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361
GATE Electrical 2018 | Question: 32
The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is $\text{j} 12 \: \Omega$ $\text{-j} 12 \: \Omega$ $\text{j} 13 \: \Omega$ $13 \: \Omega$
The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is$\text{j} 12 \: \Omega$$\text{-j} 12 \: \Omega$$\text{j} 13 \: \Omega$$13 \: \Omeg...
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362
GATE Electrical 2018 | Question: 27
A $0-1$ Ampere moving iron ammeter has an internal resistance of $50 \: m \Omega$ and inductance of $0.1 \: mH$. A shunt coil is connected to extend its range to $0-10$ Ampere for all operating frequencies. The time constant in milliseconds and resistance in $m \Omega$ of the shunt coil respectively are $2, \: 5.55$ $2, \: 1$ $2.18, \: 0.55$ $11.1, \: 2$
A $0-1$ Ampere moving iron ammeter has an internal resistance of $50 \: m \Omega$ and inductance of $0.1 \: mH$. A shunt coil is connected to extend its range to $0-10$ A...
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GATE Electrical 2018 | Question: 51
A $3$-phase $900$ kVA, $3 \: kV/ \sqrt{3} kV$ ( $\Delta/$), $50$ Hz transformer has primary (high voltage side) resistance per phase of $0.3 \: \Omega$ and secondary (low voltage side) resistance per phase of $0.02 \: \Omega$. ... is $10 \: kW$. The full load $\%$ efficiency of the transformer operated at unity power factor is _______ (up to $2$ decimal places)
A $3$-phase $900$ kVA, $3 \: kV/ \sqrt{3} kV$ ( $\Delta/$), $50$ Hz transformer has primary (high voltage side) resistance per phase of $0.3 \: \Omega$ and secondary (low...
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GATE Electrical 2018 | Question: 6
Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be greater ... $ \begin{vmatrix} \frac{V_1V_2}{Z} \end{vmatrix} \\ $
Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ are the series impedance and reactance of the...
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365
GATE Electrical 2018 | Question: 46
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is ___________ (up to $2$ decimal places).
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is _...
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GATE Electrical 2018 | Question: 29
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator $G_1$ and $G_2$ are $Q_{G1}$ and $Q_{G2}$ respectively. The per unit values of $Q_{G1}$, $Q_{G2}$, and line ... $6.34, \: 11.34, \: 2.68$ $5.00, \: 11.34, \: 1.34$
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by gene...
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367
GATE Electrical 2018 | Question: 55
The voltage $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega = 100 \text{ radian/s}$. When the inductor current $i(t)$ is in phase with the voltage $v(t)$, the magnitude of the impedance $Z$ (in $\Omega$) seen between the terminals $a$ and $b$ is __________ (up to $2$ decimal places)
The voltage $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega = 100 \text{ radian/s}$. When the inductor ...
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GATE Electrical 2018 | Question: 7
The graph of a network has $8$ nodes and $5$ independent loops. The number of branches of the graph is $11$ $12$ $13$ $14$
The graph of a network has $8$ nodes and $5$ independent loops. The number of branches of the graph is$11$$12$$13$$14$
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GATE Electrical 2018 | Question: 45
The capacitance of an air-filled parallel-plate capacitor is $60$ pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes $86$ pF. Neglecting the fringing effects, the relative permittivity of the dielectric is ___________ (up to $2$ decimal places)
The capacitance of an air-filled parallel-plate capacitor is $60$ pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of ...
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GATE Electrical 2018 | Question: 39
The signal energy of he continuous-time signal $x(t)=[(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)]$ is $11/3$ $7/3$ $1/3$ $5/3$
The signal energy of he continuous-time signal $x(t)=[(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)]$ is$11/3$$7/3$$1/3$$5/3$
Arjun
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GATE Electrical 2018 | Question: 20
The series impedance matrix of a short three-phase transmission line in phase coordinates is $\begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{bmatrix}$ ... $Z_m$ (in $\Omega$) is ___________ (up to $2$ decimal places).
The series impedance matrix of a short three-phase transmission line in phase coordinates is $\begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{b...
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GATE Electrical 2018 | Question: 25
Consider a unity feedback system with forward transfer function given by $G(s) = \frac{1}{(s+1)(s+2)}$ The steady-state error in the output of the system for a unit-step input is _______ (up to $2$ decimal places).
Consider a unity feedback system with forward transfer function given by $$G(s) = \frac{1}{(s+1)(s+2)}$$ The steady-state error in the output of the system for a unit-ste...
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GATE Electrical 2018 | Question: 38
Consider the two continuous-time signals defined below: ... than the energy of $x_1[n]$ $x_1[n]$ and $x_2[n]$ have equal energies Neither $x_1[n]$ nor $x_2[n]$ is a finite-energy signal
Consider the two continuous-time signals defined below:$$x_1(t) = \begin{cases} \mid t \mid, & -1 \leq t \leq 1 \\ 0, & \text{otherwise} \end{cases} \\ x_2(t) = \begin{ca...
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GATE Electrical 2018 | Question: 28
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$, the fault current is $I_{f1}= kI_f$, where $I_f$ is the fault current with zero fault impedance. The relation ... $Z_f=\frac{(Z_1+Z_2)k}{1-k} \\$ $Z_f=\frac{(Z_1+Z_2)k}{1+k}$
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$,...
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GATE Electrical 2018 | Question: 1
A single-phase $100$ kVA, $1000$ V / $100$ V, $50$ Hz transformer has a voltage has a voltage drop of $5 \%$ across its series impedance at full load. Of this, $3\%$ is due to resistance. The percentage regulation of the transformer at full load with $0.8$ lagging power factor is $4.8$ $6.8$ $8.8$ $10.8$
A single-phase $100$ kVA, $1000$ V / $100$ V, $50$ Hz transformer has a voltage has a voltage drop of $5 \%$ across its series impedance at full load. Of this, $3\%$ is d...
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GATE Electrical 2018 | Question: 19
In the two-port nework shown, the $h_{11}$ parameter $\bigg($ where, $h_{11} = \frac{V_1}{I_1}$, when $V_2=0 \bigg)$ in ohms is _________ (up to $2$ decimal places).
In the two-port nework shown, the $h_{11}$ parameter $\bigg($ where, $h_{11} = \frac{V_1}{I_1}$, when $V_2=0 \bigg)$ in ohms is _________ (up to $2$ decimal places).
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GATE Electrical 2018 | Question: 53
A dc to dc converter shown in the figure is charging a battery bank, $B2$ whose voltage is constant at $150 \: V$. $B1$ is another battery bank whose voltage is constant at $50 \: V$. The value of the inductor, $L$ is $5$ mH and the ... assuming the diode D to be ideal, the power transferred from $B1$ to $B2$ (in Watt) is ___________ (up to $2$ decimal places)
A dc to dc converter shown in the figure is charging a battery bank, $B2$ whose voltage is constant at $150 \: V$. $B1$ is another battery bank whose voltage is constant ...
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GATE Electrical 2018 | Question: 48
The voltage across the circuit in the figure, and the current through it, are given by the following expressions: $v(t)=5-10 \cos (\omega t+ 60^{\circ}) \: V$ $i(t)=5 + X \cos (\omega t) \: A$ where $\omega =100 \: \pi \text{ radian}/s$. If the average power delivered to the circuit is zero, then the value of $X$ (in Ampere) is _______ (up to $2$ decimal places)
The voltage across the circuit in the figure, and the current through it, are given by the following expressions:$v(t)=5-10 \cos (\omega t+ 60^{\circ}) \: V$$i(t)=5 + X \...
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GATE Electrical 2018 | Question: 24
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produces a torque of $500$ Nm at zero speed. Neglecting all mechanical losses, the no- ... motor (in $\text{radian /s}$) for an armature voltage of $150$ V is ____________ (up to $2$ decimal places).
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produ...
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GATE Electrical 2018 | Question: 2
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is $0$ $45$ $60$ $90$
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is$0$$45$$60$$90$
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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...
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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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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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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...
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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...
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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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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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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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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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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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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...
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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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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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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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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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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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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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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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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 __________.
Arjun
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Arjun
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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...
Arjun
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Arjun
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