Recent questions and answers in Network Solution Methods

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1

GATE2020-EC: 9
In the circuit shown below, the Thevenin voltage $V_{TH}$is $2.4\:V$ $2.8\:V$ $3.6\:V$ $4.5\:V$

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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2

GATE2020-EC: 15
In the given circuit, the two-port network has the impedance matrix $\begin{bmatrix} Z \end{bmatrix}=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}$. The value of $Z_{L}$ for which maximum power is transferred to the load is _____________$\Omega$.

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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3

GATE2020-EC: 16
The current in the $\text{RL}$-circuit shown below is $i\left ( t \right )=10\cos\left ( 5t-\pi /4 \right )A$. The value of the inductor $\text{(rounded off to two decimal places)}$ is _______ $\text{H}$.

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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4

GATE2020-EC: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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5

GATE2020-EC: 23
The loop transfer function of a negative feedback system is $G\left ( s \right )H\left ( s \right )=\frac{K(s+11)}{s(s+2)(s+8)}.$ The value of $K$, for which the system is marginally stable, is ___________.

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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6

GATE2020-EC: 28
The current $I$ in the given network is $0 \: A$ $2.38\angle -96.37^{\circ}A$ $2.38\angle143.63^{\circ}A$ $2.38\angle-23.63^{\circ}A$

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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7

GATE2020-EC: 30
For the given circuit, which one of the following is correct state equation? ...

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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8

GATE2020-EC: 37
Using the incremental low frequency small-signal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is $r_{ds}+R+g_{m}r_{ds}R \\$ $\dfrac{r_{ds}+R}{1+g_{m}r_{ds}} \\$ $r_{ds}+\dfrac{1}{g_{m}}+R \\$ $r_{ds}+R$

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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9

GATE2020-EC: 49
A system with transfer function $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+a \right )},\:\:a> 0$ is subjected to an input $5 \cos3t$. The steady state output of the system is $\dfrac{1}{\sqrt{10}}\cos\left ( 3t-1.892 \right )$. The value of $a$ is _______.

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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10

GATE2020-EC: 53
The transfer function of a stable discrete-time $\text{LTI}$ system is $H\left ( z \right )=\dfrac{K\left ( z-\alpha \right )}{z+0.5}$, where $K$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to one decimal place) with $\mid \alpha \mid > 1$, for which the magnitude response of the system is constant over all frequencies, is ___________.

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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11

GATE2020-EC: 55
Consider the following closed loop control system where $G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}$ and $C\left ( s \right )=K\dfrac{s+1}{s+3}$. If the steady state error for a unit ramp input is $0.1$, then the value of $K$ is ______________.

asked Feb 13 in Network Solution Methods by jothee (1.4k points)

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12

GATE2019 EC: 4
Consider the two-port resistive network shown in the figure. When an excitation of $5\: V$ is applied across Port $1$, and Port $2$ is shorted, the current through the short circuit at Port $2$ is measured to be $1\: A$ ... figure), what is the current through the short circuit at Port $1?$ $0.5\: A$ $1\: A$ $2\: A$ $2.5\: A$

asked Feb 12, 2019 in Network Solution Methods by Arjun (1.4k points)

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13

GATE2019 EC: 5
Let $Y(s)$ be the unit-step response of a causal system having a transfer function $G(s)= \dfrac{3-s}{(s+1)(s+3)}$ that is ,$Y(s)=\dfrac{G(s)}{s}.$ The forced response of the system is $u(t)-2e^{-t}u(t)+e^{-3t}u(t)$ $2u(t)-2e^{-t}u(t)+e^{-3t}u(t)$ $2u(t)$ $u(t)$

asked Feb 12, 2019 in Network Solution Methods by Arjun (1.4k points)

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14

GATE2019 EC: 30
In the circuit shown, if $v(t)=2 \sin(1000\: t)$ volts, $R=1\:k \Omega$ and $C=1\:\mu F,$ then the steady-state current $i(t)$, milliamperes (mA), is $\sin(1000\: t)+ \cos(1000\: t)$ $2 \sin(1000\: t) +2 \cos(1000\: t)$ $3 \sin(1000\: t) + \cos(1000\: t)$ $\sin(1000\: t) +3 \cos(1000\: t)$

asked Feb 12, 2019 in Network Solution Methods by Arjun (1.4k points)

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15

GATE2019 EC: 31
Consider a causal second-order system with the transfer function $G(s)=\dfrac{1}{1+2s+s^{2}}$ with a unit-step $R(s)=\dfrac{1}{s}$ as an input. Let $C(s)$ be the corresponding output. The time taken by the system output $c(t)$ to reach $94\%$ of its steady-state value $\underset{t\rightarrow \infty}{\lim}\:c(t),$ rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$

asked Feb 12, 2019 in Network Solution Methods by Arjun (1.4k points)

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16

GATE2019 EC: 32
The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\dfrac{Y(s)}{X(s)}$ is $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$

asked Feb 12, 2019 in Network Solution Methods by Arjun (1.4k points)

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17

GATE2019 EC: 42
Consider a unity feedback system, as in the figure shown, with an integral compensator $\dfrac{K}{s}$ and open-loop transfer function $G(s)=\dfrac{1}{s^{2}+3s+2}$ where $K>0.$ The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ axis is equal to ________ (rounded off to two decimal places).

asked Feb 12, 2019 in Network Solution Methods by Arjun (1.4k points)

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18

GATE2016-3-9
In the RLC circuit shown in the figure, the input voltage is given by $v_i(t) = 2\cos (200t) + 4\sin (500t).$ The output voltage $v_o(t)$ is $\cos (200t) + 2\sin (500t)$ $2\cos (200t) + 4\sin (500t)$ $\sin (200t) + 2\cos (500t)$ $2\sin (200t) + 4\cos (500t)$

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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19

GATE2016-3-13
The diodes $D1$ and $D2$ in the figure are ideal and the capacitors are identical. The product $RC$ is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage $V_o$(in volt) at the steady state is _______

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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20

GATE2016-3-32
Assume that the circuit in the figure has reached the steady state before time $t = 0$ when the $3\;\Omega$ resistor suddenly burns out, resulting in an open circuit. The current $i(t)$ (in ampere) at $t=0^+$ is _______

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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21

GATE2016-3-42
In the circuit shown in the figure, transistor $M1$ is in saturation and has transconductance $g_m = 0.01$ siemens. Ignoring internal parasitic capacitances and assuming the channel length modulation $\lambda$ to be zero,the small signal input pole frequency (in $kHz$) is _________

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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22

GATE2016-3-47
A second-order linear time-invariant system is described by the following state equations $\frac{d}{dt}x_1(t)+2x_1(t)=3u(t)$ $\frac{d}{dt}x_2(t)+x_2(t)=u(t)$ where $x_1(t)$ and $x_2(t)$ are the two state variables ... $c(t)=x_1(t)$, then the system is controllable but not observable observable but not controllable both controllable and observable neither controllable nor observable

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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23

GATE2016-3-48
The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $G(s)=\frac{K(s+2)}{s^2+2s+2}\;\text{and}\hspace{0.3cm}H(s)=1,$ respectively. If the variable parameter $K$ is real positive, then the location of the breakaway point on the root locus diagram of the system is _________

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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24

GATE2016-2-8
The figure shown an $RLC$ circuit with a sinusoidal current source. At resonance, the ratio $\mid I_{L} \mid / \mid I_{R} \mid$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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25

GATE2016-2-32
A continuous-time filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ is converted to a discrete-time filter with transfer function $G\left ( z\right )= \frac{2z^{2}-0.5032 \: z}{z^{2}-0.5032 \: z+k}$ so ... filter, sampled at $2$ $Hz$, is identical at the sampling instants to the impulse response of the discrete time-filter. The value of $k$ is _________

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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26

GATE2016-2-34
The switch $S$ in the circuit shown has been closed for a long time. It is opened at $t = 0$ and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop. The steady state magnitude of the capacitor voltage $V_{c}$ (in volts) is ______

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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27

GATE2016-1-4
Which one of the following is a property of the solutions to the Laplace equation: $\nabla^2f = 0$? The solutions have neither maxima nor minima anywhere except at the boundaries. The solutions are not separable in the coordinates. The solutions are not continuous. The solutions are not dependent on the boundary conditions.

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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28

GATE2016-1-9
Consider a two-port network with the transmission matrix: $T = \begin{pmatrix}A & B \\C & D\end{pmatrix}$. If the network is reciprocal, then $T^{-1} = T$ $T^2 = T$ Determinant $(T) = 0$ Determinant $(T) = 1$

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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29

GATE2016-1-23
The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal $s(t) = 5 \cos1600 \pi t + 20 \cos 1800 \pi t + 5 \cos 2000 \pi t$. The value of the modulation index is _________

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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30

GATE2016-1-30
The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is $F(S) = \frac{1}{1+e^{-sT/2}} \\$ $F(S) =\frac{1}{s(1+e^{-sT/2})} \\$ $F(S) = \frac{1}{s(1-e^{-sT})} \\$ $F(S) = \frac{1}{1-e^{-sT}}$

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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31

GATE2016-1-45
The open-loop transfer function of a unity-feedback control system is $G(s)= \frac{K}{s^2+5s+5}$. The value of $K$ at the breakaway point of the feedback contol system’s root-locus plot is _________

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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32

GATE2016-1-46
The open-loop transfer function of a unity feedback control system is given by $G(s)= \frac{K}{s(s+2)}$. For the peak overshoot of the closed-loop system to a unit step input to be $10 \%$, the value of $K$ is _________

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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33

GATE2016-1-47
The transfer function of a linear time invariant system is given by $H(s) = 2s^4 – 5s^3 + 5s -2$. The number of zeroes in the right half of the $s$-plane is _________

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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34

GATE2015-3-6
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $a-b$ is _______.

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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35

GATE2015-3-14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit is a modulo-$5$ binary up counter a modulo-$6$ binary down counter a modulo-$5$ binary down counter a modulo-$6$ binary up counter

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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36

GATE2015-3-21
The transfer function of a first-order controller is given as $G_{C}(s) = \dfrac{K(s+a)}{s+b}$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this controller to act as a phase lead compensator is $a<b$ $a>b$ $K<ab$ $K>ab$

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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37

GATE2015-3-31
The $ABCD$ parameters of the following $2$-port network are $\begin{bmatrix}3.5 + j2 & 20.5 \\ 20.5 & 3.5-j2 \end{bmatrix} \\$ $\begin{bmatrix}3.5 +j2 & 30.5 \\ 0.5&3.5-j2 \end{bmatrix} \\$ $\begin{bmatrix}10 &2+j0 \\2+j0 &10 \end{bmatrix} \\$ $\begin{bmatrix}7+j4 &0.5 \\ 30.5&7-j4 \end{bmatrix} $

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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38

GATE2015-3-32
A network is described by the state model as $\dot{x_{1}}=2x_{1}-x_{2}+3u \\ \dot{x_{2}}=-4x_{2}-u \\ y=3x_{1}-2x_{2}$ The transfer function $H(s)\left(=\dfrac{Y(s)}{U(s)}\right)$ is $\dfrac{11s+35}{(s-2)(s+4)} \\$ $\dfrac{11s-35}{(s-2)(s+4)} \\$ $\dfrac{11s+38}{(s-2)(s+4)} \\$ $\dfrac{11s-38}{(s-2)(s+4)}$

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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39

GATE2015-3-46
The position control of a DC servo-motor is given in the figure. The values of the parameters are $K_{T}=1 \: N-m/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kg-m^{2},B=1N-m/(rad/sec)$ and $K_{b} = 1V/(rad/sec) .$ The steady-state position response (in radians) due to unit impulse disturbance torque $T_{d}$ is _______.

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)

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40

GATE2015-2-1
The bilateral Laplace transform of a function $f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases}$ is $\dfrac{a-b}{s} \\$ $\dfrac{e^{s}(a-b)}{s} \\$ $\dfrac{e^{-as}-e^{-bs}}{s} \\$ $\dfrac{e^{s(a-b)}}{s}$

asked Mar 28, 2018 in Network Solution Methods by Milicevic3306 (15.8k points)