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81
GATE Electrical 2023 | Question: 14
In the figure, the vectors $\mathbf{u}$ and $\mathbf{v}$ are related as: $\mathbf{A u}=\mathbf{v}$ by a transformation matrix A. The correct choice of $\mathbf{A}$ ... $\left[\begin{array}{ll}\frac{4}{5} & -\frac{3}{5} \\ \frac{3}{5} & -\frac{4}{5}\end{array}\right]$
In the figure, the vectors $\mathbf{u}$ and $\mathbf{v}$ are related as: $\mathbf{A u}=\mathbf{v}$ by a transformation matrix A. The correct choice of $\mathbf{A}$ is$\le...
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82
GATE Electrical 2023 | Question: 10
For the three-bus power system shown in the figure, the trip signals to the circuit breakers $\text{B}_1$ to $\text{B}_9$ are provided by overcurrent relays $\text{R}_1$ to $\text{R}_9$, respectively, some of which have directional ... $\text{R}_4$ are directional overcurrent relays blocking faults towards Line $1$ and Line $2,$ respectively.
For the three-bus power system shown in the figure, the trip signals to the circuit breakers $\text{B}_1$ to $\text{B}_9$ are provided by overcurrent relays $\text{R}_1$ ...
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83
GATE Electrical 2023 | Question: 13
The chopper circuit shown in figure (i) feeds power to a $5 \text { A DC}$ constant current source. The switching frequency of the chopper is $100 ~\mathrm{kHz}.$ ... $10 \mathrm{~V}$ $6 \mathrm{~V}$ $12 \mathrm{~V}$ $20 \mathrm{~V}$
The chopper circuit shown in figure (i) feeds power to a $5 \text { A DC}$ constant current source. The switching frequency of the chopper is $100 ~\mathrm{kHz}.$ All the...
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84
GATE Electrical 2023 | Question: 5
The following columns present various modes of induction machine operation and the ranges of slip ... $a-r, b-q$, and $c-p$ $a-p, b-r$, and $c-q$ $a-q, b-p$, and $c-r$
The following columns present various modes of induction machine operation and the ranges of slip$$\begin{array}{ll} \qquad \qquad\textbf{A} & \qquad \textbf{B} \\ \quad...
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GATE Electrical 2023 | Question: 49
The Zener diode in circuit has a breakdown voltage of $ 5 \mathrm{~V} \text .$ The current gain $\beta$ of the transistor in the active region in $99.$ Ignore base-emitter voltage drop $ V_{B E} $. The current through the $20 \: \Omega$ resistance in milliamperes is_______(Round off to $2$ decimal places).
The Zener diode in circuit has a breakdown voltage of $ 5 \mathrm{~V} \text .$ The current gain $\beta$ of the transistor in the active region in $99.$ Ignore base-emitte...
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86
GATE Electrical 2023 | Question: 21
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t)=x(t) * y(t)$ is maximum at $t=T_1$. Then $T_1$ in seconds is_________ (Round off to the nearest integer).
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t)=x(t) * y(t)$ is maximum at $t=T_1$. Then $T_1$ in seconds is_________ (Round off to the nearest integer).
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87
GATE Electrical 2023 | Question: 22
For the circuit shown in the figure, $V_{1}=8 \mathrm{~V}, \mathrm{DC}$ and $I_{1}=8 \mathrm{~A}, \mathrm{DC}$. The voltage $V_{a b}$ in Volts is____________(Round off to $1$ decimal place).
For the circuit shown in the figure, $V_{1}=8 \mathrm{~V}, \mathrm{DC}$ and $I_{1}=8 \mathrm{~A}, \mathrm{DC}$. The voltage $V_{a b}$ in Volts is____________(Round off to...
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88
GATE Electrical 2023 | Question: 26
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$ $\frac{e^{-2.514 s}}{s+1}$ $1.04 e^{-2.514 s}$ $2.51 e^{-1.047 s}$
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$$\frac{e^{-2.514 s}}{s+1}$$1.04...
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89
GATE Electrical 2023 | Question: 19
The value of parameters of the circuit shown in the figure are $\qquad R_{1}=2 \Omega, R_{2}=2 \Omega, R_{3}=3 \Omega, L=10 \mathrm{mH}, C=100 \mu \mathrm{F}$ For time $t<0$ ... value of the voltage across the inductor $\left(V_{L}\right)$ at $t=0^{+}$in Volts is________ (Round off to $1$ decimal place).
The value of parameters of the circuit shown in the figure are $\qquad R_{1}=2 \Omega, R_{2}=2 \Omega, R_{3}=3 \Omega, L=10 \mathrm{mH}, C=100 \mu \mathrm{F}$ For time $t...
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GATE Electrical 2023 | Question: 28
Consider a lead compensator of the form $K(s)=\frac{1+\frac{s}{a}}{1+\frac{s}{\beta a}}, \beta>1, a>0$ The frequency at which this compensator produces maximum phase lead is $ 4 \mathrm{rad} / \mathrm{s}.$ At this frequency, the gain amplification provided ... $6 \mathrm{~dB}$. The values of $\alpha, \beta,$ respectively, are $1,16$ $2,4$ $3,5$ $2.66,2.25$
Consider a lead compensator of the form $$K(s)=\frac{1+\frac{s}{a}}{1+\frac{s}{\beta a}}, \beta>1, a>0$$The frequency at which this compensator produces maximum phase lea...
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GATE Electrical 2023 | Question: 27
Consider the $\mathrm{OP} \mathrm{AMP} $ based circuit shown in the figure. Ignore the conduction drops of diodes $\text{D}_{1}$ and $\text{D}_{2}$. All the components are ideal and the breakdown voltage of the Zener is $5 \mathrm{~V}.$ Which of the ... minimum values of the output voltage $\text{V}_{O} $ are $+5 \mathrm{~V}$ and $-10 \mathrm{~V}$, respectively.
Consider the $\mathrm{OP} \mathrm{AMP} $ based circuit shown in the figure. Ignore the conduction drops of diodes $\text{D}_{1}$ and $\text{D}_{2}$. All the components a...
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92
GATE Electrical 2023 | Question: 38
A three phase $415 \mathrm{~V}, 50 \mathrm{~Hz}, \text { 6-pole, } 960 \text { RPM, 4 HP}$ squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output. If the ... in $\text { RPM}$ (neglecting the stator leakage impedance and rotational losses) is ________ (Round off to the nearest integer).
A three phase $415 \mathrm{~V}, 50 \mathrm{~Hz}, \text { 6-pole, } 960 \text { RPM, 4 HP}$ squirrel cage induction motor drives a constant torque load at rated speed oper...
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93
GATE Electrical 2023 | Question: 3
In the Nyquist plot of the open-loop transfer function $G(s)H(s) = \frac{3s+5}{s-1}$ corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at $G(s)H(s) = \infty$ $G(s)H(s) = 0$ $G(s)H(s) = 3$ $G(s)H(s) = -5$
In the Nyquist plot of the open-loop transfer function$$G(s)H(s) = \frac{3s+5}{s-1}$$corresponding to the feedback loop shown in the figure, the infinite semi-circular ar...
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94
GATE Electrical 2023 | Question: 12
The four stator conductors $\left(\mathrm{A}, \mathrm{A}^{\prime}, \mathrm{B}\right.$ and $\left.\mathrm{B}^{\prime}\right)$ of a rotating machine are carrying $\mathrm{DC}$ currents of the same value, the directions of which are shown in the figure (i). The rotor coils ... with $E_{a-a^{\prime}}$ leading $E_{b-b^{\prime}}$ $E_{a-a^{\prime}}=E_{b-b^{\prime}}=0$
The four stator conductors $\left(\mathrm{A}, \mathrm{A}^{\prime}, \mathrm{B}\right.$ and $\left.\mathrm{B}^{\prime}\right)$ of a rotating machine are carrying $\mathrm{D...
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95
GATE Electrical 2023 | Question: 8
The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by $\begin{aligned} X(\omega) & =1, \text { for }|\omega|<W_o \\ & =0, \text { for }|\omega|>W_0 \end{aligned}$ Which one of the following statements is true? $x(t)$ tends to be an impulse as ... At $t=\frac{\pi}{2 W_0}, x(t)=-\frac{1}{\pi}$ At $t=\frac{\pi}{2 W_0}, x(t)=\frac{1}{\pi}$
The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by$$\begin{aligned}X(\omega) & =1, \text { for }|\omega|<W_o \\& =0, \text { for }|\omega|>W_0\end{aligned...
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96
GATE Electrical 2023 | Question: 23
A $50 \mathrm{~Hz}, 275 ~\mathrm{kV}$ line of length $400 \mathrm{~km}$ has the following parameters: Resistance, $R=0.035 ~\Omega / \mathrm{km} ;$ Inductance, $L=1 ~\mathrm{mH} / \mathrm{km} ;$ ... $2$ decimal places).
A $50 \mathrm{~Hz}, 275 ~\mathrm{kV}$ line of length $400 \mathrm{~km}$ has the following parameters: Resistance, $R=0.035 ~\Omega / \mathrm{km} ;$ Inductance, $L=1 ~\mat...
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97
GATE Electrical 2023 | Question: 20
A separately excited $\text{DC}$ motor rated $400 \mathrm{~V}, 15 \mathrm{~A}, 1500\mathrm{~ RPM}$ drives a constant torqueload at rated speed operating from $400 \mathrm{~V}$ $\text{DC}$ supply drawing rated current. The armature ... field current unaltered then the resultant speed of the motor in $\mathrm{~ RPM}$ is_________ (Round off to the nearest integer).
A separately excited $\text{DC}$ motor rated $400 \mathrm{~V}, 15 \mathrm{~A}, 1500\mathrm{~ RPM}$ drives a constant torqueload at rated speed operating from $400 \mathrm...
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98
GATE Electrical 2023 | Question: 46
Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence $\text{[ABCD]}$ of initial logic states, which will not change with clock, is_______.
Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence $\text{[ABCD]}$ of initial logic states, which ...
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99
GATE Electrical 2023 | Question: 7
A continuous-time system that is initially at rest is described by $ \frac{d y(t)}{d t}+3 y(t)=2 x(t),$ where$x(t)$ is the input voltage and $y(t)$ is the output voltage. The impulse response of the system is $3 e^{-2 t}$ $\frac{1}{3} e^{-2 t} u(t)$ $2 e^{-3 t} u(t)$ $2 e^{-3 t}$
A continuous-time system that is initially at rest is described by $$ \frac{d y(t)}{d t}+3 y(t)=2 x(t),$$ where$x(t)$ is the input voltage and $y(t)$ is the output voltag...
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GATE Electrical 2023 | Question: 4
Consider a unity-gain negative feedback system consisting of the plant $G(s)$ (given below) and a proportional-integral controller. Let the proportional gain and integral gain be $3$ and $1,$ respectively. For a unit step reference input, the final values of the controller output and ... respectively, are $G(s)=\frac{1}{s-1}$ $\infty, \infty$ $1,0$ $1,-1$ $-1,1$
Consider a unity-gain negative feedback system consisting of the plant $G(s)$ (given below) and a proportional-integral controller. Let the proportional gain and integral...
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