Download Graduate Aptitude Test in Engineering (GATE) 2015 EE Electrical Engineering Set 2 Question Paper
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
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GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
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Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
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Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
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GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
EE 7/15
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
EE 7/15
GATE 2015 SET2 ELECTRICAL ? EE
Q. 26 ? Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface ???? ( ???? , ???? ) = ???? ???? over the triangle bounded by the lines ???? = ???? ; ???? =
0; ???? = 1 in the ???????? plane is ______.
Q.27 Two coins R and S are tossed. The 4 joint events ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? have probabilities 0.28,
0.18, 0.30, 0.24, respectively, where ???? represents head and ???? represents tail. Which one of the
following is TRUE?
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28
A differential equation
???????? ???????? ? 0.2 ???? = 0 is applicable over ?10 < ???? < 10. If ???? (4) = 10, then ???? ( ?5) is
_____.
Q.29 Consider a signal defined by
???? ( ???? ) = ?
???? ???? 10 ???? for |t| ? 1
0 for |t| > 1
Its Fourier Transform is
(A)
2 sin ( ???? ?10)
???? ?10
(B) 2 ???? ???? 10
sin ( ???? ?10)
???? ?10
(C)
2 sin ???? ???? ?10
(D) ???? ???? 10 ???? 2 sin ???? ????
Q.30 The coils of a wattmeter have resistances 0.01 ? and 1000 ?; their inductances may be neglected.
The wattmeter is connected as shown in the figure, to measure the power consumed by a load,
which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The
percentage error on the wattmeter reading is _________.
Load
EE 8/15
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
EE 7/15
GATE 2015 SET2 ELECTRICAL ? EE
Q. 26 ? Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface ???? ( ???? , ???? ) = ???? ???? over the triangle bounded by the lines ???? = ???? ; ???? =
0; ???? = 1 in the ???????? plane is ______.
Q.27 Two coins R and S are tossed. The 4 joint events ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? have probabilities 0.28,
0.18, 0.30, 0.24, respectively, where ???? represents head and ???? represents tail. Which one of the
following is TRUE?
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28
A differential equation
???????? ???????? ? 0.2 ???? = 0 is applicable over ?10 < ???? < 10. If ???? (4) = 10, then ???? ( ?5) is
_____.
Q.29 Consider a signal defined by
???? ( ???? ) = ?
???? ???? 10 ???? for |t| ? 1
0 for |t| > 1
Its Fourier Transform is
(A)
2 sin ( ???? ?10)
???? ?10
(B) 2 ???? ???? 10
sin ( ???? ?10)
???? ?10
(C)
2 sin ???? ???? ?10
(D) ???? ???? 10 ???? 2 sin ???? ????
Q.30 The coils of a wattmeter have resistances 0.01 ? and 1000 ?; their inductances may be neglected.
The wattmeter is connected as shown in the figure, to measure the power consumed by a load,
which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The
percentage error on the wattmeter reading is _________.
Load
EE 8/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.31 A buck converter feeding a variable resistive load is shown in the figure. The switching frequency
of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage ???? ???? is 36 V. Assume that all
the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that
will make the inductor current (i
L
) just continuous is _______.
+
R
36 V
+
iL
S
5 mH
Vo
60 V
Q.32 For the switching converter shown in the following figure, assume steady-state operation. Also
assume that the components are ideal, the inductor current is always positive and continuous and
switching period is T
s
. If the voltage V
L
is as shown, the duty cycle of the switch S is ______.
R
C
V
in
L
V
L
15 V
-45 V
t
T
s
V
L
S
V
o
Q.33 In the given rectifier, the delay angle of the thyristor T
1
measured from the positive going zero
crossing of V
s
is 30
o
. If the input voltage V
s
is 100 sin(100 ???? ???? ) V, the average voltage across R (in
Volt) under steady-state is _______.
T
1
D
3
D
2
D
4
V
s
R V
o
+
Q.34 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the
following statements is TRUE?
(A) The impulse response will be integrable, but may not be absolutely integrable.
(B) The unit impulse response will have finite support.
(C) The unit step response will be absolutely integrable.
(D) The unit step response will be bounded.
Q.35 The ???? -Transform of a sequence ???? [ ???? ] is given as ???? ( ???? ) = 2 ???? + 4 ? 4/ ???? + 3/ ???? 2
. If ???? [ ???? ] is the first
difference of ???? [ ???? ], then ???? ( ???? ) is given by
(A) 2 ???? + 2 ? 8/ ???? + 7/ ???? 2
? 3/ ???? 3
(B) ?2 ???? + 2 ? 6/ ???? + 1/ ???? 2
? 3/ ???? 3
(C) ?2 ???? ? 2 + 8/ ???? ? 7/ ???? 2
+ 3/ ???? 3
(D) 4 ???? ? 2 ? 8/ ???? ? 1/ ???? 2
+ 3/ ???? 3
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Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
EE 7/15
GATE 2015 SET2 ELECTRICAL ? EE
Q. 26 ? Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface ???? ( ???? , ???? ) = ???? ???? over the triangle bounded by the lines ???? = ???? ; ???? =
0; ???? = 1 in the ???????? plane is ______.
Q.27 Two coins R and S are tossed. The 4 joint events ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? have probabilities 0.28,
0.18, 0.30, 0.24, respectively, where ???? represents head and ???? represents tail. Which one of the
following is TRUE?
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28
A differential equation
???????? ???????? ? 0.2 ???? = 0 is applicable over ?10 < ???? < 10. If ???? (4) = 10, then ???? ( ?5) is
_____.
Q.29 Consider a signal defined by
???? ( ???? ) = ?
???? ???? 10 ???? for |t| ? 1
0 for |t| > 1
Its Fourier Transform is
(A)
2 sin ( ???? ?10)
???? ?10
(B) 2 ???? ???? 10
sin ( ???? ?10)
???? ?10
(C)
2 sin ???? ???? ?10
(D) ???? ???? 10 ???? 2 sin ???? ????
Q.30 The coils of a wattmeter have resistances 0.01 ? and 1000 ?; their inductances may be neglected.
The wattmeter is connected as shown in the figure, to measure the power consumed by a load,
which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The
percentage error on the wattmeter reading is _________.
Load
EE 8/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.31 A buck converter feeding a variable resistive load is shown in the figure. The switching frequency
of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage ???? ???? is 36 V. Assume that all
the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that
will make the inductor current (i
L
) just continuous is _______.
+
R
36 V
+
iL
S
5 mH
Vo
60 V
Q.32 For the switching converter shown in the following figure, assume steady-state operation. Also
assume that the components are ideal, the inductor current is always positive and continuous and
switching period is T
s
. If the voltage V
L
is as shown, the duty cycle of the switch S is ______.
R
C
V
in
L
V
L
15 V
-45 V
t
T
s
V
L
S
V
o
Q.33 In the given rectifier, the delay angle of the thyristor T
1
measured from the positive going zero
crossing of V
s
is 30
o
. If the input voltage V
s
is 100 sin(100 ???? ???? ) V, the average voltage across R (in
Volt) under steady-state is _______.
T
1
D
3
D
2
D
4
V
s
R V
o
+
Q.34 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the
following statements is TRUE?
(A) The impulse response will be integrable, but may not be absolutely integrable.
(B) The unit impulse response will have finite support.
(C) The unit step response will be absolutely integrable.
(D) The unit step response will be bounded.
Q.35 The ???? -Transform of a sequence ???? [ ???? ] is given as ???? ( ???? ) = 2 ???? + 4 ? 4/ ???? + 3/ ???? 2
. If ???? [ ???? ] is the first
difference of ???? [ ???? ], then ???? ( ???? ) is given by
(A) 2 ???? + 2 ? 8/ ???? + 7/ ???? 2
? 3/ ???? 3
(B) ?2 ???? + 2 ? 6/ ???? + 1/ ???? 2
? 3/ ???? 3
(C) ?2 ???? ? 2 + 8/ ???? ? 7/ ???? 2
+ 3/ ???? 3
(D) 4 ???? ? 2 ? 8/ ???? ? 1/ ???? 2
+ 3/ ???? 3
EE 9/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.36 Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure.
A point charge of + ???? is placed at a distance of ???? from both sheets. The net force on the charge is
???? 2
4 ???? ???? 0
???? ???? 2
, where ???? is given by
d
+Q
d
x
y
(A) 0
(B) ?
1
4
???? ? ?
1
4
???? ? (C) ?
1
8
???? ? ?
1
8
???? ?
(D)
1 ?2 ?2
8 ?2
???? ? +
1 ?2 ?2
8 ?2
???? ?
Q.37 In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is
???? 1
???? ???? = 00. The state ( ???? 1
???? ???? ), immediately after the 333
rd
clock pulse is
J
0
Q
0
K
0
Q
0
J
1
Q
1
K
1
Q
1
Q
0
Q
1
CLK
(A) 00 (B) 01 (C) 10 (D) 11
Q.38 A Boolean function ???? ( ???? , ???? , ???? , ???? ) = ?(1,5,12,15) is to be implemented using an 8 ? 1 multiplexer
(A is MSB). The inputs ABC are connected to the select inputs S
2
S
1
S
0
of the multiplexer
respectively.
Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?
(A) ???? , 0, ???? , 0, 0, 0, ???? ?
, ????
(B) ???? ?
, 1, ???? ?
, 1, 1, 1, ???? , ???? ?
(C) ???? , 1, ???? , 1, 1, 1, ???? ?
, ????
(D) ???? ?
, 0, ???? ?
, 0, 0, 0, ???? , ???? ?
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Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
EE 7/15
GATE 2015 SET2 ELECTRICAL ? EE
Q. 26 ? Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface ???? ( ???? , ???? ) = ???? ???? over the triangle bounded by the lines ???? = ???? ; ???? =
0; ???? = 1 in the ???????? plane is ______.
Q.27 Two coins R and S are tossed. The 4 joint events ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? have probabilities 0.28,
0.18, 0.30, 0.24, respectively, where ???? represents head and ???? represents tail. Which one of the
following is TRUE?
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28
A differential equation
???????? ???????? ? 0.2 ???? = 0 is applicable over ?10 < ???? < 10. If ???? (4) = 10, then ???? ( ?5) is
_____.
Q.29 Consider a signal defined by
???? ( ???? ) = ?
???? ???? 10 ???? for |t| ? 1
0 for |t| > 1
Its Fourier Transform is
(A)
2 sin ( ???? ?10)
???? ?10
(B) 2 ???? ???? 10
sin ( ???? ?10)
???? ?10
(C)
2 sin ???? ???? ?10
(D) ???? ???? 10 ???? 2 sin ???? ????
Q.30 The coils of a wattmeter have resistances 0.01 ? and 1000 ?; their inductances may be neglected.
The wattmeter is connected as shown in the figure, to measure the power consumed by a load,
which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The
percentage error on the wattmeter reading is _________.
Load
EE 8/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.31 A buck converter feeding a variable resistive load is shown in the figure. The switching frequency
of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage ???? ???? is 36 V. Assume that all
the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that
will make the inductor current (i
L
) just continuous is _______.
+
R
36 V
+
iL
S
5 mH
Vo
60 V
Q.32 For the switching converter shown in the following figure, assume steady-state operation. Also
assume that the components are ideal, the inductor current is always positive and continuous and
switching period is T
s
. If the voltage V
L
is as shown, the duty cycle of the switch S is ______.
R
C
V
in
L
V
L
15 V
-45 V
t
T
s
V
L
S
V
o
Q.33 In the given rectifier, the delay angle of the thyristor T
1
measured from the positive going zero
crossing of V
s
is 30
o
. If the input voltage V
s
is 100 sin(100 ???? ???? ) V, the average voltage across R (in
Volt) under steady-state is _______.
T
1
D
3
D
2
D
4
V
s
R V
o
+
Q.34 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the
following statements is TRUE?
(A) The impulse response will be integrable, but may not be absolutely integrable.
(B) The unit impulse response will have finite support.
(C) The unit step response will be absolutely integrable.
(D) The unit step response will be bounded.
Q.35 The ???? -Transform of a sequence ???? [ ???? ] is given as ???? ( ???? ) = 2 ???? + 4 ? 4/ ???? + 3/ ???? 2
. If ???? [ ???? ] is the first
difference of ???? [ ???? ], then ???? ( ???? ) is given by
(A) 2 ???? + 2 ? 8/ ???? + 7/ ???? 2
? 3/ ???? 3
(B) ?2 ???? + 2 ? 6/ ???? + 1/ ???? 2
? 3/ ???? 3
(C) ?2 ???? ? 2 + 8/ ???? ? 7/ ???? 2
+ 3/ ???? 3
(D) 4 ???? ? 2 ? 8/ ???? ? 1/ ???? 2
+ 3/ ???? 3
EE 9/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.36 Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure.
A point charge of + ???? is placed at a distance of ???? from both sheets. The net force on the charge is
???? 2
4 ???? ???? 0
???? ???? 2
, where ???? is given by
d
+Q
d
x
y
(A) 0
(B) ?
1
4
???? ? ?
1
4
???? ? (C) ?
1
8
???? ? ?
1
8
???? ?
(D)
1 ?2 ?2
8 ?2
???? ? +
1 ?2 ?2
8 ?2
???? ?
Q.37 In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is
???? 1
???? ???? = 00. The state ( ???? 1
???? ???? ), immediately after the 333
rd
clock pulse is
J
0
Q
0
K
0
Q
0
J
1
Q
1
K
1
Q
1
Q
0
Q
1
CLK
(A) 00 (B) 01 (C) 10 (D) 11
Q.38 A Boolean function ???? ( ???? , ???? , ???? , ???? ) = ?(1,5,12,15) is to be implemented using an 8 ? 1 multiplexer
(A is MSB). The inputs ABC are connected to the select inputs S
2
S
1
S
0
of the multiplexer
respectively.
Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?
(A) ???? , 0, ???? , 0, 0, 0, ???? ?
, ????
(B) ???? ?
, 1, ???? ?
, 1, 1, 1, ???? , ???? ?
(C) ???? , 1, ???? , 1, 1, 1, ???? ?
, ????
(D) ???? ?
, 0, ???? ?
, 0, 0, 0, ???? , ???? ?
EE 10/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.39 The saturation voltage of the ideal op-amp shown below is ?10 V. The output voltage ???? 0
of the
following circuit in the steady-state is
1 k?
v
0
2 k?
2 k?
0.25 ?F
?
+
+ 10 V
- 10 V
(A) square wave of period 0.55 ms. (B) triangular wave of period 0.55 ms.
(C) square wave of period 0.25 ms. (D) triangular wave of period 0.25 ms.
Q.40 The incremental costs (in Rupees/MWh) of operating two generating units are functions of their
respective powers ???? 1
and ???? 2
in MW, and are given by
???? ???? 1
???? ???? 1
= 0.2???? 1
+ 50
???? ???? 2
???? ???? 2
= 0.24 ???? 2
+ 40
where
20 MW ? ???? 1
? 150 MW
20 MW ? ???? 2
? 150 MW.
For a certain load demand, ???? 1
and ???? 2
have been chosen such that ???? ???? 1
???? ???? 1
? = 76 Rs/MWh
and ???? ???? 2
???? ???? 2
? = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then
???? 2
is ________.
Q.41 A composite conductor consists of three conductors of radius R each. The conductors are arranged
as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is ???????? . The
value of ???? is ______.
R
3R
60?
60?
EE 11/15
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GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
EE 7/15
GATE 2015 SET2 ELECTRICAL ? EE
Q. 26 ? Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface ???? ( ???? , ???? ) = ???? ???? over the triangle bounded by the lines ???? = ???? ; ???? =
0; ???? = 1 in the ???????? plane is ______.
Q.27 Two coins R and S are tossed. The 4 joint events ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? have probabilities 0.28,
0.18, 0.30, 0.24, respectively, where ???? represents head and ???? represents tail. Which one of the
following is TRUE?
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28
A differential equation
???????? ???????? ? 0.2 ???? = 0 is applicable over ?10 < ???? < 10. If ???? (4) = 10, then ???? ( ?5) is
_____.
Q.29 Consider a signal defined by
???? ( ???? ) = ?
???? ???? 10 ???? for |t| ? 1
0 for |t| > 1
Its Fourier Transform is
(A)
2 sin ( ???? ?10)
???? ?10
(B) 2 ???? ???? 10
sin ( ???? ?10)
???? ?10
(C)
2 sin ???? ???? ?10
(D) ???? ???? 10 ???? 2 sin ???? ????
Q.30 The coils of a wattmeter have resistances 0.01 ? and 1000 ?; their inductances may be neglected.
The wattmeter is connected as shown in the figure, to measure the power consumed by a load,
which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The
percentage error on the wattmeter reading is _________.
Load
EE 8/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.31 A buck converter feeding a variable resistive load is shown in the figure. The switching frequency
of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage ???? ???? is 36 V. Assume that all
the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that
will make the inductor current (i
L
) just continuous is _______.
+
R
36 V
+
iL
S
5 mH
Vo
60 V
Q.32 For the switching converter shown in the following figure, assume steady-state operation. Also
assume that the components are ideal, the inductor current is always positive and continuous and
switching period is T
s
. If the voltage V
L
is as shown, the duty cycle of the switch S is ______.
R
C
V
in
L
V
L
15 V
-45 V
t
T
s
V
L
S
V
o
Q.33 In the given rectifier, the delay angle of the thyristor T
1
measured from the positive going zero
crossing of V
s
is 30
o
. If the input voltage V
s
is 100 sin(100 ???? ???? ) V, the average voltage across R (in
Volt) under steady-state is _______.
T
1
D
3
D
2
D
4
V
s
R V
o
+
Q.34 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the
following statements is TRUE?
(A) The impulse response will be integrable, but may not be absolutely integrable.
(B) The unit impulse response will have finite support.
(C) The unit step response will be absolutely integrable.
(D) The unit step response will be bounded.
Q.35 The ???? -Transform of a sequence ???? [ ???? ] is given as ???? ( ???? ) = 2 ???? + 4 ? 4/ ???? + 3/ ???? 2
. If ???? [ ???? ] is the first
difference of ???? [ ???? ], then ???? ( ???? ) is given by
(A) 2 ???? + 2 ? 8/ ???? + 7/ ???? 2
? 3/ ???? 3
(B) ?2 ???? + 2 ? 6/ ???? + 1/ ???? 2
? 3/ ???? 3
(C) ?2 ???? ? 2 + 8/ ???? ? 7/ ???? 2
+ 3/ ???? 3
(D) 4 ???? ? 2 ? 8/ ???? ? 1/ ???? 2
+ 3/ ???? 3
EE 9/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.36 Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure.
A point charge of + ???? is placed at a distance of ???? from both sheets. The net force on the charge is
???? 2
4 ???? ???? 0
???? ???? 2
, where ???? is given by
d
+Q
d
x
y
(A) 0
(B) ?
1
4
???? ? ?
1
4
???? ? (C) ?
1
8
???? ? ?
1
8
???? ?
(D)
1 ?2 ?2
8 ?2
???? ? +
1 ?2 ?2
8 ?2
???? ?
Q.37 In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is
???? 1
???? ???? = 00. The state ( ???? 1
???? ???? ), immediately after the 333
rd
clock pulse is
J
0
Q
0
K
0
Q
0
J
1
Q
1
K
1
Q
1
Q
0
Q
1
CLK
(A) 00 (B) 01 (C) 10 (D) 11
Q.38 A Boolean function ???? ( ???? , ???? , ???? , ???? ) = ?(1,5,12,15) is to be implemented using an 8 ? 1 multiplexer
(A is MSB). The inputs ABC are connected to the select inputs S
2
S
1
S
0
of the multiplexer
respectively.
Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?
(A) ???? , 0, ???? , 0, 0, 0, ???? ?
, ????
(B) ???? ?
, 1, ???? ?
, 1, 1, 1, ???? , ???? ?
(C) ???? , 1, ???? , 1, 1, 1, ???? ?
, ????
(D) ???? ?
, 0, ???? ?
, 0, 0, 0, ???? , ???? ?
EE 10/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.39 The saturation voltage of the ideal op-amp shown below is ?10 V. The output voltage ???? 0
of the
following circuit in the steady-state is
1 k?
v
0
2 k?
2 k?
0.25 ?F
?
+
+ 10 V
- 10 V
(A) square wave of period 0.55 ms. (B) triangular wave of period 0.55 ms.
(C) square wave of period 0.25 ms. (D) triangular wave of period 0.25 ms.
Q.40 The incremental costs (in Rupees/MWh) of operating two generating units are functions of their
respective powers ???? 1
and ???? 2
in MW, and are given by
???? ???? 1
???? ???? 1
= 0.2???? 1
+ 50
???? ???? 2
???? ???? 2
= 0.24 ???? 2
+ 40
where
20 MW ? ???? 1
? 150 MW
20 MW ? ???? 2
? 150 MW.
For a certain load demand, ???? 1
and ???? 2
have been chosen such that ???? ???? 1
???? ???? 1
? = 76 Rs/MWh
and ???? ???? 2
???? ???? 2
? = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then
???? 2
is ________.
Q.41 A composite conductor consists of three conductors of radius R each. The conductors are arranged
as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is ???????? . The
value of ???? is ______.
R
3R
60?
60?
EE 11/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.42 A 3-phase transformer rated for 33 kV/11 kV is connected in delta/star as shown in figure. The
current transformers (CTs) on low and high voltage sides have a ratio of 500/5. Find the currents
???? 1
and ???? 2
, if the fault current is 300 A as shown in figure.
a
b
c
300 A
i
1
i
2
(A) ???? 1
= 1/ ?3 ???? , ???? 2
= 0 ????
(B) ???? 1
= 0 ???? , ???? 2
= 0 ????
(C) ???? 1
= 0 ???? , ???? 2
= 1/ ?3 ???? (D) ???? 1
= 1/ ?3 ???? , ???? 2
= 1/ ?3 ????
Q.43 A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star
connected load through a star-delta transformer as shown in the figure. The line-to-line voltage
rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected
and ???? ???? ?
= 100 ?0
?
A, then what is the value of ???? ???? ?
in Ampere?
a
b
c
A
B
C
Ip Is
R
R R
(A) 50 ?30?
(B) 50 ? ? 30?
(C) 50 ?3 ?30?
(D) 200 ?30?
Q.44 In the given network ???? 1
= 100?0? V, ???? 2
= 100? ? 120? V, ???? 3
= 100? + 120? V. The phasor
current ???? (in Ampere) is
-j1
j1
V
1
V
2
V
3
i
(A) 173.2? ? 60? (B) 173.2? 120? (C) 100.0? ? 60? (D) 100.0? 120?
EE 12/15
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
EE 3/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
EE 4/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
EE 7/15
GATE 2015 SET2 ELECTRICAL ? EE
Q. 26 ? Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface ???? ( ???? , ???? ) = ???? ???? over the triangle bounded by the lines ???? = ???? ; ???? =
0; ???? = 1 in the ???????? plane is ______.
Q.27 Two coins R and S are tossed. The 4 joint events ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? have probabilities 0.28,
0.18, 0.30, 0.24, respectively, where ???? represents head and ???? represents tail. Which one of the
following is TRUE?
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28
A differential equation
???????? ???????? ? 0.2 ???? = 0 is applicable over ?10 < ???? < 10. If ???? (4) = 10, then ???? ( ?5) is
_____.
Q.29 Consider a signal defined by
???? ( ???? ) = ?
???? ???? 10 ???? for |t| ? 1
0 for |t| > 1
Its Fourier Transform is
(A)
2 sin ( ???? ?10)
???? ?10
(B) 2 ???? ???? 10
sin ( ???? ?10)
???? ?10
(C)
2 sin ???? ???? ?10
(D) ???? ???? 10 ???? 2 sin ???? ????
Q.30 The coils of a wattmeter have resistances 0.01 ? and 1000 ?; their inductances may be neglected.
The wattmeter is connected as shown in the figure, to measure the power consumed by a load,
which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The
percentage error on the wattmeter reading is _________.
Load
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GATE 2015 SET2 ELECTRICAL ? EE
Q.31 A buck converter feeding a variable resistive load is shown in the figure. The switching frequency
of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage ???? ???? is 36 V. Assume that all
the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that
will make the inductor current (i
L
) just continuous is _______.
+
R
36 V
+
iL
S
5 mH
Vo
60 V
Q.32 For the switching converter shown in the following figure, assume steady-state operation. Also
assume that the components are ideal, the inductor current is always positive and continuous and
switching period is T
s
. If the voltage V
L
is as shown, the duty cycle of the switch S is ______.
R
C
V
in
L
V
L
15 V
-45 V
t
T
s
V
L
S
V
o
Q.33 In the given rectifier, the delay angle of the thyristor T
1
measured from the positive going zero
crossing of V
s
is 30
o
. If the input voltage V
s
is 100 sin(100 ???? ???? ) V, the average voltage across R (in
Volt) under steady-state is _______.
T
1
D
3
D
2
D
4
V
s
R V
o
+
Q.34 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the
following statements is TRUE?
(A) The impulse response will be integrable, but may not be absolutely integrable.
(B) The unit impulse response will have finite support.
(C) The unit step response will be absolutely integrable.
(D) The unit step response will be bounded.
Q.35 The ???? -Transform of a sequence ???? [ ???? ] is given as ???? ( ???? ) = 2 ???? + 4 ? 4/ ???? + 3/ ???? 2
. If ???? [ ???? ] is the first
difference of ???? [ ???? ], then ???? ( ???? ) is given by
(A) 2 ???? + 2 ? 8/ ???? + 7/ ???? 2
? 3/ ???? 3
(B) ?2 ???? + 2 ? 6/ ???? + 1/ ???? 2
? 3/ ???? 3
(C) ?2 ???? ? 2 + 8/ ???? ? 7/ ???? 2
+ 3/ ???? 3
(D) 4 ???? ? 2 ? 8/ ???? ? 1/ ???? 2
+ 3/ ???? 3
EE 9/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.36 Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure.
A point charge of + ???? is placed at a distance of ???? from both sheets. The net force on the charge is
???? 2
4 ???? ???? 0
???? ???? 2
, where ???? is given by
d
+Q
d
x
y
(A) 0
(B) ?
1
4
???? ? ?
1
4
???? ? (C) ?
1
8
???? ? ?
1
8
???? ?
(D)
1 ?2 ?2
8 ?2
???? ? +
1 ?2 ?2
8 ?2
???? ?
Q.37 In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is
???? 1
???? ???? = 00. The state ( ???? 1
???? ???? ), immediately after the 333
rd
clock pulse is
J
0
Q
0
K
0
Q
0
J
1
Q
1
K
1
Q
1
Q
0
Q
1
CLK
(A) 00 (B) 01 (C) 10 (D) 11
Q.38 A Boolean function ???? ( ???? , ???? , ???? , ???? ) = ?(1,5,12,15) is to be implemented using an 8 ? 1 multiplexer
(A is MSB). The inputs ABC are connected to the select inputs S
2
S
1
S
0
of the multiplexer
respectively.
Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?
(A) ???? , 0, ???? , 0, 0, 0, ???? ?
, ????
(B) ???? ?
, 1, ???? ?
, 1, 1, 1, ???? , ???? ?
(C) ???? , 1, ???? , 1, 1, 1, ???? ?
, ????
(D) ???? ?
, 0, ???? ?
, 0, 0, 0, ???? , ???? ?
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GATE 2015 SET2 ELECTRICAL ? EE
Q.39 The saturation voltage of the ideal op-amp shown below is ?10 V. The output voltage ???? 0
of the
following circuit in the steady-state is
1 k?
v
0
2 k?
2 k?
0.25 ?F
?
+
+ 10 V
- 10 V
(A) square wave of period 0.55 ms. (B) triangular wave of period 0.55 ms.
(C) square wave of period 0.25 ms. (D) triangular wave of period 0.25 ms.
Q.40 The incremental costs (in Rupees/MWh) of operating two generating units are functions of their
respective powers ???? 1
and ???? 2
in MW, and are given by
???? ???? 1
???? ???? 1
= 0.2???? 1
+ 50
???? ???? 2
???? ???? 2
= 0.24 ???? 2
+ 40
where
20 MW ? ???? 1
? 150 MW
20 MW ? ???? 2
? 150 MW.
For a certain load demand, ???? 1
and ???? 2
have been chosen such that ???? ???? 1
???? ???? 1
? = 76 Rs/MWh
and ???? ???? 2
???? ???? 2
? = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then
???? 2
is ________.
Q.41 A composite conductor consists of three conductors of radius R each. The conductors are arranged
as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is ???????? . The
value of ???? is ______.
R
3R
60?
60?
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GATE 2015 SET2 ELECTRICAL ? EE
Q.42 A 3-phase transformer rated for 33 kV/11 kV is connected in delta/star as shown in figure. The
current transformers (CTs) on low and high voltage sides have a ratio of 500/5. Find the currents
???? 1
and ???? 2
, if the fault current is 300 A as shown in figure.
a
b
c
300 A
i
1
i
2
(A) ???? 1
= 1/ ?3 ???? , ???? 2
= 0 ????
(B) ???? 1
= 0 ???? , ???? 2
= 0 ????
(C) ???? 1
= 0 ???? , ???? 2
= 1/ ?3 ???? (D) ???? 1
= 1/ ?3 ???? , ???? 2
= 1/ ?3 ????
Q.43 A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star
connected load through a star-delta transformer as shown in the figure. The line-to-line voltage
rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected
and ???? ???? ?
= 100 ?0
?
A, then what is the value of ???? ???? ?
in Ampere?
a
b
c
A
B
C
Ip Is
R
R R
(A) 50 ?30?
(B) 50 ? ? 30?
(C) 50 ?3 ?30?
(D) 200 ?30?
Q.44 In the given network ???? 1
= 100?0? V, ???? 2
= 100? ? 120? V, ???? 3
= 100? + 120? V. The phasor
current ???? (in Ampere) is
-j1
j1
V
1
V
2
V
3
i
(A) 173.2? ? 60? (B) 173.2? 120? (C) 100.0? ? 60? (D) 100.0? 120?
EE 12/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.45 A symmetrical square wave of 50% duty cycle has amplitude of ?15 V and time period of 0.4 ????
ms. This square wave is applied across a series RLC circuit with ???? = 5 ?, ???? = 10 mH, and
???? = 4 ?F. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is
______.
L C
R
Q.46 Two identical coils each having inductance L are placed together on the same core. If an overall
inductance of ???????? is obtained by interconnecting these two coils, the minimum value of ???? is ____.
Q.47 A three-winding transformer is connected to an AC voltage source as shown in the figure. The
number of turns are as follows: ???? 1
= 100, ???? 2
= 50, ???? 3
= 50. If the magnetizing current is
neglected, and the currents in two windings are ???? 2
?
= 2 ?30? A and ???? 3
?
= 2?150? A, then what is
the value of the current ???? 1
?
in Ampere?
I
1
I
I
2
3
N
1
N
3
N
2
(A) 1 ?90? (B) 1 ?270? (C) 4 ?90? (D) 4 ?270?
Q.48 With an armature voltage of 100 V and rated field winding voltage, the speed of a separately
excited DC motor driving a fan is 1000 rpm, and its armature current is 10 A. The armature
resistance is 1 ?. The load torque of the fan load is proportional to the square of the rotor speed.
Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor
speed to 500 rpm is ______.
Q.49 A three-phase, 11 kV, 50 Hz, 2 pole, star connected, cylindrical rotor synchronous motor is
connected to an 11 kV, 50 Hz source. Its synchronous reactance is 50 ? per phase, and its stator
resistance is negligible. The motor has a constant field excitation. At a particular load torque, its
stator current is 100 A at unity power factor. If the load torque is increased so that the stator current
is 120 A, then the load angle (in degrees) at this load is ________.
Q.50 A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage
and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The
maximum torque produced by the rotor is 225 % of full load torque and it occurs at 15% slip. The
actual rotor resistance is 0.03 ?/phase. The value of external resistance (in Ohm) which must be
inserted in a rotor phase if the maximum torque is to occur at start is ______.
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GATE 2015 SET2 ELECTRICAL ? EE
Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
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GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
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GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
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Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
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GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
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GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
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GATE 2015 SET2 ELECTRICAL ? EE
Q. 26 ? Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface ???? ( ???? , ???? ) = ???? ???? over the triangle bounded by the lines ???? = ???? ; ???? =
0; ???? = 1 in the ???????? plane is ______.
Q.27 Two coins R and S are tossed. The 4 joint events ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? have probabilities 0.28,
0.18, 0.30, 0.24, respectively, where ???? represents head and ???? represents tail. Which one of the
following is TRUE?
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28
A differential equation
???????? ???????? ? 0.2 ???? = 0 is applicable over ?10 < ???? < 10. If ???? (4) = 10, then ???? ( ?5) is
_____.
Q.29 Consider a signal defined by
???? ( ???? ) = ?
???? ???? 10 ???? for |t| ? 1
0 for |t| > 1
Its Fourier Transform is
(A)
2 sin ( ???? ?10)
???? ?10
(B) 2 ???? ???? 10
sin ( ???? ?10)
???? ?10
(C)
2 sin ???? ???? ?10
(D) ???? ???? 10 ???? 2 sin ???? ????
Q.30 The coils of a wattmeter have resistances 0.01 ? and 1000 ?; their inductances may be neglected.
The wattmeter is connected as shown in the figure, to measure the power consumed by a load,
which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The
percentage error on the wattmeter reading is _________.
Load
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GATE 2015 SET2 ELECTRICAL ? EE
Q.31 A buck converter feeding a variable resistive load is shown in the figure. The switching frequency
of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage ???? ???? is 36 V. Assume that all
the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that
will make the inductor current (i
L
) just continuous is _______.
+
R
36 V
+
iL
S
5 mH
Vo
60 V
Q.32 For the switching converter shown in the following figure, assume steady-state operation. Also
assume that the components are ideal, the inductor current is always positive and continuous and
switching period is T
s
. If the voltage V
L
is as shown, the duty cycle of the switch S is ______.
R
C
V
in
L
V
L
15 V
-45 V
t
T
s
V
L
S
V
o
Q.33 In the given rectifier, the delay angle of the thyristor T
1
measured from the positive going zero
crossing of V
s
is 30
o
. If the input voltage V
s
is 100 sin(100 ???? ???? ) V, the average voltage across R (in
Volt) under steady-state is _______.
T
1
D
3
D
2
D
4
V
s
R V
o
+
Q.34 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the
following statements is TRUE?
(A) The impulse response will be integrable, but may not be absolutely integrable.
(B) The unit impulse response will have finite support.
(C) The unit step response will be absolutely integrable.
(D) The unit step response will be bounded.
Q.35 The ???? -Transform of a sequence ???? [ ???? ] is given as ???? ( ???? ) = 2 ???? + 4 ? 4/ ???? + 3/ ???? 2
. If ???? [ ???? ] is the first
difference of ???? [ ???? ], then ???? ( ???? ) is given by
(A) 2 ???? + 2 ? 8/ ???? + 7/ ???? 2
? 3/ ???? 3
(B) ?2 ???? + 2 ? 6/ ???? + 1/ ???? 2
? 3/ ???? 3
(C) ?2 ???? ? 2 + 8/ ???? ? 7/ ???? 2
+ 3/ ???? 3
(D) 4 ???? ? 2 ? 8/ ???? ? 1/ ???? 2
+ 3/ ???? 3
EE 9/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.36 Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure.
A point charge of + ???? is placed at a distance of ???? from both sheets. The net force on the charge is
???? 2
4 ???? ???? 0
???? ???? 2
, where ???? is given by
d
+Q
d
x
y
(A) 0
(B) ?
1
4
???? ? ?
1
4
???? ? (C) ?
1
8
???? ? ?
1
8
???? ?
(D)
1 ?2 ?2
8 ?2
???? ? +
1 ?2 ?2
8 ?2
???? ?
Q.37 In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is
???? 1
???? ???? = 00. The state ( ???? 1
???? ???? ), immediately after the 333
rd
clock pulse is
J
0
Q
0
K
0
Q
0
J
1
Q
1
K
1
Q
1
Q
0
Q
1
CLK
(A) 00 (B) 01 (C) 10 (D) 11
Q.38 A Boolean function ???? ( ???? , ???? , ???? , ???? ) = ?(1,5,12,15) is to be implemented using an 8 ? 1 multiplexer
(A is MSB). The inputs ABC are connected to the select inputs S
2
S
1
S
0
of the multiplexer
respectively.
Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?
(A) ???? , 0, ???? , 0, 0, 0, ???? ?
, ????
(B) ???? ?
, 1, ???? ?
, 1, 1, 1, ???? , ???? ?
(C) ???? , 1, ???? , 1, 1, 1, ???? ?
, ????
(D) ???? ?
, 0, ???? ?
, 0, 0, 0, ???? , ???? ?
EE 10/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.39 The saturation voltage of the ideal op-amp shown below is ?10 V. The output voltage ???? 0
of the
following circuit in the steady-state is
1 k?
v
0
2 k?
2 k?
0.25 ?F
?
+
+ 10 V
- 10 V
(A) square wave of period 0.55 ms. (B) triangular wave of period 0.55 ms.
(C) square wave of period 0.25 ms. (D) triangular wave of period 0.25 ms.
Q.40 The incremental costs (in Rupees/MWh) of operating two generating units are functions of their
respective powers ???? 1
and ???? 2
in MW, and are given by
???? ???? 1
???? ???? 1
= 0.2???? 1
+ 50
???? ???? 2
???? ???? 2
= 0.24 ???? 2
+ 40
where
20 MW ? ???? 1
? 150 MW
20 MW ? ???? 2
? 150 MW.
For a certain load demand, ???? 1
and ???? 2
have been chosen such that ???? ???? 1
???? ???? 1
? = 76 Rs/MWh
and ???? ???? 2
???? ???? 2
? = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then
???? 2
is ________.
Q.41 A composite conductor consists of three conductors of radius R each. The conductors are arranged
as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is ???????? . The
value of ???? is ______.
R
3R
60?
60?
EE 11/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.42 A 3-phase transformer rated for 33 kV/11 kV is connected in delta/star as shown in figure. The
current transformers (CTs) on low and high voltage sides have a ratio of 500/5. Find the currents
???? 1
and ???? 2
, if the fault current is 300 A as shown in figure.
a
b
c
300 A
i
1
i
2
(A) ???? 1
= 1/ ?3 ???? , ???? 2
= 0 ????
(B) ???? 1
= 0 ???? , ???? 2
= 0 ????
(C) ???? 1
= 0 ???? , ???? 2
= 1/ ?3 ???? (D) ???? 1
= 1/ ?3 ???? , ???? 2
= 1/ ?3 ????
Q.43 A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star
connected load through a star-delta transformer as shown in the figure. The line-to-line voltage
rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected
and ???? ???? ?
= 100 ?0
?
A, then what is the value of ???? ???? ?
in Ampere?
a
b
c
A
B
C
Ip Is
R
R R
(A) 50 ?30?
(B) 50 ? ? 30?
(C) 50 ?3 ?30?
(D) 200 ?30?
Q.44 In the given network ???? 1
= 100?0? V, ???? 2
= 100? ? 120? V, ???? 3
= 100? + 120? V. The phasor
current ???? (in Ampere) is
-j1
j1
V
1
V
2
V
3
i
(A) 173.2? ? 60? (B) 173.2? 120? (C) 100.0? ? 60? (D) 100.0? 120?
EE 12/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.45 A symmetrical square wave of 50% duty cycle has amplitude of ?15 V and time period of 0.4 ????
ms. This square wave is applied across a series RLC circuit with ???? = 5 ?, ???? = 10 mH, and
???? = 4 ?F. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is
______.
L C
R
Q.46 Two identical coils each having inductance L are placed together on the same core. If an overall
inductance of ???????? is obtained by interconnecting these two coils, the minimum value of ???? is ____.
Q.47 A three-winding transformer is connected to an AC voltage source as shown in the figure. The
number of turns are as follows: ???? 1
= 100, ???? 2
= 50, ???? 3
= 50. If the magnetizing current is
neglected, and the currents in two windings are ???? 2
?
= 2 ?30? A and ???? 3
?
= 2?150? A, then what is
the value of the current ???? 1
?
in Ampere?
I
1
I
I
2
3
N
1
N
3
N
2
(A) 1 ?90? (B) 1 ?270? (C) 4 ?90? (D) 4 ?270?
Q.48 With an armature voltage of 100 V and rated field winding voltage, the speed of a separately
excited DC motor driving a fan is 1000 rpm, and its armature current is 10 A. The armature
resistance is 1 ?. The load torque of the fan load is proportional to the square of the rotor speed.
Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor
speed to 500 rpm is ______.
Q.49 A three-phase, 11 kV, 50 Hz, 2 pole, star connected, cylindrical rotor synchronous motor is
connected to an 11 kV, 50 Hz source. Its synchronous reactance is 50 ? per phase, and its stator
resistance is negligible. The motor has a constant field excitation. At a particular load torque, its
stator current is 100 A at unity power factor. If the load torque is increased so that the stator current
is 120 A, then the load angle (in degrees) at this load is ________.
Q.50 A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage
and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The
maximum torque produced by the rotor is 225 % of full load torque and it occurs at 15% slip. The
actual rotor resistance is 0.03 ?/phase. The value of external resistance (in Ohm) which must be
inserted in a rotor phase if the maximum torque is to occur at start is ______.
EE 13/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.51 Two three-phase transformers are realized using single-phase transformers as shown in the figure.
The phase difference (in degree) between voltages V
1
and V
2
is _______.
Q.52 The following discrete-time equations result from the numerical integration of the differential
equations of an un-damped simple harmonic oscillator with state variables ???? and ???? . The integration
time step is h.
???? ???? +1
? ???? ???? ?
= ???? ????
???? ???? +1
? ???? ???? ?
= ? ???? ????
For this discrete-time system, which one of the following statements is TRUE?
(A) The system is not stable for ? > 0
(B) The system is stable for ? >
1
????
(C) The system is stable for 0 < ? <
1
2 ????
(D) The system is stable for
1
2 ???? < ? <
1
????
A2
B2
C2
A1
B1
C1
a1
b1
c1
a2
b2
c2
A2
B2
C2
A1
B1
C1
a1
b1
c1
a2
b2
c2
V1
V2
EE 14/15
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Q. 1 ? Q. 25 carry one mark each.
Q.1 Given ???? ( ???? ) = ???? ( ???? ) + ?( ???? ), where ???? , ???? , ? are complex valued functions of a complex variable ???? .
Which one of the following statements is TRUE?
(A) If ???? ( ???? ) is differentiable at ???? 0
, then ???? ( ???? ) and ?( ???? ) are also differentiable at ???? 0
.
(B) If ???? ( ???? ) and ?( ???? ) are differentiable at ???? 0
, then ???? ( ???? ) is also differentiable at ???? 0
.
(C) If ???? ( ???? ) is continuous at ???? 0
, then it is differentiable at ???? 0
.
(D) If ???? ( ???? ) is differentiable at ???? 0
, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ? ???? ? ???? ? means ???? and ???? are equivalent
statements and ? ???? ? ???? ? means ???? and ???? are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) ???? ? ???? ? ???? ? ???? (B) ???? ? ???? ? ???? ? ????
(C) ???? ? ???? ? ???? ? ???? (D) ???? ? ???? ? ???? ? ????
Q.3 Match the following.
P. Stokes?s Theorem 1. ? ????. ???????? = ????
Q. Gauss?s Theorem 2. ? ???? ( ???? ) ???????? = 0
R. Divergence Theorem 3. ?( ?. ???? ) ???????? = ? ???? . ????????
S. Cauchy?s Integral Theorem 4. ?( ? ? ???? ). ???????? = ? ???? . ????????
(A)
P-2
Q-1
R-4
S-3
(B)
P-4
Q-1
R-3
S-2
(C)
P-4
Q-3
R-1
S-2
(D)
P-3
Q-4
R-2
S-1
Q.4
The Laplace transform of ???? ( ???? ) = 2 ? ???? ???? ? is ???? ?3 2 ?
. The Laplace transform of ???? ( ???? ) = ? 1 ???????? ? is
(A) 3 ???? ?5 2 ?
2 ? (B) ???? ?1 2 ?
(C) ???? 1 2 ?
(D) ???? 3 2 ?
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
S. Electrodynamometer
(A)
P-1
Q-2
R-1
S-3
(B)
P-1
Q-3
R-1
S-2
(C)
P-1
Q-2
R-3
S-3
(D)
P-3
Q-1
R-2
S-1
EE 1/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The
power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The
readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW (B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage ???? ???????????? in a high-voltage 50 Hz AC
system as shown in the figure. The measurement capacitors ???? 1
and ???? 2
have tolerances of ?10% on
their nominal capacitance values. If the bus voltage ???? ???????????? is 100 kV rms, the maximum rms output
voltage ???? ???????????? (in kV), considering the capacitor tolerances, is __________.
1?F ? 10% C
1
C
2
9?F ? 10%
v
out
v
bus
Q.8 In the following circuit, the input voltage V
in
is 100 sin(100 ???? ???? ). For 100 ???????????? = 50, the average
voltage across ????
(in Volts) under steady-state is nearest to
V
in
R
C
C
(A) 100 (B) 31.8 (C) 200 (D) 63.6
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at ???? = 0. The dielectric
constants of region 1 ( ???? < 0) and region 2 ( ???? > 0) are 2 and 5, respectively. Region 1 has uniform
electric field ???? ? ?
= 3 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
???? , where ???? ?
???? , ???? ?
???? , and ???? ?
???? are unit vectors along the ???? , ???? and ????
axes, respectively. The electric field in region 2 is
(A) 3 ???? ?
???? + 1.6 ???? ?
???? + 2 ???? ?
???? (B) 1.2 ???? ?
???? + 4 ???? ?
???? + 2 ???? ?
????
(C) 1.2 ???? ?
???? + 4 ???? ?
???? + 0.8 ???? ?
???? (D) 3 ???? ?
???? + 10 ???? ?
???? + 0.8 ???? ?
????
EE 2/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown
in the figure. The value of ?
0
is 4 ???? ? 10
?7
in SI unit. If a uniform magnetic field intensity ???? ? ? ?
=
10
7
???? ?
A/m is applied, then the peak value of the induced voltage, V
turn
( in Volts), is _________.
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is
???? ???? = 2 sin(2 ? ? 2000t). The amplitude of the output voltage ???? ???? (in Volt) is _______.
+
-
V
i
1 k ?
1 k ?
0.1 F
?
V
o
Q.12 In the following circuit, the transistor is in active mode and ???? ???? = 2 V. To get ???? ???? = 4 V, we replace
???? ???? with ???? ???? ?
. Then the ratio ???? ???? ?
/ ???? ???? is ______.
R
C
R
B
+10 V
V
C
Q.13 Consider the following Sum of Products expression, F.
???? = ???????????? + ???? ? ???? ?
???? + ???? ???? ?
???? + ???? ? ???????? + ???? ? ???? ?
???? ?
The equivalent Product of Sums expression is
(A) ???? = ( ???? + ???? ?
+ ???? )( ???? ? + ???? + ???? ) ( ???? ? + ???? ?
+ ???? )
(B) ???? = ( ???? + ???? ?
+ ???? ? )( ???? + ???? + ???? )( ???? ? + ???? ?
+ ???? ? )
(C) ???? = ( ???? ? + ???? + ???? ? )( ???? + ???? ?
+ ???? ? ) ( ???? + ???? + ???? )
(D) ???? = ( ???? ? + ???? ?
+ ???? )( ???? + ???? + ???? ? ) ( ???? + ???? + ???? )
H
X
Z
V
turn
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GATE 2015 SET2 ELECTRICAL ? EE
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown
in Figure (c).
The cut-off frequencies of F1 and F2 are f
1
and f
2
respectively. If f
1
< f
2
, the resultant circuit
exhibits the characteristic of a
(A) Band-pass filter (B) Band-stop filter
(C) All pass filter (D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following
statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
(D) Both the CB and BE junctions are reverse biased.
vo/vi
f
vo/vi
f
vi
vo
vi
vo
F1
F2
+
-
vo
R
R/2
+Vsat
-Vsat
R
F1
F2
vi
(a) (b)
(c)
f1 f2
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GATE 2015 SET2 ELECTRICAL ? EE
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two
short, lossless transmission lines, and is initially in steady state. The mechanical power input to the
generator and the voltage magnitude E are constant. If one line is tripped at time ???? 1
by opening the
circuit breakers at the two ends (although there is no fault), then it is seen that the generator
undergoes a stable transient. Which one of the following waveforms of the rotor angle ???? shows the
transient correctly?
? ?
1 0
Infinite Bus
Line 1
Line 2
Xs
Synchronous generator
(A)
?
time
t1
? = 0
(B)
?
time
t1
? = 0
(C)
?
time
? = 0
t1
(D)
?
time
? = 0
t1
EE 5/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the
uncompensated system is
?
? ???? 6 ???? 3 ???? 4
????3 ? ????7 ????5
????4 ????5 ? ????8
? pu.
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3
rd
row 3
rd
column element (in pu) of the bus admittance matrix after compensation is
(A) ? ???? 7.0 (B) ? ???? 8.5 (C) ? ???? 7.5 (D) ? ???? 9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero
initial conditions, the value of
???? 2
???? ???? ???? 2
at t = 0
+
is
(A)
???? ???? (B)
? ???? ????
(C) 0
(D)
? ???????? ???? 2
Q.19 The current i (in Ampere) in the 2 ? resistor of the given network is ______.
5 V
2 ?
1 ?
1 ?
1 ?
1 ?
i
Q.20 Find the transformer ratios ???? and ???? such that the impedance ( ???? ???????? ) is resistive and equals 2.5 ?
when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
R=2.5 ?
L=1 mH
C=10 uF
Z
in
1:b 1:a
(A) ???? = 0.5, ???? = 2.0 (B) ???? = 2.0, ???? = 0.5
(C) ???? = 1.0, ???? = 1.0 (D) ???? = 4.0, ???? = 0.5
Q.21 A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200
radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to
directly drive a load whose load torque T
L
depends on its rotational speed ???? ???? (in radian/second),
such that ???? ???? = 2.78 ? ???? ???? . Neglecting rotational losses, the steady-state speed (in radian/second) of
the motor, when it drives this load, is _______.
R
V L
EE 6/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor
operating at 50 Hz. The ?air-gap? voltage, ???? ???? across the magnetizing inductance, is 210 V rms, and
the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.
?
0.05
s
V
s
V
g
0.04 ? j0.22 ? j0.22 ?
j6.28 ?
Q.23 A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated
for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a
lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the
reconnected machine if the field circuit is left unchanged ?
(A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5
Q.24 An open loop control system results in a response of ???? ?2 ???? (sin 5 ???? + cos 5 ???? ) for a unit impulse
input. The DC gain of the control system is ______.
Q.25 Nyquist plots of two functions G
1
(s) and G
2
(s) are shown in figure.
Im
Re
?= ?
?
?
0
G
1
(s)
Im
Re
?= 0
?
?
?
G
2
(s)
Nyquist plot of the product of G
1
(s) and G
2
(s) is
(A)
Im
Re
?= 0
???
(B)
Im
Re 1
(C)
Im
Re
(D)
Im
Re
?
?
?
?
?
0
EE 7/15
GATE 2015 SET2 ELECTRICAL ? EE
Q. 26 ? Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface ???? ( ???? , ???? ) = ???? ???? over the triangle bounded by the lines ???? = ???? ; ???? =
0; ???? = 1 in the ???????? plane is ______.
Q.27 Two coins R and S are tossed. The 4 joint events ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? , ???? ???? ???? ???? have probabilities 0.28,
0.18, 0.30, 0.24, respectively, where ???? represents head and ???? represents tail. Which one of the
following is TRUE?
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28
A differential equation
???????? ???????? ? 0.2 ???? = 0 is applicable over ?10 < ???? < 10. If ???? (4) = 10, then ???? ( ?5) is
_____.
Q.29 Consider a signal defined by
???? ( ???? ) = ?
???? ???? 10 ???? for |t| ? 1
0 for |t| > 1
Its Fourier Transform is
(A)
2 sin ( ???? ?10)
???? ?10
(B) 2 ???? ???? 10
sin ( ???? ?10)
???? ?10
(C)
2 sin ???? ???? ?10
(D) ???? ???? 10 ???? 2 sin ???? ????
Q.30 The coils of a wattmeter have resistances 0.01 ? and 1000 ?; their inductances may be neglected.
The wattmeter is connected as shown in the figure, to measure the power consumed by a load,
which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The
percentage error on the wattmeter reading is _________.
Load
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GATE 2015 SET2 ELECTRICAL ? EE
Q.31 A buck converter feeding a variable resistive load is shown in the figure. The switching frequency
of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage ???? ???? is 36 V. Assume that all
the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that
will make the inductor current (i
L
) just continuous is _______.
+
R
36 V
+
iL
S
5 mH
Vo
60 V
Q.32 For the switching converter shown in the following figure, assume steady-state operation. Also
assume that the components are ideal, the inductor current is always positive and continuous and
switching period is T
s
. If the voltage V
L
is as shown, the duty cycle of the switch S is ______.
R
C
V
in
L
V
L
15 V
-45 V
t
T
s
V
L
S
V
o
Q.33 In the given rectifier, the delay angle of the thyristor T
1
measured from the positive going zero
crossing of V
s
is 30
o
. If the input voltage V
s
is 100 sin(100 ???? ???? ) V, the average voltage across R (in
Volt) under steady-state is _______.
T
1
D
3
D
2
D
4
V
s
R V
o
+
Q.34 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the
following statements is TRUE?
(A) The impulse response will be integrable, but may not be absolutely integrable.
(B) The unit impulse response will have finite support.
(C) The unit step response will be absolutely integrable.
(D) The unit step response will be bounded.
Q.35 The ???? -Transform of a sequence ???? [ ???? ] is given as ???? ( ???? ) = 2 ???? + 4 ? 4/ ???? + 3/ ???? 2
. If ???? [ ???? ] is the first
difference of ???? [ ???? ], then ???? ( ???? ) is given by
(A) 2 ???? + 2 ? 8/ ???? + 7/ ???? 2
? 3/ ???? 3
(B) ?2 ???? + 2 ? 6/ ???? + 1/ ???? 2
? 3/ ???? 3
(C) ?2 ???? ? 2 + 8/ ???? ? 7/ ???? 2
+ 3/ ???? 3
(D) 4 ???? ? 2 ? 8/ ???? ? 1/ ???? 2
+ 3/ ???? 3
EE 9/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.36 Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure.
A point charge of + ???? is placed at a distance of ???? from both sheets. The net force on the charge is
???? 2
4 ???? ???? 0
???? ???? 2
, where ???? is given by
d
+Q
d
x
y
(A) 0
(B) ?
1
4
???? ? ?
1
4
???? ? (C) ?
1
8
???? ? ?
1
8
???? ?
(D)
1 ?2 ?2
8 ?2
???? ? +
1 ?2 ?2
8 ?2
???? ?
Q.37 In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is
???? 1
???? ???? = 00. The state ( ???? 1
???? ???? ), immediately after the 333
rd
clock pulse is
J
0
Q
0
K
0
Q
0
J
1
Q
1
K
1
Q
1
Q
0
Q
1
CLK
(A) 00 (B) 01 (C) 10 (D) 11
Q.38 A Boolean function ???? ( ???? , ???? , ???? , ???? ) = ?(1,5,12,15) is to be implemented using an 8 ? 1 multiplexer
(A is MSB). The inputs ABC are connected to the select inputs S
2
S
1
S
0
of the multiplexer
respectively.
Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?
(A) ???? , 0, ???? , 0, 0, 0, ???? ?
, ????
(B) ???? ?
, 1, ???? ?
, 1, 1, 1, ???? , ???? ?
(C) ???? , 1, ???? , 1, 1, 1, ???? ?
, ????
(D) ???? ?
, 0, ???? ?
, 0, 0, 0, ???? , ???? ?
EE 10/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.39 The saturation voltage of the ideal op-amp shown below is ?10 V. The output voltage ???? 0
of the
following circuit in the steady-state is
1 k?
v
0
2 k?
2 k?
0.25 ?F
?
+
+ 10 V
- 10 V
(A) square wave of period 0.55 ms. (B) triangular wave of period 0.55 ms.
(C) square wave of period 0.25 ms. (D) triangular wave of period 0.25 ms.
Q.40 The incremental costs (in Rupees/MWh) of operating two generating units are functions of their
respective powers ???? 1
and ???? 2
in MW, and are given by
???? ???? 1
???? ???? 1
= 0.2???? 1
+ 50
???? ???? 2
???? ???? 2
= 0.24 ???? 2
+ 40
where
20 MW ? ???? 1
? 150 MW
20 MW ? ???? 2
? 150 MW.
For a certain load demand, ???? 1
and ???? 2
have been chosen such that ???? ???? 1
???? ???? 1
? = 76 Rs/MWh
and ???? ???? 2
???? ???? 2
? = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then
???? 2
is ________.
Q.41 A composite conductor consists of three conductors of radius R each. The conductors are arranged
as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is ???????? . The
value of ???? is ______.
R
3R
60?
60?
EE 11/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.42 A 3-phase transformer rated for 33 kV/11 kV is connected in delta/star as shown in figure. The
current transformers (CTs) on low and high voltage sides have a ratio of 500/5. Find the currents
???? 1
and ???? 2
, if the fault current is 300 A as shown in figure.
a
b
c
300 A
i
1
i
2
(A) ???? 1
= 1/ ?3 ???? , ???? 2
= 0 ????
(B) ???? 1
= 0 ???? , ???? 2
= 0 ????
(C) ???? 1
= 0 ???? , ???? 2
= 1/ ?3 ???? (D) ???? 1
= 1/ ?3 ???? , ???? 2
= 1/ ?3 ????
Q.43 A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star
connected load through a star-delta transformer as shown in the figure. The line-to-line voltage
rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected
and ???? ???? ?
= 100 ?0
?
A, then what is the value of ???? ???? ?
in Ampere?
a
b
c
A
B
C
Ip Is
R
R R
(A) 50 ?30?
(B) 50 ? ? 30?
(C) 50 ?3 ?30?
(D) 200 ?30?
Q.44 In the given network ???? 1
= 100?0? V, ???? 2
= 100? ? 120? V, ???? 3
= 100? + 120? V. The phasor
current ???? (in Ampere) is
-j1
j1
V
1
V
2
V
3
i
(A) 173.2? ? 60? (B) 173.2? 120? (C) 100.0? ? 60? (D) 100.0? 120?
EE 12/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.45 A symmetrical square wave of 50% duty cycle has amplitude of ?15 V and time period of 0.4 ????
ms. This square wave is applied across a series RLC circuit with ???? = 5 ?, ???? = 10 mH, and
???? = 4 ?F. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is
______.
L C
R
Q.46 Two identical coils each having inductance L are placed together on the same core. If an overall
inductance of ???????? is obtained by interconnecting these two coils, the minimum value of ???? is ____.
Q.47 A three-winding transformer is connected to an AC voltage source as shown in the figure. The
number of turns are as follows: ???? 1
= 100, ???? 2
= 50, ???? 3
= 50. If the magnetizing current is
neglected, and the currents in two windings are ???? 2
?
= 2 ?30? A and ???? 3
?
= 2?150? A, then what is
the value of the current ???? 1
?
in Ampere?
I
1
I
I
2
3
N
1
N
3
N
2
(A) 1 ?90? (B) 1 ?270? (C) 4 ?90? (D) 4 ?270?
Q.48 With an armature voltage of 100 V and rated field winding voltage, the speed of a separately
excited DC motor driving a fan is 1000 rpm, and its armature current is 10 A. The armature
resistance is 1 ?. The load torque of the fan load is proportional to the square of the rotor speed.
Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor
speed to 500 rpm is ______.
Q.49 A three-phase, 11 kV, 50 Hz, 2 pole, star connected, cylindrical rotor synchronous motor is
connected to an 11 kV, 50 Hz source. Its synchronous reactance is 50 ? per phase, and its stator
resistance is negligible. The motor has a constant field excitation. At a particular load torque, its
stator current is 100 A at unity power factor. If the load torque is increased so that the stator current
is 120 A, then the load angle (in degrees) at this load is ________.
Q.50 A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage
and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The
maximum torque produced by the rotor is 225 % of full load torque and it occurs at 15% slip. The
actual rotor resistance is 0.03 ?/phase. The value of external resistance (in Ohm) which must be
inserted in a rotor phase if the maximum torque is to occur at start is ______.
EE 13/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.51 Two three-phase transformers are realized using single-phase transformers as shown in the figure.
The phase difference (in degree) between voltages V
1
and V
2
is _______.
Q.52 The following discrete-time equations result from the numerical integration of the differential
equations of an un-damped simple harmonic oscillator with state variables ???? and ???? . The integration
time step is h.
???? ???? +1
? ???? ???? ?
= ???? ????
???? ???? +1
? ???? ???? ?
= ? ???? ????
For this discrete-time system, which one of the following statements is TRUE?
(A) The system is not stable for ? > 0
(B) The system is stable for ? >
1
????
(C) The system is stable for 0 < ? <
1
2 ????
(D) The system is stable for
1
2 ???? < ? <
1
????
A2
B2
C2
A1
B1
C1
a1
b1
c1
a2
b2
c2
A2
B2
C2
A1
B1
C1
a1
b1
c1
a2
b2
c2
V1
V2
EE 14/15
GATE 2015 SET2 ELECTRICAL ? EE
Q.53
The unit step response of a system with the transfer function ???? ( ???? ) =
1 ?2 ???? 1+ ???? is given by which one of
the following waveforms?
(A)
t
y
-2
1
5
0
(B)
t
y
2
1
5
0
(C)
t
y
2
1
5
0
-0.75
(D)
t
y
-2
1
5
0
Q.54 An open loop transfer function G(s) of a system is
???? ( ???? ) =
???? ???? ( ???? + 1)( ???? + 2)
For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,
(A) ?0.42 (B) ?1.58
(C) ?0.42 and ?1.58 (D) none of the above
Q.55 For the system governed by the set of equations:
???? ???? 1
/ dt = 2 ???? 1
+ ???? 2
+ u
???? ???? 2
/ dt = ? 2 ???? 1
+ u
y = 3 ???? 1
the transfer function Y(s)/U(s) is given by
(A) 3(s+1)/( ???? 2
? 2s + 2) (B) 3(2s+1)/( ???? 2
? 2s + 1)
(C) (s+1)/( ???? 2
? 2s + 1) (D) 3(2s+1)/( ???? 2
? 2s + 2)
END OF THE QUESTION PAPER
EE 15/15
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This post was last modified on 19 December 2019