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381

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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382

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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Arjun asked Feb 19, 2018

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383

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...

Arjun

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Arjun asked Feb 19, 2018

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384

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...

Arjun

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Arjun asked Feb 26, 2017

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385

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...

Arjun

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386

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...

Arjun

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387

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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388

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...

Arjun

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389

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...

Arjun

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390

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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391

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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392

GATE Electrical 2017 Set 1 | Question: 31
Let the signal $x(t)=\sum_{k=-\infty }^{+\infty } (-1)^{k} \delta (t-\frac{k}{2000})$ be passed through an LTI system with frequency response $H(\omega )$ ... $2000+2000\cos (2000 \pi t)+2000\cos (4000 \pi t)$ $4000\cos (2000 \pi t)$ $2000\cos (2000 \pi t)$

Let the signal$x(t)=\sum_{k=-\infty }^{+\infty } (-1)^{k} \delta (t-\frac{k}{2000})$be passed through an LTI system with frequency response $H(\omega )$, as given in the ...

Arjun

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393

GATE Electrical 2017 Set 1 | Question: 46
Two parallel connected, three-phase, $50$Hz, $11$kV, star-connected synchronous machines $A$ and $B$, are operating as synchronous condensers. They together supply $50$MVAR to a $11$kV grid. Current supplied by both the machines are equal. ... excitation current of machine $A$ to that of machine $B$ is _______. (Give the answer up to two decimal places.)

Two parallel connected, three-phase, $50$Hz, $11$kV, star-connected synchronous machines $A$ and $B$, are operating as synchronous condensers. They together supply $50$MV...

Arjun

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394

GATE Electrical 2017 Set 1 | Question: 51
Consider a causal and stable $LTI$ system with rational transfer function $H(z)$, whose corresponding impulse response begins at $n=0$. Furthermore, $H(1)=\frac{5}{4}$. The poles of $H(z)$ ... $g[n]=j^{n}h[n]$. The value of $g[8]$ equals __________. (Give the answer up to three decimal places.)

Consider a causal and stable $LTI$ system with rational transfer function $H(z)$, whose corresponding impulse response begins at $n=0$. Furthermore, $H(1)=\frac{5}{4}$. T...

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395

GATE Electrical 2017 Set 2 | Question: 53
Two generating units rated $300$MW and $400$MW have governor speed regulation of $6 \%$ and $4 \%$ respectively from no load to full load. Both the generating units are operating in parallel to share a load of $600$MW. Assuming free governor action, the load shared by the larger unit is _________ MW.

Two generating units rated $300$MW and $400$MW have governor speed regulation of $6 \%$ and $4 \%$ respectively from no load to full load. Both the generating units are o...

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396

GATE Electrical 2017 Set 1 | Question: 49
A separately excited $DC$ generator supplies $150$A to a $145$V DC grid. The generator is running at $800$RPM. The armature resistance of the generator is $0.1\Omega$. If the speed of the generator is increased to $1000$ RPM, the current in amperes supplied by the generator to the $DC$ grid is ______. (Give the answer up to one decimal place.)

A separately excited $DC$ generator supplies $150$A to a $145$V DC grid. The generator is running at $800$RPM. The armature resistance of the generator is $0.1\Omega$. If...

Arjun

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397

GATE Electrical 2017 Set 2 | Question: 2
Consider a solid sphere of radius $5$ cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed Uniformly over the entire volume of the sphere. Uniformly over the ... the sphere. Concentrated around the centre of the sphere. Along a straight line passing through the centre of the sphere.

Consider a solid sphere of radius $5$ cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributedUnifo...

Arjun

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398

GATE Electrical 2017 Set 1 | Question: 20
A three-phase, $50$Hz, star-connected cylindrical rotor synchronous machine is running as a motor. The machine is operated from a $6.6$ kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is $30 \Omega$ ... $30^{\circ}$. The power delivered to the motor in kW is __________. (Give the answer up to one decimal place).

A three-phase, $50$Hz, star-connected cylindrical rotor synchronous machine is running as a motor. The machine is operated from a $6.6$ kV grid and draws current at unity...

Arjun

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399

GATE Electrical 2017 Set 1 | Question: 55
The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $1.5 \sin \delta$, where $\delta$ is the rotor angle. The system is operating at the stable equilibrium point with ... $P_{\max}$, in pu is ______. (Give the answer up to three decimal places.)

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $1.5 \sin \delta$, where $\delt...

Arjun

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400

GATE Electrical 2017 Set 2 | Question: 31
The output $y(t)$ of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is $1000$ samples/s $1500$ samples/s $2000$ samples/s $3000$ samples/s

The output $y(t)$ of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is$1000$ samples/s$1500$...

Arjun

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Arjun asked Feb 26, 2017