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GATE2019 EE: 41
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to $1$ V is _________
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GATE2019 EE: 42
The current $I$ flowing in the circuit shown in amperes is ____________
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GATE2019 EE: 43
The voltage across and the current through a load are expressed as follows $v(t)=-170 \sin \bigg( 377t- \frac{\pi}{6} \bigg) V$ $i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \bigg) A$ The average power in watts (round off to one decimal place) consumed by the load is _________.
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GATE2019 EE: 44
The magnetic circuit shown below has uniform cross-sectional area and air gap of $0.2$ cm. The mean path length of the core is $40$ cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the ... to be $1000$ (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is _______
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GATE2019 EE: 45
A single-phase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ________
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GATE2019 EE: 46
A $220$ V DC shunt motor takes $3$ A at no-load. It draws $25$ A when running at full-load at $1500$ rpm. The armature and shunt resistance are $0.5 \: \Omega$ and $220 \: \Omega$, respectively. The no-load speed in rpm (round off to two decimal places) is _____.
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GATE2019 EE: 47
A delta-connected, $3.7$ kW, $400$ V(line), three-phase, $4$-pole, $50$-Hz squirrel-cage induction moor has the following equivalent circuit parameters per phase referred to the stator: $R_1=5.39 \: \Omega$, $R_2=5.72 \: \Omega$ ... in amperes (round off to two decimal places) when it is connected to a $100$ V(line), $10$ Hz, three-phase AC source is _______
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GATE2019 EE: 48
A $220$ V(line), three-phase, Y-connected, synchronous motor has a synchronous impedance of $(0.25+j2.5) \: \Omega/\text{phase}$. The motor draws the rated current of $10$ A at $0.8$ pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is _________
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GATE2019 EE: 49
A three-phase $50$ Hz, $400$ kV transmission line is $300$ km long. The line inductance is $1$ mH/km per phase, and the capacitance is $0.01 \: \mu F/km$ per phase. The line is under open circuit condition at the receiving end and energized with $400$ kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be _________
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GATE2019 EE: 50
A $30$ kV, $50$ Hz, $50$ MVA generator has the positive, negative, and zero sequence reactances of $0.25$ pu, $0.15$ pu, and $0.05$ pu, respectively. The neutral of the generator is grounded with a reactance so that the fault ... bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is ___________
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GATE2019 EE: 51
In the single machine infinite bus system shown below, the generator is delivering the real power of $0.8$ pu at $0.8$ power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is _________
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GATE2019 EE: 52
In a $132$ kV system, the series inductance up to the point of circuit breaker location is $50$ mH. The shunt capacitance at the circuit breaker terminal is $0.05 \: \mu F$. The critical value of resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is ______
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GATE2019 EE: 53
In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at $48$ V. The input DC voltage is $24$ V. The output power is $120$ W. The switching frequency is $50$ kHz. Assume ideal components and a very ... converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in $\mu H$) is ________
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GATE2019 EE: 54
A fully-controlled three-phase bridge converter is working from a $415$ V, $50$ Hz AC supply. It is supplying constant current of $100$ A a $400$ V to a DC load. Assume large inductive smoothing and neglect overlap. The rms value of the AC line current in amperes (round off to two decimal places) is _______
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GATE2019 EE: 55
A single-phase fully-controlled thyristor converter is used to obtain an average voltage of $180$ V with $10$ A constant current to feed a DC load. It is fed from single-phase AC supply of $230$ V, $50$ Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is _________
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16
GATE2012-51
With $10$ V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1 \: \Omega$ connected at port B draws a current of $3$ A $2.5 \: \Omega$ connected at port B draws a current of $2$ A With $10$ V dc connected at port A, the current drawn by $7 \: \Omega$ connected at port B is $3/7$ A $5/7$ A $1$ A $9/7$ A
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GATE2012-52
In the circuit shown, the three voltmeter readings are $V_1 =220$ V, $V_2=122$ V, $V_3=136$ V. The power factor of the load is $0.45$ $0.50$ $0.55$ $0.60$
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GATE2012-53
In the circuit shown, the three voltmeter readings are $V_1 =220$ V, $V_2=122$ V, $V_3=136$ V. If $R_L=5 \: \Omega$, the approximate power consumption in the load is $700$ W $750$ W $800$ W $850$ W
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19
GATE2012-54
The transfer function of a compensator is given as $G_c(s) = \frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $a=1, \: b=2$ $a=3, \: b=2$ $a=-3, \: b=-1$ $a=3, \: b=1$
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GATE2012-55
The transfer function of a compensator is given as $G_c(s) = \frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at $\sqrt{2}$ rad/s $\sqrt{3}$ rad/s $\sqrt{6}$ rad/s $1 / \sqrt{3}$ rad/s
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21
GATE2012-50
With $10$ V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1 \: \Omega$ connected at port B draws a current of $3$ A $2.5 \: \Omega$ connected at port B draws a current of $2$ A For the same network, with $6$ V dc ... $8$ V dc is connected to port A, the open circuit voltage at port B is $6$ V $7$ V $8$ V $9$ V
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22
GATE2012-43
The feedback system shown below oscillates at $2$ rads /s when $K=2$ and $a=0.75$ $K=3$ and $a=0.75$ $K=4$ and $a=0.5$ $K=2$ and $a=0.5$
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23
GATE2012-44
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)= \int_ {- \infty}^t x(\tau) \cos(3 \tau) d \tau$. The system is time-invariant and stable stable and not time-invariant time-invariant and not stable not time-invariant and not stable
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24
GATE2012-45
An analog voltmeter uses external multiplier settings. With a multiplier setting of $20 \: k \Omega$, it reads $440$ V and with a multiplier setting of $80 \: k \Omega$, it reads $352$ V. For a multiplier setting of $40 \: k \Omega$, the voltmeter reads $371$ V $383$ V $394$ V $406$ V
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25
GATE2012-46
The locked rotor current in a $3$-phase, star connected $15$ kW, $4$-pole, $230$ V, $50$ Hz induction motor at rated conditions is $50$ A. Neglecting losses and magnetizing current, the approximate locked rotor line current drawn when the motor is connected to a $236$ V, $57$ Hz supply is $58.5$ A $45.0$ A $42.7$ A $55.6$ A
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26
GATE2012-47
A single phase $10$ kVA, $50$ Hz transformer with $1$ kV primary winding draws $0.5$ A and $55$ W, at rated voltage and frequency, on no load. A second transformer has a core with all its linear dimensions $\sqrt{2}$ times the corresponding dimensions of the first transformer. The core material and lamination ... , are $0.7$ A, $77.8$ W $0.7$ A, $155.6$ W $1$ A, $110$ W $1$ A, $220$ W
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27
GATE2012-48
In the $3$-phase inverter circuit shown, the load is balanced and the gating scheme is $180^{\circ}$-conduction mode. All the switching devices are ideal. The rms value of load phase voltage is $106.1$ V $141.4$ V $212.2$ V $282.8$ V
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28
GATE2012-49
In the $3$-phase inverter circuit shown, the load is balanced and the gating scheme is $180^{\circ}$-conduction mode. All the switching devices are ideal. If the dc bus voltage $V_d=300$ V, the power consumed by $3$-phase load is $1.5$ kW $2.0$ kW $2.5$ kW $3.0$ kW
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29
GATE2012-36
A $220$ V, $15$ kW, $1000$ rpm shunt motor with armature resistance of $0.25 \: \Omega$, has a rated line current of $68$ A and a rated field current of $2.2$ A. The change on field flux required to obtain a speed of $1600$ rpm while drawing a line current of $52.8$ A and a field current of $1.8$ A is $18.18 \%$ increase $18.18 \%$ decrease $36.36 \%$ increase $36.36 \%$ decrease
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GATE2012-37
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
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GATE2012-38
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla \cdot \textbf{A} = 0$ is $-2$ $2$ $1$ $0$
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GATE2012-39
Consider the differential equation $\frac{d^2y(t)}{dt^2} + 2 \frac{dy(t)}{dt} + y(t)=\delta (t)$ with $y(t) \mid_{t=0^-}= -2$ and $\frac{dy}{dt} \mid _{t=0^-} =0$. The numerical value of $\frac{dy}{dt} \mid _{t=0^+}$ is $-2$ $-1$ $0$ $1$
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33
GATE2012-40
Assuming both the voltages sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is $0.8 \: \Omega$ $1.4 \: \Omega$ $2 \: \Omega$ $2.8 \: \Omega$
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GATE2012-41
The state variable description of an LTI system is given by ... $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$ $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
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GATE2012-42
The Fourier transform of a signal $h(t)$ is $H(j \omega) = (2 \cos \omega) (\sin 2 \omega )/ \omega$. The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$
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GATE2012-33
For the system shown below, $S_{D1}$ and $S_{D2}$ are complex power demands at bus $1$ and bus $2$ respectively. If $\mid V_2 \mid =1$ pu, the VAR rating of the capacitor $(Q_{G2})$ connected at bus $2$ is $0.2$ pu $0.268$ pu $0.312$ pu $0.4$ pu
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37
GATE2012-34
A cylindrical rotor generator delivers $0.5$ pu power in the steady-state to an infinite bus through a transmission line of reactance $0.5$ pu. The generator no-load voltage is $1.5$ pu and the infinite bus voltage is $1$ pu. The inertia constant of the generator is $5$ ... , in degrees, for a three-phase dead short circuit fault at the generator terminal is $53.5$ $60.2$ $70.8$ $79.6$
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38
GATE2012-35
In the circuit shown, an ideal switch $S$ is operated at $100$ kHz with a duty ratio of $50 \%$. Given that $\Delta i_c$ is $1.6$ A peak-to-peak and $I_0$ is $5$ A dc, the peak current in $S$ is $6.6$ A $5.0$ A $5.8$ A $4.2$ A
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GATE2012-29
The voltage gain $A_V$ of the circuit shown below is $\mid A_V \mid \approx 200$ $\mid A_V \mid \approx 100$ $\mid A_V \mid \approx 20$ $\mid A_V \mid \approx 10$
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GATE2012-30
The state transition diagram for the logic circuit shown is
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