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GATE2020EC: 9
In the circuit shown below, the Thevenin voltage $V_{TH}$is $2.4\:V$ $2.8\:V$ $3.6\:V$ $4.5\:V$
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GATE2020EC: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steadystate output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
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GATE2020EC: 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 ___________.
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GATE2020EC: 30
For the given circuit, which one of the following is correct state equation? ...
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5
GATE2020EC: 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 $\dfrac{1}{\sqrt{10}}\cos\left ( 3t1.892 \right )$. The value of $a$ is _______.
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6
GATE2020EC: 53
The transfer function of a stable discretetime $\text{LTI}$ 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 ___________.
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7
GATE2020EC: 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 ______________.
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8
GATE2019 EC: 5
Let $Y(s)$ be the unitstep response of a causal system having a transfer function $G(s)= \dfrac{3s}{(s+1)(s+3)}$ that is ,$Y(s)=\dfrac{G(s)}{s}.$ The forced response of the system is $u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)$ $u(t)$
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Feb 12, 2019
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gate2019ec
networksolutionmethods
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9
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 steadystate current $i(t)$, milliamperes (mA), is $\sin(1000\: t)+ \cos(1000\: t)$ $2 \sin(1000\: t) +2 \cos(1000\: t)$ $3 \sin(1000\: t) + \cos(1000\: t)$ $\sin(1000\: t) +3 \cos(1000\: t)$
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10
GATE2019 EC: 31
Consider a causal secondorder system with the transfer function $G(s)=\dfrac{1}{1+2s+s^{2}}$ with a unitstep $R(s)=\dfrac{1}{s}$ as an input. Let $C(s)$ be the corresponding output. The time taken by the system output $c(t)$ to reach $94\%$ of its steadystate value $\underset{t\rightarrow \infty}{\lim}\:c(t),$ rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$
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11
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 $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$
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12
GATE201639
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 $\cos (200t) + 2\sin (500t)$ $2\cos (200t) + 4\sin (500t)$ $\sin (200t) + 2\cos (500t)$ $2\sin (200t) + 4\cos (500t)$
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Mar 28, 2018
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gate2016ec3
networksolutionmethods
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13
GATE2016313
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 _______
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0
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14
GATE2016320
For the unity feedback control system shown in the figure, the openloop transfer function $G(s)$ is given as $G(s) = \frac{2}{s(s+1)}$ The steady state error $e_{ss}$ due to a unit step input is $0$ $0.5$ $1.0$ $\infty$
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gate2016ec3
controlsystems
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15
GATE2016332
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 _______
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gate2016ec3
numericalanswers
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16
GATE2016347
A secondorder linear timeinvariant 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
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17
GATE2016348
The forwardpath transfer function and the feedbackpath 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 _________
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18
GATE201628
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 ________
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19
GATE2016232
A continuoustime filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ is converted to a discretetime 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 timefilter. The value of $k$ is _________
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20
GATE2016234
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 ______
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21
GATE201614
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.
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gate2016ec1
networksolutionmethods
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laplaceequation
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22
GATE2016123
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 _________
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23
GATE2016130
The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is $F(S) = \frac{1}{1+e^{sT/2}} \\$ $F(S) =\frac{1}{s(1+e^{sT/2})} \\$ $F(S) = \frac{1}{s(1e^{sT})} \\$ $F(S) = \frac{1}{1e^{sT}}$
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gate2016ec1
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24
GATE2016145
The openloop transfer function of a unityfeedback 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 rootlocus plot is _________
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25
GATE2016146
The openloop transfer function of a unity feedback control system is given by $G(s)= \frac{K}{s(s+2)}$. For the peak overshoot of the closedloop system to a unit step input to be $10 \%$, the value of $K$ is _________
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26
GATE2016147
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 _________
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27
GATE201536
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $ab$ is _______.
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gate2015ec3
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thevenintheorem
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28
GATE2015314
The circuit shown consists of JK flipflops, 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
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29
GATE2015321
The transfer function of a firstorder 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 $a<b$ $a>b$ $K<ab$ $K>ab$
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30
GATE2015346
The position control of a DC servomotor is given in the figure. The values of the parameters are $K_{T}=1 \: Nm/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kgm^{2},B=1Nm/(rad/sec)$ and $K_{b} = 1V/(rad/sec) .$ The steadystate position response (in radians) due to unit impulse disturbance torque $T_{d}$ is _______.
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31
GATE201521
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 $\dfrac{ab}{s} \\$ $\dfrac{e^{s}(ab)}{s} \\$ $\dfrac{e^{as}e^{bs}}{s} \\$ $\dfrac{e^{s(ab)}}{s}$
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networksolutionmethods
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32
GATE201527
In the circuit shown, the average value of the voltage $V_{ab}$ (in Volts) in steady state condition is ________.
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33
GATE2015217
Let the signal ݂$f(t) = 0$ outside the interval $[T_{1},T_{2}]$, where ܶ$T_{1}$ and ܶ$T_{2}$ are finite. Furthermore, $\mid f(t) \mid < \infty$. The region of convergence (RoC) of the signal's bilateral Laplace transform $F(s)$ is a parallel ... the ݆$j\Omega$ axis a parallel strip not containing the ݆$j\Omega$ axis the entire $s$ plane a half plane containing the ݆$j\Omega$ axis
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gate2015ec2
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laplacetransform
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34
GATE2015219
By performing cascading and/or summing/differencing operations using transfer function blocks $G_{1}(s )$ and $G_{2}(s),$ one CANNOT realize a transfer function of the form $G_{1}(s)G_{2}(s) \\$ $\dfrac{G_{1}(s)}{G_{2}(s)} \\$ $G_{1}(s)\left(\dfrac{1}{G_{1}(s)} + G_{2}(s)\right) \\$ $G_{1}(s)\left(\dfrac{1}{G_{1}(s)}  G_{2}(s)\right)$
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gate2015ec2
networksolutionmethods
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35
GATE2015221
A unity negative feedback system has an openloop transfer function $G(S) = \dfrac{K}{s(s+10)}$. The gain $K$ for the system to have a damping ratio of $0.25$ is ________.
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36
GATE2015222
A sinusoidal signal of amplitude $A$ is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is $31.8\: dB,$ the number of levels in the quantizer is __________.
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sinusoidalsignal
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37
GATE2015231
In the circuit shown, the Norton equivalent resistance $(\text{in}\: \Omega)$ across terminals $ab$ is _______.
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norton's
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38
GATE2015232
In the circuit shown, the initial voltages across the capacitors $C_{1}$ and $C_{2}$ are $1\: V$ and $3\: V,$ respectively. The switch is closed at time $t = 0$. The total energy dissipated (in Joules) in the resistor $R$ until steady state is reached, is __________.
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39
GATE2015245
Let $x(t) = \alpha s(t) + s(t)$ with $s(t) = \beta e^{4t}u(t),$ where $u(t)$ is unit step function. If the bilateral Laplace transform of $x(t)$ is $X(s) = \dfrac{16}{s^{2} – 16}\:\: 4 < Re\{s\}<4;$ then the value of $\beta$ is ______.
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gate2015ec2
numericalanswers
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0
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40
GATE2015247
The output of a standard secondorder system for a unit step input is given as $y(t) = 1\dfrac{2}{\sqrt{3}}e^{t}\cos \left(\sqrt{3t}\dfrac{\pi}{6}\right)$. The transfer function of the system is $\dfrac{2}{(s+2)(s+\sqrt{3})}$ $\dfrac{1}{s^{2}+2s+1}$ $\dfrac{3}{s^{2}+2s+3}$ $\dfrac{3}{s^{2}+2s+4}$
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