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441
GATE Electrical 2012 | Question: 17
In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12$ V before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for all $t$ is zero a step function an exponentially decaying function an impulse function
In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12$ V before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for all...
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442
GATE Electrical 2012 | Question: 15
The unilateral Laplace transform of $f(t)$ is $\dfrac{1}{s^2+s+1}$. The unilateral Laplace transform of $t f(t)$ is $ – \dfrac{s}{(s^2+s+1)^2} \\ $ $ – \dfrac{2s+1}{(s^2+s+1)^2} \\$ $ \dfrac{s}{(s^2+s+1)^2} \\$ $ \dfrac{2s+1}{(s^2+s+1)^2}$
The unilateral Laplace transform of $f(t)$ is $\dfrac{1}{s^2+s+1}$. The unilateral Laplace transform of $t f(t)$ is$ – \dfrac{s}{(s^2+s+1)^2} \\ $$ – \dfrac{2s+1}{(s^...
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Transform Theory
gate2012-ee
transform-theory
laplace-transform
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answers
443
GATE Electrical 2012 | Question: 18
The $i-v$ characteristics of the diode in the circuit given below are $i= \begin{cases} \dfrac{v-0.7}{500}A, & v \geq 0.7 \: V \\ 0 A, & v <0.7 \: V \end{cases}$ The current in the circuit is $10 \: mA$ $9.3\: mA$ $6.67\: mA$ $6.2\: mA$
The $i-v$ characteristics of the diode in the circuit given below are $$i= \begin{cases} \dfrac{v-0.7}{500}A, & v \geq 0.7 \: V \\ 0 A, & v <0.7 \: V \end{cases}$$ The cu...
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444
GATE Electrical 2012 | Question: 20
Consider the given circuit. In this circuit, the race around does not occur occurs when $\text{CLK}=0$ occurs when $\text{CLK}=1$ and $A=B=1$ occurs when $\text{CLK}=1$ and $A=B=0$
Consider the given circuit. In this circuit, the race arounddoes not occuroccurs when $\text{CLK}=0$occurs when $\text{CLK}=1$ and $A=B=1$occurs when $\text{CLK}=1$ and $...
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445
GATE Electrical 2012 | Question: 19
The output $Y$ of a $2$-bit comparator is logic $1$ whenever the $2$-bit input A is greater than the $2$-bit input B. The number of combinations of which the output is logic $1$, is $4$ $6$ $8$ $10$
The output $Y$ of a $2$-bit comparator is logic $1$ whenever the $2$-bit input A is greater than the $2$-bit input B. The number of combinations of which the output is lo...
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446
GATE Electrical 2012 | Question: 16
The average power delivered to an impedance $(4-j3) \Omega$ by a current $5 \cos (100 \pi \:t +100)$A is $44.2$ W $50$ W $62.5$ W $125$ W
The average power delivered to an impedance $(4-j3) \Omega$ by a current $5 \cos (100 \pi \:t +100)$A is$44.2$ W$50$ W$62.5$ W$125$ W
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447
GATE Electrical 2012 | Question: 21
The figure shows a two-generator system supplying a load of $P_D = 40$ MW, connected at bus $2$. The fuel cost of generations $G_1$ and $G_2$ are: $C_1(P_{G1})=10,000$ Rs/MWh and $C_2(P_{G2})=12,500$ ... $P_{G2}=22$ $P_{G1}=22$, $P_{G2}=20$ $P_{G1}=20$, $P_{G2}=20$ $P_{G1}=0$, $P_{G2}=42$
The figure shows a two-generator system supplying a load of $P_D = 40$ MW, connected at bus $2$. The fuel cost of generations $G_1$ and $G_2$ are:$C_1(P_{G1})=10,000$ Rs/...
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448
GATE Electrical 2012 | Question: 9
The bus admittance matrix of a three-bus three-line system is $Y=j \begin{bmatrix} -13 & 10 & 5 \\ 10 & -18 & 10 \\ 5 & 10 & -13 \end{bmatrix}$ If each transmission line between the two buses is represented by an equivalent $\pi$-network, the magnitude of the shunt susceptance of the line connecting bus $1$ and $2$ is $4$ $2$ $1$ $0$
The bus admittance matrix of a three-bus three-line system is $Y=j \begin{bmatrix} -13 & 10 & 5 \\ 10 & -18 & 10 \\ 5 & 10 & -13 \end{bmatrix}$ If each transmission line ...
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449
GATE Electrical 2012 | Question: 8
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$-transform in the $Z$-plane will be $\dfrac{1}{3} < \mid z \mid < 3 \\$ $\dfrac{1}{3} < \mid z \mid < \dfrac{1}{2} \\$ $\dfrac{1}{2} < \mid z \mid < 3 \\$ $\dfrac{1}{3} < \mid z \mid $
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$-transform in the $Z$-plane will be$\dfrac{1}{3} < \mid z \mid < 3 \\$$\...
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450
GATE Electrical 2012 | Question: 14
With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is $x=t-\dfrac{1}{2} \\ $ $x=t^2-\dfrac{1}{2} \\ $ $x=\dfrac{t^2}{2} \\$ $x=\dfrac{t}{2}$
With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is$x=t-\dfrac{1}{2} \\ $$x=t^2-\dfrac{1}{2} \\ $$x=\dfrac{t^2}{2} \\$$x...
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Differential Equations
gate2012-ee
differential-equations
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451
GATE Electrical 2012 | Question: 10
The slip of an induction motor normally does not depend on rotor speed synchronous speed shaft torque core-loss component
The slip of an induction motor normally does not depend onrotor speedsynchronous speedshaft torquecore-loss component
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452
GATE Electrical 2012 | Question: 12
A periodic voltage waveform observed on an oscilloscope across a load is shown. A permane magnet moving coil (PMMC) meter connected across the same load reads $4$V $5$ V $8$ V $10$ V
A periodic voltage waveform observed on an oscilloscope across a load is shown. A permane magnet moving coil (PMMC) meter connected across the same load reads$4$V$5$ V$8$...
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453
GATE Electrical 2012 | Question: 13
The bridge method commonly used for finding mutual inductance is Heaviside Campbell bridge Schering bridge De Sauty bridge Wien bridge
The bridge method commonly used for finding mutual inductance isHeaviside Campbell bridgeSchering bridgeDe Sauty bridgeWien bridge
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454
GATE Electrical 2012 | Question: 11
A two-phase load draws the following phase currens: $i_1(t)=I_m \sin(\omega t – \phi_1), i_2(t) = I_m \cos(\omega t – \phi_2)$. These currents are balanced if $\phi_1$ is equal to $- \phi_2$ $\phi_2$ $\pi/2 - \phi_2$ $\pi/2 + \phi_2$
A two-phase load draws the following phase currens: $i_1(t)=I_m \sin(\omega t – \phi_1), i_2(t) = I_m \cos(\omega t – \phi_2)$. These currents are balanced if $\phi_1...
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455
GATE Electrical 2012 | Question: 2
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{- \pi/2}$ $e^{\pi/2}$ $x$ $1$
If $x=\sqrt{-1}$, then the value of $x^x$ is$e^{- \pi/2}$$e^{\pi/2}$$x$$1$
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Complex Variables
gate2012-ee
complex-variables
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0
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answers
456
GATE Electrical 2012 | Question: 6
A system with transfer function $G(s) =\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$ is excited by $\sin (\omega t)$. The steady-state output of the system is zero at $\omega = 1 \text{ rad/s}$ $\omega = 2\text{ rad/s}$ $\omega = 3 \text{ rad/s}$ $\omega = 4 \text{ rad/s}$
A system with transfer function $$G(s) =\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$$ is excited by $\sin (\omega t)$. The steady-state output of the system is zero at$\omega = ...
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457
GATE Electrical 2012 | Question: 3
Given $f(z) = \dfrac{1}{z+1} – \dfrac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$-plane such that $\mid z+1 \mid =1$, the value of $\dfrac{1}{2 \pi \: j} \oint_c f(z) dz$ is $-2$ $-1$ $1$ $2$
Given $f(z) = \dfrac{1}{z+1} – \dfrac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$-plane such that $\mid z+1 \mid =1$, the value of $\dfrac{1}{2 \pi \: j} \oi...
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Complex Variables
gate2012-ee
complex-variables
cauchys-integral-theorem
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votes
0
answers
458
GATE Electrical 2012 | Question: 7
In the sum of products function $f(X,Y,Z) = \Sigma(2,3,4,5)$, the prime implicants are $\overline{X}Y, X \overline{Y}$ $\overline{X}Y, X \overline{Y}\overline{Z}, X \overline{Y}Z$ $\overline{X} Y \overline{Z}, \overline{X}YZ, X \overline{Y}$ $\overline{X} Y \overline{Z}, \overline{X}YZ, X \overline{Y} \overline{Z}, X \overline{Y}Z$
In the sum of products function $f(X,Y,Z) = \Sigma(2,3,4,5)$, the prime implicants are$\overline{X}Y, X \overline{Y}$$\overline{X}Y, X \overline{Y}\overline{Z}, X \overli...
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Analog and Digital Electronics
gate2012-ee
analog-and-digital-electronics
boolean-algebra
sum-of-products
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0
answers
459
GATE Electrical 2012 | Question: 5
The impedance looking into nodes $1$ and $2$ in the given circuit is $50 \: \Omega$ $100 \: \Omega$ $5 \: \Omega$ $10.1 \: \Omega$
The impedance looking into nodes $1$ and $2$ in the given circuit is$50 \: \Omega$$100 \: \Omega$$5 \: \Omega$$10.1 \: \Omega$
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460
GATE Electrical 2012 | Question: 4
In the circuit shown below, the current through the inductor is $\dfrac{2}{1+j} A\\ $ $\dfrac{-1}{1+j} A\\$ $\dfrac{1}{1+j} A \\$ $0 A$
In the circuit shown below, the current through the inductor is$\dfrac{2}{1+j} A\\ $$\dfrac{-1}{1+j} A\\$$\dfrac{1}{1+j} A \\$$0 A$
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461
GATE Electrical 2012 | Question: 1
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that $\text{max}[X,Y]$ is less than $1/2$ is $3/4$ $9/16$ $1/4$ $2/3$
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that $\text{max}[X,Y]$ is less than $1/2$ is$3/4$$9/16$$1...
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Mar 23, 2018
Probability & Statistics
gate2012-ee
probability-and-statistics
probability
random-variable
uniform-distribution
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–
0
votes
2
answers
462
GATE Electrical 2018 | GA Question: 7
In a certain code, $AMCF$ is written as $EQGJ$ and $NKUF$ is written as $ROYJ.$ How will $DHLP$ be written in that code$?$ $RSTN$ $TLPH$ $HLPT$ $XSVR$
In a certain code, $AMCF$ is written as $EQGJ$ and $NKUF$ is written as $ROYJ.$ How will $DHLP$ be written in that code$?$$RSTN$ $TLPH$ $HLPT$ $XSVR$
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Analytical Aptitude
gate2018-ee
analytical-aptitude
logical-reasoning
sequence-series
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–
0
votes
1
answer
463
GATE Electrical 2018 | GA Question: 6
An e-mail password must contain three characters. The password has to contain one numeral from $0$ to $9,$ one upper case and one lower case character from the English alphabet. How many distinct passwords are possible$?$ $6,760$ $13,520$ $40,560$ $1,05,456$
An e-mail password must contain three characters. The password has to contain one numeral from $0$ to $9,$ one upper case and one lower case character from the English al...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Quantitative Aptitude
gate2018-ee
numerical-ability
counting
+
–
0
votes
1
answer
464
GATE Electrical 2018 | GA Question: 8
A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys? $0 \\ $ $\frac{325}{864} \\ $ $\frac{525}{864} \\ $ $\frac{5}{12}$
A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is t...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Quantitative Aptitude
gate2018-ee
numerical-ability
probability
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0
votes
1
answer
465
GATE Electrical 2018 | GA Question: 9
A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by $25 \%$. ... $35.75$ $40.25$ $43.75$ $46.25$
A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage o...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Quantitative Aptitude
gate2018-ee
numerical-ability
percentage
+
–
0
votes
1
answer
466
GATE Electrical 2018 | GA Question: 4
For what values of $k$ given below is $\dfrac{(k + 2)^2}{(k - 3)}$ an integer? $4 , 8 , 18 $ $4 , 10 , 16$ $ 4 , 8 , 28 $ $8 , 26 , 28$
For what values of $k$ given below is $\dfrac{(k + 2)^2}{(k - 3)}$ an integer?$4 , 8 , 18 $ $4 , 10 , 16$$ 4 , 8 , 28 $ $8 , 26 , 28$
Arjun
15.9k
points
Arjun
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Feb 19, 2018
Quantitative Aptitude
gate2018-ee
numerical-ability
algebra
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0
votes
1
answer
467
GATE Electrical 2018 | GA Question: 10
$P, Q, R,$ and $S$ crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available. The boat held two persons on each of the three forward trips across the lake and one person ... person rowed for at least one trip. Only one person can row during a trip. Who rowed twice? $P$ $Q$ $R$ $S$
$P, Q, R,$ and $S$ crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.The boat held ...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Analytical Aptitude
gate2018-ee
analytical-aptitude
logical-reasoning
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–
0
votes
1
answer
468
GATE Electrical 2018 | GA Question: 5
Functions $F(a,b)$ and $G(a,b)$ are defined as follows: $F(a,b)=(a-b)^{2}$ and $G(a,b)=\mid a-b\mid ,$ where $\mid x\mid$ represents the absolute value of $x.$ What would be the value of $G(F(1,3),G(1,3))?$ $2$ $4$ $6$ $36$
Functions $F(a,b)$ and $G(a,b)$ are defined as follows:$F(a,b)=(a-b)^{2}$ and $G(a,b)=\mid a-b\mid ,$ where $\mid x\mid$ represents the absolute value of $x.$What would b...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Quantitative Aptitude
gate2018-ee
numerical-ability
functions
+
–
0
votes
0
answers
469
GATE Electrical 2018 | GA Question: 3
The three roots of the equation $f(x) = 0$ are $x = {−2, 0, 3}.$ What are the three values of $ x $ for which $f(x − 3) = 0?$ $−5 , −3 , 0 $ $−2 , 0 , 3$ $0 , 6 , 8$ $1 , 3 , 6$
The three roots of the equation $f(x) = 0$ are $x = {−2, 0, 3}.$ What are the three values of $ x $ for which $f(x − 3) = 0?$$−5 , −3 , 0 $ $−2 , 0 , ...
Arjun
15.9k
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Arjun
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Feb 19, 2018
Quantitative Aptitude
gate2018-ee
numerical-ability
quadratic-equations
cubic-equations
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0
votes
1
answer
470
GATE Electrical 2018 | GA Question: 1
“Since you have gone off the ________, the _________ sand is likely to damage the car.” The words that best fill the blanks in the above sentence are course, coarse course, course coarse, course coarse, coarse
“Since you have gone off the ________, the _________ sand is likely to damage the car.”The words that best fill the blanks in the above sentence arecourse, coarse ...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Verbal Aptitude
gate2018-ee
verbal-ability
most-appropriate-word
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–
0
votes
1
answer
471
GATE Electrical 2018 | GA Question: 2
“A common misconception among writers is that sentence structure mirrors thought; the more _________ the structure, the more complicated the ideas.” The word that best fills the blank in the above sentence is detailed simple clear convoluted
“A common misconception among writers is that sentence structure mirrors thought; themore _________ the structure, the more complicated the ideas.”The word that best ...
Arjun
15.9k
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Arjun
asked
Feb 19, 2018
Verbal Aptitude
gate2018-ee
verbal-ability
most-appropriate-word
+
–
0
votes
0
answers
472
GATE Electrical 2018 | Question: 54
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S$ is the slip. At no-load, the motor speed can be approximated to the synchronous speed. The no-load lagging power factor of the motor is __________ (up to $3$ decimal places).
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
new
gate2018-ee
numerical-answers
+
–
0
votes
0
answers
473
GATE Electrical 2018 | Question: 55
The voltage $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega = 100 \text{ radian/s}$. When the inductor current $i(t)$ is in phase with the voltage $v(t)$, the magnitude of the impedance $Z$ (in $\Omega$) seen between the terminals $a$ and $b$ is __________ (up to $2$ decimal places)
The voltage $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega = 100 \text{ radian/s}$. When the inductor ...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
new
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numerical-answers
+
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votes
1
answer
474
GATE Electrical 2018 | Question: 52
A $200$ V DC series motor, when operating from rated voltage while driving a certain load, draws $10$ A current and runs at $1000$ r.p.m. The total series resistance is $1 \: \Omega$. The magnetic circuit is assumed to be linear. At the ... the load torque is increased by $44 \%$. The speed of the motor in r.p.m (rounded to the nearest integer) is _____________
A $200$ V DC series motor, when operating from rated voltage while driving a certain load, draws $10$ A current and runs at $1000$ r.p.m. The total series resistance is $...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
new
gate2018-ee
numerical-answers
+
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0
votes
0
answers
475
GATE Electrical 2018 | Question: 50
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of identical value. The load resistance is $1 \: \Omega$. The capacitor voltage has negligible ... of $i_{s1}$, the current of switch $S1$ (in Ampere), is ____________ (up to $2$ decimal places).
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of ide...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
new
gate2018-ee
numerical-answers
+
–
0
votes
0
answers
476
GATE Electrical 2018 | Question: 51
A $3$-phase $900$ kVA, $3 \: kV/ \sqrt{3} kV$ ( $\Delta/$), $50$ Hz transformer has primary (high voltage side) resistance per phase of $0.3 \: \Omega$ and secondary (low voltage side) resistance per phase of $0.02 \: \Omega$. ... is $10 \: kW$. The full load $\%$ efficiency of the transformer operated at unity power factor is _______ (up to $2$ decimal places)
A $3$-phase $900$ kVA, $3 \: kV/ \sqrt{3} kV$ ( $\Delta/$), $50$ Hz transformer has primary (high voltage side) resistance per phase of $0.3 \: \Omega$ and secondary (low...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
new
gate2018-ee
numerical-answers
+
–
0
votes
0
answers
477
GATE Electrical 2018 | Question: 46
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is ___________ (up to $2$ decimal places).
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is _...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
new
gate2018-ee
numerical-answers
+
–
0
votes
0
answers
478
GATE Electrical 2018 | Question: 53
A dc to dc converter shown in the figure is charging a battery bank, $B2$ whose voltage is constant at $150 \: V$. $B1$ is another battery bank whose voltage is constant at $50 \: V$. The value of the inductor, $L$ is $5$ mH and the ... assuming the diode D to be ideal, the power transferred from $B1$ to $B2$ (in Watt) is ___________ (up to $2$ decimal places)
A dc to dc converter shown in the figure is charging a battery bank, $B2$ whose voltage is constant at $150 \: V$. $B1$ is another battery bank whose voltage is constant ...
Arjun
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GATE Electrical 2018 | Question: 48
The voltage across the circuit in the figure, and the current through it, are given by the following expressions: $v(t)=5-10 \cos (\omega t+ 60^{\circ}) \: V$ $i(t)=5 + X \cos (\omega t) \: A$ where $\omega =100 \: \pi \text{ radian}/s$. If the average power delivered to the circuit is zero, then the value of $X$ (in Ampere) is _______ (up to $2$ decimal places)
The voltage across the circuit in the figure, and the current through it, are given by the following expressions:$v(t)=5-10 \cos (\omega t+ 60^{\circ}) \: V$$i(t)=5 + X \...
Arjun
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Arjun
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GATE Electrical 2018 | Question: 47
A three-phase load is connected to a three-phase balanced supply as shown in the figure. If $V_{\text{an}} = 100 \angle 0^{\circ} \: V$, $V_{\text{bn}}=100 \angle - 120 ^{\circ} \: V$ ... in the anti-clockwise direction), the value of $R$ for zero current in the neutral wire is __________ $\Omega$ (up to $2$ decimal places).
A three-phase load is connected to a three-phase balanced supply as shown in the figure. If $V_{\text{an}} = 100 \angle 0^{\circ} \: V$, $V_{\text{bn}}=100 \angle – 120...
Arjun
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Arjun
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