode device
(c) a p-channel depletion mode device
(d) a p-channel enhancement mode device

17. In the circuit of Fig.Q17, assume that the transistor has
99 and 0.7 .
FE BE
h V V = = The value of collector current I
C
of the transistor is
approximately
(a) [3.3/3.3] mA
(b) [3.3/(3.3+.33] mA
(c) [3.3/33] mA
(d) [3.3/(33+3.3] mA

18. For the circuit of Fig.Q18 with an ideal operational amplifier, the maximum phase
shift of the output V
out
with reference to the input V
in
is

(a) 0° (b) -90° (c) +90° (d) ±180°
I D
V GS 0
3.3kO
33kO
4V
3.3kO
12V
I C
+
-
R
C
R 1
R 1
v out
V in
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19. Fig.Q19 shows a 4 to 1 MUX to be used to implement the sum S of a 1-bit full
adder with input bits P and Q and the carry input C
in
. Which of the following
combinations of inputs to I
0
, I
1
, I
2
and I
3
of the MUX will realize the sum S?
(a)
0 1 2 3
;
in in
I I C I I C = = = =
(b)
0 1 2 3
;
in in
I I C I I C = = = =
(c)
0 3 1 2
;
in in
I I C I I C = = = =
(d)
0 3 1 2
;
in in
I I C I I C = = = =

20. When a program is being executed in an 8085 microprocessor, its Program
Counter contains
(a) the number of instructions in the current program that have already been
executed
(b) the total number of instructions in the program being executed
(c) the memory address of the instruction that is being currently executed
(d) the memory address of the instruction that is to be executed next

21. A control system is defined by the following mathematical relationship

( )
2
2
2
6 5 12 1
t
d x dx
x e
dt
dt
-
+ + = -
The response of the system as t  8 is
(a) x = 6 (b) x = 2 (c) x = 2.4 (d) x = -2

22. A lead compensator used for a closed loop controller has the following transfer
function
1
1
s
K
a
s
b
? ?
+
? ?
? ?
? ?
+
? ?
? ?
.
(a) a < b (b) b < a (c) a > Kb (d) a < Kb

23. A second order system starts with an initial condition of
2
3
? ?
? ?
? ?
without any external
input. The state transition matrix for the system is given by
2
0
.
0
t
t
e
e
-
-
? ?
? ?
? ?
? ?
The
state of the system at the end of 1 second is given by
(a)
0.271
1.100
? ?
? ?
? ?
(b)
0.135
0.368
? ?
? ?
? ?
(c)
0.271
0.736
? ?
? ?
? ?
(d)
0.135
1.100
? ?
? ?
? ?

P Q
I 0
F
S 1
S
4 to 1 MUX
I 1
I 3
I 2
S 0
```
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