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GATE ECE 2014 Set 2 | Question: 33
In the magnetically coupled circuit shown in the figure, $56 \%$ of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ____ .
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82
GATE ECE 2014 Set 1 | Question: 7
Consider the configuration shown in the figure which is a portion of a larger electrical network For $R = 1\: \Omega$ and currents $i_{1} = 2A,i_{4} = -1A,i_{5} = -4A,$ which one of the following is $\textbf{TRUE}?$ ... is sufficient to conclude that the supposed currents are impossible Data is insufficient to identify the currents $i_{2},i_{3},$ and $i_{6}$
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83
GATE ECE 2014 Set 1 | Question: 19
A continuous, linear time-invariant filter has an impulse response $h(t)$ described by $h(t) = \begin{cases}3 & \text{for } 0 \leq t \leq 3 \\ 0 & \text{otherwise} \end{cases}$ When a constant input of value $5$ is applied to this filter, the steady state output is ________.
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84
GATE ECE 2014 Set 1 | Question: 20
The forward path transfer function of a unity negative feedback system is given by $G(s) = \frac{K}{(s+2)(s-1)}$. The value of $K$ which will place both the poles of the closed-loop system at the same location, is _______.
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85
GATE ECE 2014 Set 1 | Question: 24
A two-port network has scattering parameters given by $[S] = \begin{bmatrix}s_{11} &s_{12} \\s_{21} &s_{22} \end{bmatrix}.$ If the port-2 of the two-port is short circuited, the $s_{11}$ ... $\dfrac{s_{11} - s_{11}s_{22} + s_{12}s_{21}}{1 - s_{22}}$
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86
GATE ECE 2014 Set 1 | Question: 30
A $Y$-network has resistances of $10\Omega$ each in two of its arms, while the third arm has a resistance of $11\Omega.$ In the equivalent $\Delta$ – network, the lowest value (in $\Omega)$ among the three resistances is ______.
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87
GATE ECE 2013 | Question: 29
The open-loop transfer function of a dc motor is given as $\dfrac{\omega(s)}{V_{a}(s)} = \dfrac{10}{1+10s}.$ When connected in feedback as shown below, the approximate value of $K_{a}$ that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is $1$ $5$ $10$ $100$
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88
GATE ECE 2013 | Question: 28
In the circuit shown below, if the source voltage $V_S = 100\angle 53.13^{\circ}\: V$ then the Thevenin’s equivalent voltage in Volts as seen by the load resistance $R_{L}$ is $100\angle 90^{\circ}$ $800\angle 0^{\circ}$ $800\angle 90^{\circ}$ $100\angle 60^{\circ}$
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89
GATE ECE 2013 | Question: 11
Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor $k, \: k> 0,$ the elements of the corresponding star equivalent will be scaled by a factor of $k^{2}$ $k$ $1/k$ $\sqrt{k}$
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90
GATE ECE 2012 | Question: 49
With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ For the same network, with ... $6\:V$ $7\:V$ $8\:V$ $9\:V$
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91
GATE ECE 2012 | Question: 54
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $a=1,b=2$ $a=3,b=2$ $a=-3,b=-1$ $a=3,b=1$
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92
GATE ECE 2012 | Question: 55
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at $\sqrt{2}$ rad/s $\sqrt{3}$ rad/s $\sqrt{6}$ rad/s $\frac{1}{\sqrt{3}}$ rad/s
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93
GATE ECE 2012 | Question: 48
With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ With $10\: V$ dc connected at ... $\frac{3}{7}\: A$ $\frac{5}{7}\: A$ $1\: A$ $\frac{9}{7}\: A$
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94
GATE ECE 2012 | Question: 20
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 $\omega=1\:rad/s$ $\omega=2\:rad/s$ $\omega=3\:rad/s$ $\omega=4\:rad/s$
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95
GATE ECE 2012 | Question: 11
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of $tf(t)$ is $-\frac{s}{(s^2+s+1)^2}$ $-\frac{2s+1}{(s^2+s+1)^2}$ $\frac{s}{(s^2+s+1)^2}$ $\frac{2s+1}{(s^2+s+1)^2}$
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96
GATE ECE 2018 | Question: 53
Consider the network shown below with $R_{1}=1\:\Omega,R_{2}=2\:\Omega$ and $R_{3}=3\:\Omega.$ The network is connected to a constant voltage source of $11\:V$. The magnitude of the current (in amperes, accurate to two decimal places ) through the source is _________.
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97
GATE ECE 2018 | Question: 41
For a unity feedback control system with the forward path transfer function $G\left ( s \right )=\dfrac{K}{s\left ( s+2 \right )}$The peak resonant magnitude $M_{r}$ of the closed-loop frequency response is $2$. The corresponding value of the gain $\text{K}$ (correct to two decimal places) is _________.
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98
GATE ECE 2018 | Question: 42
The figure below shows the Bode magnitude and phase plots of a stable transfer function $G\left ( s \right )=\dfrac{n_{0}}{s^{3}+d_{2}s^{2}+d_{1}s+d_{0}}.$ Consider the negative unity feedback configuration with gain $k$ in the feedforward path. The closed loop is stable for $k < k_{0}.$ The maximum value of $k_{0}$ is _________.
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99
GATE ECE 2018 | Question: 29
The state equation and the output equation of a control system are given below: $\dot{x}=\begin{bmatrix} -4 & -1.5\\ 4& 0 \end{bmatrix}x+\begin{bmatrix} 2\\ 0 \end{bmatrix}u,$ $y=\begin{bmatrix} 1.5 & 0.625 \end{bmatrix}x.$ The transfer function representation of the ... $\dfrac{4s+1.5}{s^{2}+4s+6}$ $\dfrac{6s+5}{s^{2}+4s+6}$
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100
GATE ECE 2018 | Question: 25
The $\text{ABCD}$ matrix for a two-port network is defined by: $\begin{bmatrix} V_{1}\\ I_{1} \end{bmatrix}=\begin{bmatrix} A &B \\ C& D \end{bmatrix}\begin{bmatrix} V_{2}\\ -I_{2} \end{bmatrix}$ The parameter $\text{B}$ for the given two-port network (in ohms, correct to two decimal places) is _________.
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101
GATE ECE 2017 Set 2 | Question: 32
Consider the circuit shown in the figure. The Thevenin equivalent resistance (in Ω) across P-Q is _____________
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102
GATE ECE 2017 Set 2 | Question: 5
In the circuit shown, V is a sinusoidal voltage source. The current $I$ is in phase with voltage V. The ratio$\frac{\text{amplitude of voltage across the capacitor}}{\text{amplitude of voltage across the resistor}}$ is ___________.
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103
GATE ECE 2017 Set 2 | Question: 6
A connection is made consisting of resistance A in series with a parallel combination of resistances $B$ and $C$. Three resistors of value $10 Ω, 5 Ω, 2 Ω$ are provided. Consider all possible permutations of the given resistors ... possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ___________.
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104
GATE ECE 2017 Set 1 | Question: 34
The figure shows an RLC circuit excited by the sinusoidal voltage $100 \cos(3t)$ Volts, where $t$ is in seconds. The ratio $\frac{\text{amplitude of }V_{2}}{\text{amplitude of }V{1}}$ is______.
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