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GATE Electrical 2017 Set 1 | Question: 43
In the circuit shown below, the maximum power transferred to the resistor $R$ is ______ W.

In the circuit shown below, the maximum power transferred to the resistor $R$ is ______ W.

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642

GATE Electrical 2017 Set 1 | Question: 50
For a system having transfer function $G(s)=\frac{-s+1}{s+1}$, a unit step input is applied at time $t=0$. The value of the response of the system at $t=1.5 sec$ (rounded off to three decimal places) is ________.

For a system having transfer function $G(s)=\frac{-s+1}{s+1}$, a unit step input is applied at time $t=0$. The value of the response of the system at $t=1.5 sec$ (rounded...

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643

GATE Electrical 2017 Set 1 | Question: 13
The Boolean expression $AB+A\bar{C}+BC$ simplifies to $BC + A\bar{C}$ $AB + A\bar{C} + B$ $AB + A\bar{C}$ $AB + BC$

The Boolean expression $AB+A\bar{C}+BC$ simplifies to$BC + A\bar{C}$$AB + A\bar{C} + B$$AB + A\bar{C}$$AB + BC$

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GATE Electrical 2017 Set 1 | Question: 30
Let a causal LTI system be characterised by the following differential equation, with initial rest condition $\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(t)}{dt}$ where, $x(t)$ and $y(t)$ are the input and output respectively. The impulse response of the system ... $7e^{-2t}u(t)-2e^{-5t}u(t)$ $-7e^{-2t}u(t)+2e^{-5t}u(t)$

Let a causal LTI system be characterised by the following differential equation, with initial rest condition$\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(...

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645

GATE Electrical 2017 Set 1 | Question: 48
A three-phase, three winding $\Delta / \Delta / Y (1.1kV/6.6kV/400V)$ transformer is energized from $AC$ mains at the $1.1kV$ side. It supplies $900kVA$ load at $0.8$ power factor lag from the $6.6kV$ winding and $300kVA$ load ... $1.1kV$ winding from the mains is ________. (Give the answer up to one decimal place.)

A three-phase, three winding $\Delta / \Delta / Y (1.1kV/6.6kV/400V)$ transformer is energized from $AC$ mains at the $1.1kV$ side. It supplies $900kVA$ load at $0.8$ pow...

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646

GATE Electrical 2017 Set 2 | Question: 35
The range of $K$ for which all the roots of the equation $s^{3}+3s^{2}+2s+K=0$ are in the left half of the complex $s$-plane is $0 < K < 6$ $0 < K < 16$ $6 < K < 36$ $6 < K < 16$

The range of $K$ for which all the roots of the equation $s^{3}+3s^{2}+2s+K=0$ are in the left half of the complex $s$-plane is$0 < K < 6$$0 < K < 16$$6 < K < 36$$6 < K <...

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647

GATE Electrical 2017 Set 2 | Question: 8
Two resistors with nominal resistance values $R_{1}$ and $R_{2}$ have additive uncertainties $\bigtriangleup R_{1}$ and $\bigtriangleup R_{2}$, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent ...

Two resistors with nominal resistance values $R_{1}$ and $R_{2}$ have additive uncertainties $\bigtriangleup R_{1}$ and $\bigtriangleup R_{2}$, respectively. When these r...

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648

GATE Electrical 2017 Set 1 | Question: 19
The equivalent resistance between the terminals $A$ and $B$ is __________ $\Omega$.

The equivalent resistance between the terminals $A$ and $B$ is __________ $\Omega$.

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649

GATE Electrical 2017 Set 1 | Question: 2
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is $-2i$ $-i$ $i$ $2i$

For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is$-2i$$-i$$i$$2i$

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650

GATE Electrical 2017 Set 2 | Question: 11
A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive $DC$ load. The converter is fed from a $230$ V, $50$ Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the $DC$ side is $25$ $50$ $100$ $300$

A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive $DC$ load. The converter is fed from a $230$ V, $50$ Hz, AC source. The fundamenta...

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651

GATE Electrical 2017 Set 2 | Question: 32
A cascade system having the impulse responses $h_{1}(n)= \{ \underset{\uparrow}{1}-1 \}$ and $h_{2}(n)= \{ \underset{\uparrow}{1}-1, 1 \}$ is shown in the figure below, where symbol $\uparrow$ denotes the time origin. The input sequence $x(n)$ for which the ... $x(n)= \{\underset{\uparrow}{1}-1, 2, 2, 1 \}$

A cascade system having the impulse responses $h_{1}(n)= \{ \underset{\uparrow}{1}-1 \}$ and $h_{2}(n)= \{ \underset{\uparrow}{1}-1, 1 \}$ is shown in the figure below, ...

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652

GATE Electrical 2017 Set 2 | Question: 9
A stationary closed Lissajous pattern on an oscilloscope has $3$ horizontal tangencies and $2$ vertical tangencies for a horizontal input with frequency $3$kHz. The frequency of the vertical input is $1.5$kHz $2$kHz $3$kHz $4.5$kHz

A stationary closed Lissajous pattern on an oscilloscope has $3$ horizontal tangencies and $2$ vertical tangencies for a horizontal input with frequency $3$kHz. The frequ...

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653

GATE Electrical 2017 Set 2 | Question: 34
The root locus of the feedback control system having the characteristic equation $s^{2}+6Ks+2s+5=0$ where $K>0$, enters into the real axis at. $s=-1$ $s=-\sqrt{5}$ $s=-5$ $s=\sqrt{5}$

The root locus of the feedback control system having the characteristic equation $s^{2}+6Ks+2s+5=0$ where $K>0$, enters into the real axis at.$s=-1$$s=-\sqrt{5}$$s=-5$$s=...

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654

GATE Electrical 2017 Set 1 | Question: 52
The circuit shown in the figure uses matched transistors with a thermal voltage $V_{T}=25$m V. The base currents of the transistors are negligible. The value of the resistance $R$ in $k\Omega$ that is required to provide $1 \mu A$ bias current for the differential amplifier block shown is ________.(Give the answer up to one decimal place.)

The circuit shown in the figure uses matched transistors with a thermal voltage $V_{T}=25$m V. The base currents of the transistors are negligible. The value of the resis...

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655

GATE Electrical 2017 Set 2 | Question: 29
For the balanced $Y-Y$ connected $3$-phase circuit shown in the figure below, the line-line voltage is $208$ V rms and the total power absorbed by the load is $432$ W at a power factor of $0.6$ leading. The approximate value of the impedance $Z$ ... $60 \angle 53.1^{\circ}\Omega $ $60 \angle -53.1^{\circ}\Omega $ $180 \angle -53.1^{\circ}\Omega $

For the balanced $Y-Y$ connected $3$-phase circuit shown in the figure below, the line-line voltage is $208$ V rms and the total power absorbed by the load is $432$ W at ...

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656

GATE Electrical 2017 Set 1 | Question: 35
The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

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657

GATE Electrical 2017 Set 1 | Question: 54
The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are $0.2$pu, $0.2$pu, and $0.1$pu, respectively. The generator is an open circuit with a terminal voltage of $1$pu. The minimum value of ... fault occurs at the terminals is ___________ (assume fault impedance to be zero). (Give the answer up to one decimal place.)

The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are $0.2$pu, $0.2$pu, and $0.1$pu, respectively. The generator is an open ci...

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658

GATE Electrical 2017 Set 1 | Question: 32
In the system whose signal flow graph is shown in the figure, $U_{1}(s)$ and $U_{2}(s)$ are inputs. The transfer function $\frac{Y(s)}{U_{1}(s)}$ is $\frac{k_{1}}{J Ls^{2}+J Rs+k_{1}k_{2}}$ $\frac{k_{1}}{J Ls^{2}-J Rs-k_{1}k_{2}}$ ... $\frac{k_{1}-U_{2}(sL-R)}{J Ls^{2}-(J R+U_{2}L)s-k_{1}k_{2}+U_{2}R}$

In the system whose signal flow graph is shown in the figure, $U_{1}(s)$ and $U_{2}(s)$ are inputs. The transfer function $\frac{Y(s)}{U_{1}(s)}$ is$\frac{k_{1}}{J Ls^{2}...

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659

GATE Electrical 2017 Set 1 | Question: 33
The transfer function of the system $Y(s)/U(s)$ ... $\frac{(s-4)}{(s^{2}+s-4)} \\ $ $\frac{(s+4)}{(s^{2}-s-4)} \\$

The transfer function of the system $Y(s)/U(s)$ whose state-space equations are given below is:$\begin{bmatrix} \dot{x}_{1}(t)\\ \dot{x}_{2}(t) \end{bmatrix}=\begin{bma...

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660

GATE Electrical 2017 Set 1 | Question: 5
Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At $t=0$, the particles are released ... these will collide first? The particles will never collide. All will collide together. Proton and neutron. Electron and neutron.

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the ele...

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661

GATE Electrical 2017 Set 1 | Question: 6
The transfer function of a system is given by, $\frac{V_{0}(s)}{V_{i}(s)}=\frac{1-s}{1+s}$ Let the output of the system be $v_{0}(t)=V_{m} \sin (\omega t + \varphi )$ for the input, $v_{i}(t)=V_{m} \sin (\omega t )$. Then the minimum and maximum values of ... $\frac{\pi}{2}$ $\frac{-\pi}{2}$ and $0$ $0$ and $\frac{\pi}{2}$ $-\pi$ and $0$

The transfer function of a system is given by,$\frac{V_{0}(s)}{V_{i}(s)}=\frac{1-s}{1+s}$Let the output of the system be $v_{0}(t)=V_{m} \sin (\omega t + \varphi )$ for t...

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662

GATE Electrical 2017 Set 2 | Question: 33
A $220$ V, $10$ kW, $900$ rpm separately excited $DC$ motor has an armature resistance $R_{a}=0.02 \Omega$. When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is $70$Nm. Neglecting the ... the current drawn by the motor from the $220$V supply is $34.2$ A $30$ A $22$ A $4.84$ A

A $220$ V, $10$ kW, $900$ rpm separately excited $DC$ motor has an armature resistance $R_{a}=0.02 \Omega$. When the motor operates at rated speed and with rated terminal...

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663

GATE Electrical 2017 Set 2 | Question: 7
The transfer function $C(s)$ of a compensator is given below. $C(s)=\frac{(1+\frac{s}{0.1})(1+\frac{s}{100})}{(1+s)(1+\frac{s}{10})}$ The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is $0.1 < \omega < 1$ $1 < \omega < 10$ $10 < \omega < 100$ $ \omega > 100$

The transfer function $C(s)$ of a compensator is given below.$C(s)=\frac{(1+\frac{s}{0.1})(1+\frac{s}{100})}{(1+s)(1+\frac{s}{10})}$The frequency range in which the phase...

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664

GATE Electrical 2017 Set 1 | Question: 11
A closed loop system has the characteristic equation given by $s^{3}+Ks^{2}+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be satisfied? $0 < K < 0.5$ $0.5 < K < 1$ $0 < K < 1$ $K > 1$

A closed loop system has the characteristic equation given by $s^{3}+Ks^{2}+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be sat...

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665

GATE Electrical 2017 Set 1 | Question: 3
Let $z(t) = x(t) *y(t)$, where "*" denotes convolution. Let $c$ be a positive real-valued constant. Choose the correct expression for $z(ct)$. $c . x(ct) * y (ct)$ $x (ct) * y (ct)$ $c . x (t) * y(ct)$ $c . x (ct) * y(t)$

Let $z(t) = x(t) *y(t)$, where "*" denotes convolution. Let $c$ be a positive real-valued constant. Choose the correct expression for $z(ct)$.$c . x(ct) * y (ct)$$x (ct) ...

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666

GATE Electrical 2017 Set 2 | Question: 17
Assume that in traffic junction, the cycle of the traffic signal lights is $2$ minutes of green (Vehicle does not stop) and $3$ minutes of red (Vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over $5$ minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ________.

Assume that in traffic junction, the cycle of the traffic signal lights is $2$ minutes of green (Vehicle does not stop) and $3$ minutes of red (Vehicle stops). Consider t...

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667

GATE Electrical 2017 Set 1 | Question: 25
A $3$-phase voltage source inverter is supplied from a $600V$ DC source as shown in the figure below. For a star connected resistive load of $20\Omega$ per phase, the load power for $120^{\circ}$ device conduction, in kW, is ________.

A $3$-phase voltage source inverter is supplied from a $600V$ DC source as shown in the figure below. For a star connected resistive load of $20\Omega$ per phase, the loa...

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668

GATE Electrical 2017 Set 1 | Question: 29
The passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port $1$. Given $V_{1}=A_{1}V_{2}+B_{1}I_{2}$ $I_{1}=C_{1}V_{2}+D_{1}I_{2}$ $V_{2}=A_{2}V_{3}+B_{2}I_{3}$ $I_{2}=C_{2}V_{3}+D_{2}I_{3}$ ...

The passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port $1$.Given$V_{1}=A_{1}V_{2}+B_{1}I_{2}$$I_{1}=C_{1}V_{2}+D...

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669

GATE Electrical 2017 Set 1 | Question: 39
A load is supplied by a $230$ V, $50$ Hz source. The active power $P$ and the reactive power $Q$ consumed by the load are such that $1kW \leq P \leq 2kW$ and $1kVAR \leq Q \leq 2kVAR$. A capacitor connected across the load for power factor ... power factor after power factor correction is $0.447 \text{ lag}$ $0.707 \text{ lag}$ $0.894 \text{ lag}$ $1$

A load is supplied by a $230$ V, $50$ Hz source. The active power $P$ and the reactive power $Q$ consumed by the load are such that $1kW \leq P \leq 2kW$ and $1kVAR \leq ...

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670

GATE Electrical 2017 Set 2 | Question: 13
A three-phase voltage source inverter with ideal devices operating in $180^{\circ}$ conduction mode is feeding a balanced star-connected resistive load. The $DC$ voltage input is $V_{dc}$. The peak of the fundamental component of the phase voltage is $\frac{V_{dc}}{\pi} \\$ $\frac{2V_{dc}}{\pi} \\$ $\frac{3V_{dc}}{\pi} \\$ $\frac{4V_{dc}}{\pi} $

A three-phase voltage source inverter with ideal devices operating in $180^{\circ}$ conduction mode is feeding a balanced star-connected resistive load. The $DC$ voltage ...

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671

GATE Electrical 2017 Set 1 | Question: 21
A $10$-bus power system consists of four generator buses indexed as $G1, G2, G3, G4$ and six load buses indexed as $L1, L2, L3, L4, L5, L6$. The generator-bus $G1$ is considered as slack bus, and the load buses ... limit. The number of non-linear equations required for solving the load flow problem using Newton - Raphson method in polar form is ___________.

A $10$-bus power system consists of four generator buses indexed as $G1, G2, G3, G4$ and six load buses indexed as $L1, L2, L3, L4, L5, L6$. The generator-bus $G1$ is con...

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672

GATE Electrical 2017 Set 1 | Question: 38
The input voltage $V_{DC}$ of the buck-boost converter shown below varies from $32$V to $72$V. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio $D$ of the converter for which the magnitude of the ... $0 \leq D \leq 1$ $\frac{1}{3}\leq D \leq \frac{2}{3}$

The input voltage $V_{DC}$ of the buck-boost converter shown below varies from $32$V to $72$V. Assume that all components are ideal, inductor current is continuous, and o...

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673

GATE Electrical 2017 Set 1 | Question: 10
A $3$-bus power system is shown in the figure below, where the diagonal elements of $Y$-bus matrix are: $Y_{11}= -j12$ pu, $Y_{22}= -j15$ pu, $\text{and}$ $Y_{33} = -j7$ pu. The per unit values of the line reactances $p, q$ and $r$ shown in the figure are $p= -0.2, q= -0.1, r= -0.5$ $p= 0.2, q= 0.1, r= 0.5$ $p= -5, q= -10, r= -2$ $p= 5, q= 10, r= 2$

A $3$-bus power system is shown in the figure below, where the diagonal elements of $Y$-bus matrix are: $Y_{11}= -j12$ pu, $Y_{22}= -j15$ pu, $\text{and}$ $Y_{33} = -j7$ ...

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674

GATE Electrical 2017 Set 1 | Question: 7
Consider the system with following input-output relation $y[n]=(1+(-1)^{n}x[n]$ where, $x[n]$ is the input and $y[n]$ is the output. The system is Invertible and time invariant Invertible and time varying Non-invertible and time invariant Non-invertible and time varying

Consider the system with following input-output relation$y[n]=(1+(-1)^{n}x[n]$where, $x[n]$ is the input and $y[n]$ is the output. The system isInvertible and time invari...

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675

GATE Electrical 2017 Set 1 | Question: 16
Consider $g(t)= \begin{cases} t-\lfloor t \rfloor, & t \geq 0 \\ t-\lceil t \rceil, & \text{otherwise } \end{cases}$, where $t \in \mathbb{R}$. Here, $\lfloor t \rfloor$ represents the largest integer ... integer greater than or equal to $t$. The coefficient of the second harmonic component of the Fourier series representing $g(t)$ is __________.

Consider $g(t)= \begin{cases} t-\lfloor t \rfloor, & t \geq 0 \\ t-\lceil t \rceil, & \text{otherwise }\end{cases}$, where $t \in \mathbb{R}$.Here, $\lfloor t \rfloor$ r...

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676

GATE Electrical 2017 Set 1 | Question: 23
The following measurements are obtained on a single phase load $V=220 V \pm 1$%, $I=5.0 A \pm 1$% and $W=555 W \pm 2$%. If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is _______. (Give answer up to one decimal place.)

The following measurements are obtained on a single phase load $V=220 V \pm 1$%, $I=5.0 A \pm 1$% and $W=555 W \pm 2$%. If the power factor is calculated using these meas...

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677

GATE Electrical 2017 Set 1 | Question: 14
For the circuit shown in the figure below, assume that diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal. The $DC$ components of voltages $v_{1}$ and $v_{2}$, respectively are $0$V and $1$V $-0.5$V and $0.5$V $1$V and $0.5$V $1$V and $1$V

For the circuit shown in the figure below, assume that diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal. The $DC$ components of voltages $v_{1}$ and $v_{2}$, respectively are$...

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678

GATE Electrical 2017 Set 1 | Question: 15
For the power semiconductor devices $IGBT, MOSFET$, Diode and Thyristor, which one of the following statements is TRUE? All the four are majority carrier devices. All the four are minority carrier devices. $IGBT$ and $MOSFET$ ... minority carrier devices. $MOSFET$ is majority carrier device, whereas $IGBT$, Diode, Thyristor are minority carrier devices.

For the power semiconductor devices $IGBT, MOSFET$, Diode and Thyristor, which one of the following statements is TRUE?All the four are majority carrier devices.All the f...

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679

GATE Electrical 2017 Set 1 | Question: 40
The bus admittance matrix for a power system network is $\begin{bmatrix} -j39.9 & j20 & j20\\ j20 & -j39.9 & j20 \\ j20 & j20 & -j39.9 \end{bmatrix} pu.$ There is a transmission line, connected between buses $1$ and $3$, ...

The bus admittance matrix for a power system network is$\begin{bmatrix}-j39.9 & j20 & j20\\ j20 & -j39.9 & j20 \\ j20 & j20 & -j39.9\end{bmatrix} pu.$There is a transmi...

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680

GATE Electrical 2017 Set 1 | Question: 8
A $4$ pole induction machine is working as an induction generator. The generator supply frequency is $60$Hz. The rotor current frequency is $5$Hz. The mechanical speed of the rotor in $RPM$ is $1350$ $1650$ $1950$ $2250$

A $4$ pole induction machine is working as an induction generator. The generator supply frequency is $60$Hz. The rotor current frequency is $5$Hz. The mechanical speed of...

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