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381

GATE Electrical 2018 | Question: 22
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _________ (up to $2$ decimal places).

A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ non-zero elements. The minimum number of branches (transmission lines and transformers)...

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382

GATE Electrical 2018 | Question: 31
A DC voltage source is connected to a series $L-C$ circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the following circular loci represents the plot of $i(t)$ versus $v(t)$?

A DC voltage source is connected to a series $L-C$ circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the fo...

Arjun

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383

GATE Electrical 2018 | Question: 30
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, $P=1.4 \sin \delta + 0.15 \sin 2 \delta$, where $\delta$ is the load angle. Newton-Raphson method is used to calculate the value of $\delta$ ... at the end of the first iteration is $15^{\circ}$ $28.28^{\circ}$ $28.74^{\circ}$ $31.20^{\circ}$

The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, $P=1.4 \sin \delta + 0.15 \sin 2 \delta$, where $...

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384

GATE Electrical 2018 | Question: 47
A three-phase load is connected to a three-phase balanced supply as shown in the figure. If $V_{\text{an}} = 100 \angle 0^{\circ} \: V$, $V_{\text{bn}}=100 \angle - 120 ^{\circ} \: V$ ... in the anti-clockwise direction), the value of $R$ for zero current in the neutral wire is __________ $\Omega$ (up to $2$ decimal places).

A three-phase load is connected to a three-phase balanced supply as shown in the figure. If $V_{\text{an}} = 100 \angle 0^{\circ} \: V$, $V_{\text{bn}}=100 \angle – 120...

Arjun

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385

GATE Electrical 2018 | Question: 3
A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current? $v_o \geq 0$ & $i_o<0$ $v_o < 0$ & $i_o <0$ $v_o \geq 0$ & $i_o \geq 0$ $v_0 < 0$ & $i_o\geq 0$

A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the foll...

Arjun

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386

GATE Electrical 2018 | Question: 10
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85 \times 10^{-12}$ F/m. The $Z$ component of the E field at $(0,0,0.1)$ is closest to $899.18$ V/m $-899.18$ V/m $999.09$ V/m $-999.09$ V/m

A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85...

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387

GATE Electrical 2018 | Question: 49
A phase controlled single phase rectifier, supplied by an AC source, feeds power to an $R-L-E$ load as shown in the figure. The rectifier output voltage has an average value given by $V_{\text{o}}= \frac{V_m}{2 \pi} (3+\cos \alpha)$, ... . If the power delivered to the lossless battery is $1600$ W, $\alpha$ in degree is ___________ (up to $2$ decimal places).

A phase controlled single phase rectifier, supplied by an AC source, feeds power to an $R-L-E$ load as shown in the figure. The rectifier output voltage has an average va...

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388

GATE Electrical 2018 | Question: 15
The op-amp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by $Z \frac{R_1}{R_2}$ $ – Z \frac{R_2}{R_1}$ $Z$ $ – Z \frac{R_1}{R_1 + R_2}$

The op-amp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by$Z \frac{R_1}{R_2}$$ – Z \frac{R_2}{R_1}$$Z$$ – Z \frac{...

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389

GATE Electrical 2018 | Question: 16
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is $k \: x(t)$, where $k$ is an eigenvalue $k \: e^{j \omega t} \: x(t)$, where $k$ is an eigenvalue and $e^{j \omega t}$ is a complex ... $k \: H(\omega)$, where $k$ is an eigenvalue and $H(\omega)$ is a frequency response of the system

A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is$k \: x(t)$, where $k$ is an eigenvalue$k \: e^{j \omega t} \: x(t)$, where $k...

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390

GATE Electrical 2018 | Question: 8
In the figure, the voltages are $v_1(t)=100 \cos (\omega t)$, $v_2(t)=100 \cos (\omega t + \pi /18)$ and $v_3(t)=100 \cos (\omega t + \pi / 36)$. The circuit is in sinusoidal steady state, and $R< < \omega L$. $P_1$, $P_2$ and $P_3$ are the ... $P_1 <0$, $P_2>0$, $P_3>0$ $P_1 <0$, $P_2>0$, $P_3<0$ $P_1 > 0$, $P_2<0$, $P_3>0$

In the figure, the voltages are $v_1(t)=100 \cos (\omega t)$, $v_2(t)=100 \cos (\omega t + \pi /18)$ and $v_3(t)=100 \cos (\omega t + \pi / 36)$. The circuit is in sinuso...

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391

GATE Electrical 2018 | Question: 5
Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is $0.532$ $0.632$ $0.707$ $0.866$

Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of t...

Arjun

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392

GATE Electrical 2018 | Question: 9
Match the transfer functions of the second-order systems with the nature of the systems given below. ... P-I, Q-II, R-III P-II, Q-I, R-III P-III, Q-II, R-I P-III, Q-I, R-II

Match the transfer functions of the second-order systems with the nature of the systems given below.$\begin{array} {} \underline{\textit{Transfer functions}} & \underline...

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393

GATE Electrical 2017 Set 2 | Question: 1
An urn contains $5$ red balls and $5$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a Red ball in the second draw is $\frac{1}{2} \\$ $\frac{4}{9} \\$ $\frac{5}{9} \\$ $\frac{6}{9} $

An urn contains $5$ red balls and $5$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a Red...

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394

GATE Electrical 2017 Set 2 | Question: 40
A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $3$ tosses. Let the random variable $Y$ denote the number of heads. The value of $\text{var} \{Y\}$, where $\text{var} \{ \cdot \}$ denotes the variance, equals $\frac{7}{8} \\$ $\frac{49}{64} \\$ $\frac{7}{64} \\$ $\frac{105}{64}$

A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $3$ tosses. Let the random variable $Y$ denote the number of heads. The value o...

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395

GATE Electrical 2017 Set 2 | Question: 14
A $3$-phase, $4$-pole, $400$V, $50$Hz squirrel-cage induction motor is operating at a slip of $0.02$. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to $1500$ $1470$ $157$ $154$

A $3$-phase, $4$-pole, $400$V, $50$Hz squirrel-cage induction motor is operating at a slip of $0.02$. The speed of the rotor flux in mechanical rad/sec, sensed by a stati...

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396

GATE Electrical 2017 Set 2 | Question: 55
A thin soap bubble of radius $R=1$ cm, and thickness $a=3.3 \mu m (a << R)$, is at a potential of $1$ V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop ... resulting single spherical drop with respect to the same reference point at infinity is _________. (Give the answer up to two decimal places.)

A thin soap bubble of radius $R=1$ cm, and thickness $a=3.3 \mu m (a << R)$, is at a potential of $1$ V with respect to a reference point at infinity. The bubble bursts a...

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397

GATE Electrical 2017 Set 2 | Question: 47
A $10 \frac{1}{2}$ digit timer counter possesses a base clock of frequency $100$ MHz. When measuring a particular input, the reading obtained is the same in: Frequency mode of operation with a gating time of one second and Period mode of operation (in the $\times 10$ns scale). The frequency of the unknown input (reading obtained) in Hz is _______.

A $10 \frac{1}{2}$ digit timer counter possesses a base clock of frequency $100$ MHz. When measuring a particular input, the reading obtained is the same in:Frequency mod...

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398

GATE Electrical 2017 Set 2 | Question: 24
The nominal- $\pi$ circuit of a transmission line is shown in the figure. Impedance $Z=100 \angle 80^{\circ} \Omega$ and reactance $X=3300 \Omega$. The magnitude of the characteristic impedance of the transmission line, in $\Omega$, is __________. (Give the answer up to one decimal place.)

The nominal- $\pi$ circuit of a transmission line is shown in the figure.Impedance $Z=100 \angle 80^{\circ} \Omega$ and reactance $X=3300 \Omega$. The magnitude of the ch...

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399

GATE Electrical 2017 Set 2 | Question: 23
The mean square value of the given periodic waveform $f(t)$ is __________.

The mean square value of the given periodic waveform $f(t)$ is __________.

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400

GATE Electrical 2017 Set 1 | Question: 4
A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will Bend closer to the cylinder axis Bend farther away from the axis Remain uniform as before Cease to exist inside the cylinder

A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic fiel...

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Arjun asked Feb 26, 2017