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61
GATE Electrical 2024 | Question: 44
A $3$-phase star connected slip ring induction motor has the following parameters referred to the stator: \[ R_{s}=3 \Omega, X_{s}=2 \Omega, X_{r}^{\prime}=2 \Omega, R_{r}^{\prime}=2.5 \Omega \] The per phase stator to rotor ... to the rotor side) to be connected in series with each phase of the rotor winding is ____________ (rounded off to $2$ decimal places).
A $3$-phase star connected slip ring induction motor has the following parameters referred to the stator:\[R_{s}=3 \Omega, X_{s}=2 \Omega, X_{r}^{\prime}=2 \Omega, R_{r}^...
Arjun
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62
GATE Electrical 2024 | Question: 40
In the circuit shown, $Z_{1}=50 \angle-90^{\circ} \Omega$ and $Z_{2}=200 \angle-30^{\circ} \Omega$. It is supplied by a three phase $400 \mathrm{~V}$ source with the phase sequence being R-Y-B. Assume the watt meters $W_{1}$ ... The magnitude of the difference between the readings of $W_{1}$ and $W_{2}$ in watts is __________ (rounded off to $2$ decimal places).
In the circuit shown, $Z_{1}=50 \angle-90^{\circ} \Omega$ and $Z_{2}=200 \angle-30^{\circ} \Omega$. It is supplied by a three phase $400 \mathrm{~V}$ source with the phas...
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63
GATE Electrical 2024 | Question: 51
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The $\text{CMRR}$ (in $\mathrm{dB}$ ) of the difference amplifier is ___________ (rounded off to $2$ decimal places).
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The $\text{CMRR}$ (in $\mathrm{dB}$ ) of the difference amplifier is ___________ (rounded of...
Arjun
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64
GATE Electrical 2024 | Question: 49
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $\text{G(s)}$ are given in the table. The value of the gain $K_{I}(>0)$ for a $50^{\circ}$ phase margin is __________ (rounded off to $2$ ... -80 \\ \hline 2.0 & -18 & -130 \\ \hline 10.0 & -40 & -200 \\ \hline \end{array}
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $\text{G(s)}$ are given in the table. The value of...
Arjun
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Arjun
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65
GATE Electrical 2024 | Question: 46
The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being $P_{\max } \sin \delta$, where $\delta$ is the load angle ... , the accelerating area on the power angle curve is __________ times $P_{\max }$ (rounded off to $2$ decimal places).
The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the ge...
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66
GATE Electrical 2023 | Question: 6
A $10-\text { pole, } 50 \mathrm{~Hz}, 240 \mathrm{~V},$ single phase induction motor runs at $540 ~\mathrm{RPM}$ while driving rated load. The frequency of induced rotor currents due to backward field is $100 \mathrm{~Hz}$ $95 \mathrm{~Hz}$ $10 \mathrm{~Hz}$ $5 \mathrm{~Hz}$
A $10-\text { pole, } 50 \mathrm{~Hz}, 240 \mathrm{~V},$ single phase induction motor runs at $540 ~\mathrm{RPM}$ while driving rated load. The frequency of induced rotor...
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67
GATE Electrical 2023 | Question: 35
The expected number of trials for first occurrence of a "head" in a biased coin is known to be $4.$ The probability of first occurrence of a "head" in the second trial is ____________(Round off to $3$ decimal places).
The expected number of trials for first occurrence of a "head" in a biased coin is known to be $4.$ The probability of first occurrence of a "head" in the second trial is...
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68
GATE Electrical 2023 | Question: 1
For a given vector $\mathbf{w}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{\mathrm{T}}$, the vector normal to the plane defined by $\mathbf{w}^{\mathrm{T}} \mathbf{x}=1$ ... $\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^T$
For a given vector $\mathbf{w}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{\mathrm{T}}$, the vector normal to the plane defined by $\mathbf{w}^{\mathrm{T}} \math...
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69
GATE Electrical 2023 | Question: 2
For the block diagram shown in the figure, the transfer function $\frac{\text{Y(s)}}{\text{R(s)}}$ is $\frac{2s+3}{s+1}$ $\frac{3s+2}{s-1}$ $\frac{s+1}{3s+2}$ $\frac{3s+2}{s+1}$
For the block diagram shown in the figure, the transfer function $\frac{\text{Y(s)}}{\text{R(s)}}$ is$\frac{2s+3}{s+1}$ $\frac{3s+2}{s-1}$ $\frac{s+1}{3s+2}$ $\frac{3s+2}...
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70
GATE Electrical 2023 | Question: 9
The $\text{Z}$-transform of a discrete signal $\text{x[n]}$ is $\text{X(z)}=\frac{4 z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)}$ with $\text{ROC=R}$ Which one of the following statements is true? Discrete-time Fourier ... transform of $\mathrm{x}[\mathrm{n}]$ converges if $\text{R}$ is such that $ \mathrm{x}[\mathrm{n}]$ is a right-sided sequence
The $\text{Z}$-transform of a discrete signal $\text{x[n]}$ is$\text{X(z)}=\frac{4 z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)}$ with $\text{ROC=R}$ Whic...
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71
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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72
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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73
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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74
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$$\begin{array}{ll} \qquad \qquad\textbf{A} & \qquad \textbf{B} \\ \quad...
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75
GATE Electrical 2023 | Question: 49
The Zener diode in circuit has a breakdown voltage of $ 5 \mathrm{~V} \text .$ The current gain $\beta$ of the transistor in the active region in $99.$ Ignore base-emitter voltage drop $ V_{B E} $. The current through the $20 \: \Omega$ resistance in milliamperes is_______(Round off to $2$ decimal places).
The Zener diode in circuit has a breakdown voltage of $ 5 \mathrm{~V} \text .$ The current gain $\beta$ of the transistor in the active region in $99.$ Ignore base-emitte...
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76
GATE Electrical 2023 | Question: 21
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t)=x(t) * y(t)$ is maximum at $t=T_1$. Then $T_1$ in seconds is_________ (Round off to the nearest integer).
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t)=x(t) * y(t)$ is maximum at $t=T_1$. Then $T_1$ in seconds is_________ (Round off to the nearest integer).
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77
GATE Electrical 2023 | Question: 26
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$ $\frac{e^{-2.514 s}}{s+1}$ $1.04 e^{-2.514 s}$ $2.51 e^{-1.047 s}$
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$$\frac{e^{-2.514 s}}{s+1}$$1.04...
admin
1.7k
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78
GATE Electrical 2023 | Question: 22
For the circuit shown in the figure, $V_{1}=8 \mathrm{~V}, \mathrm{DC}$ and $I_{1}=8 \mathrm{~A}, \mathrm{DC}$. The voltage $V_{a b}$ in Volts is____________(Round off to $1$ decimal place).
For the circuit shown in the figure, $V_{1}=8 \mathrm{~V}, \mathrm{DC}$ and $I_{1}=8 \mathrm{~A}, \mathrm{DC}$. The voltage $V_{a b}$ in Volts is____________(Round off to...
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79
GATE Electrical 2023 | Question: 19
The value of parameters of the circuit shown in the figure are $\qquad R_{1}=2 \Omega, R_{2}=2 \Omega, R_{3}=3 \Omega, L=10 \mathrm{mH}, C=100 \mu \mathrm{F}$ For time $t<0$ ... value of the voltage across the inductor $\left(V_{L}\right)$ at $t=0^{+}$in Volts is________ (Round off to $1$ decimal place).
The value of parameters of the circuit shown in the figure are $\qquad R_{1}=2 \Omega, R_{2}=2 \Omega, R_{3}=3 \Omega, L=10 \mathrm{mH}, C=100 \mu \mathrm{F}$ For time $t...
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80
GATE Electrical 2023 | Question: 28
Consider a lead compensator of the form $K(s)=\frac{1+\frac{s}{a}}{1+\frac{s}{\beta a}}, \beta>1, a>0$ The frequency at which this compensator produces maximum phase lead is $ 4 \mathrm{rad} / \mathrm{s}.$ At this frequency, the gain amplification provided ... $6 \mathrm{~dB}$. The values of $\alpha, \beta,$ respectively, are $1,16$ $2,4$ $3,5$ $2.66,2.25$
Consider a lead compensator of the form $$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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