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1

GATE2016-1-55
In the circuit shown below, the node voltage $V_{A}$ is ___________ $V$.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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GATE2016-1-54
The circuit below is excited by a sinusoidal source. The value of $R$, in $\Omega$, for which the admittance of the circuit becomes a pure conductance at all frequencies is _____________.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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GATE2016-1-53
A dc voltage with ripple is given by $v(t)=\left [ 100+10\sin\left ( \omega t \right )-5\sin\left ( 3\omega t \right ) \right ]$ volts. Measurements of this voltage $v(t)$ made by moving-coil and moving-iron voltmeters, show readings of $V_{1}$ and $V_{2}$ respectively. The value of $V_{2} − V_{1}$, in volts, is ________.

retagged 1 day ago in Electromagnetic Fields by jothee (100 points)

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GATE2016-1-52
In the circuit shown below, the supply voltage is $10 \sin(1000t)$ volts. The peak value of the steady state current through the $1 \Omega$ resistor, in amperes, is ________.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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GATE2016-1-51
A single-phase transmission line has two conductors each of $10$ mm radius. These are fixed at a center-to-center distance of $1$ m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same ... $5$% more than that of the inductance per conductor of the single-phase system. The distance $D$, in meters, is _________.

retagged 1 day ago in Power Systems by jothee (100 points)

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6

GATE2016-1-48
A three-phase, $50 Hz$ salient-pole synchronous motor has a per-phase direct-axis reactance $(X_{d})$ of $0.8$ pu and a per-phase quadrature-axis reactance $(X_{q})$ of $0.6$ pu. Resistance of the machine is negligible. It is drawing full-load current at $0.8$ pf(leading). When the terminal voltage is $1$ pu, per-phase induced voltage, in pu, is _______.

retagged 1 day ago in Electrical Machines by jothee (100 points)

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GATE2016-1-47
A $DC$ shunt generator delivers $45 A$ at a terminal voltage of $220 V$. The armature and the shunt field resistances are $0.01 \Omega$ and $44 \Omega$ respectively. The stray losses are $375 W$. The percentage efficiency of the $DC$ generator is _________.

retagged 1 day ago in Electrical Machines by jothee (100 points)

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8

GATE2016-1-46
A single-phase $400 V, 50 Hz$ transformer has an iron loss of $5000 W$ at the rated condition. When operated at $200 V, 25 Hz$, the iron loss is $2000 W$. When operated at $416 V, 52 Hz$, the value of the hysteresis loss divided by the eddy current loss is _______.

retagged 1 day ago in Electrical Machines by jothee (100 points)

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GATE2016-1-45
The voltage $(v_{s})$ across and the current $(i_{s})$ through a semiconductor switch during a turn-ON transition are shown in figure. The energy dissipated during the turn-ON transition, in $mJ$, is _______.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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GATE2016-1-44
The switches $T1$ and $T2$ in Figure (a) are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage $v_{m}(t)=0.8\sin (200\pi t) V$ and the triangular carrier voltage $(v_{c})$ are as shown in Figure (b). The ... frequency is $5 kHz$. The peak value of the $100 Hz$ component of the load current $(i_{L})$, in ampere, is ________ .

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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11

GATE2016-1-41
A $30 MVA$, $3$-phase, $50 Hz$, $13.8 kV$, star-connected synchronous generator has positive, negative and zero sequence reactances, $15$%, $15$% and $5$% respectively. A reactance $(X_{n})$ is connected between the neutral of the generator and ground. A double ... $X_{n}$ (in p.u.) that will limit the positive sequence generator current to $4270$ A is ________.

retagged 1 day ago in Power Systems by jothee (100 points)

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GATE2016-1-40
A three-phase cable is supplying $800 kW$ and $600 kVAr$ to an inductive load. It is intended to supply an additional resistive load of $100 kW$ through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of ... the line voltage is $3.3 kV$, $50 Hz$, the capacitance per phase of the bank, expressed in microfarads, is ________.

retagged 1 day ago in Power Systems by jothee (100 points)

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GATE2016-1-39
In the circuit shown, switch $S_{2}$ has been closed for a long time. At time $t=0$ switch $S_{1}$ is closed. At $t=0^{+}$, the rate of change of current through the inductor, in amperes per second, is _____.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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GATE2016-1-33
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.

retagged 1 day ago in Linear Algebra by jothee (100 points)

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15

GATE2016-1-31
Consider the following state-space representation of a linear time-invariant system. $x(t)=\begin{pmatrix} 1&0 \\ 0&2 \end{pmatrix} x(t), y(t)= c^{T} x(t), c =\begin{pmatrix} 1& \\ 1& \end{pmatrix} \text {and} x(0)= \begin{pmatrix} 1& \\ 1& \end{pmatrix}$ The value of y(t) for $t =\log_{e} 2$ is __________.

retagged 1 day ago in Control Systems by jothee (100 points)

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GATE2016-1-27
Let $S=\sum_{n=0}^{\infty} n\alpha^{n}$ where $|\alpha| < 1$. The value of $\alpha$ in the range $0 < \alpha < 1$, such that $S=2 \alpha$ is _________.

retagged 1 day ago in Signals and Systems by jothee (100 points)

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17

GATE2016-1-26
Candidates were asked to come to an interview with $3$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all $3$ pens having the same colour is _________.

retagged 1 day ago in Probability & Statistics by jothee (100 points)

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GATE2016-1-23
A steady dc current of $100$ $A$ is flowing through a power module $(S, D)$ as shown in Figure (a). The $V-I$ characteristics of the $IGBT (S)$ and the diode $(D)$ are shown in Figures $(b)$ and $(c)$, respectively. The conduction power loss in the power module $(S, D)$, in watts, is _________.

retagged 1 day ago in Analog and Digital Electronics by jothee (100 points)

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19

GATE2016-1-22
A buck converter, as shown in Figure (a) below, is working in steady state. The output voltage and the inductor current can be assumed to be ripple free. Figure (b) shows the inductor voltage $v_{L}$ during a complete switching interval. Assuming all devices are ideal, the duty cycle of the buck converter is ___________.

retagged 1 day ago in Electrical and Electronic Measurements by jothee (100 points)

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20

GATE2016-1-20
The magnitude of three-phase fault currents at buses $A$ and $B$ of a power system are $10$ pu and $8$ pu, respectively. Neglect all resistances in the system and consider the pre-fault system to be unloaded. The pre-fault voltage at all buses in the system is $1.0$ pu. ... $A$ is $0.8$ pu. The voltage magnitude at bus $A$ during a three-phase fault at bus $B$, in pu, is __________.

retagged 1 day ago in Power Systems by jothee (100 points)

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21

GATE2016-1-18
In the given circuit, the current supplied by the battery, in ampere, is ________.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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22

GATE2016-1-17
In the portion of a circuit shown, if the heat generated in $5 \Omega$ resistance is $10$ calories per second, then heat generated by the $4 \Omega$ resistance, in calories per second, is ________.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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23

GATE2016-1-14
A soft-iron toroid is concentric with a long straight conductor carrying a direct current $I$. If the relative permeability $\mu_{r}$ of soft-iron is $100$, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is ________.

retagged 1 day ago in Electromagnetic Fields by jothee (100 points)

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24

GATE2016-1-12
A transistor circuit is given below. The Zener diode breakdown voltage is $5.3$ V as shown. Take base to emitter voltage drop to be $0.6$ V. The value of the current gain $\beta$ is _________.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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25

GATE2016-1-2
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.

retagged 1 day ago in Linear Algebra by jothee (100 points)

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26

GATE2016-1-1
The maximum value attained by the function. $f(x) = x(x-1) (x-2)$ in the interval $[1, 2]$ is ___________.

retagged 1 day ago in Differential Equations by jothee (100 points)

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27

GATE2015-2-34
For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE? The impulse response will be integrable, but may not be absolutely integrable. The unit impulse response will have finite support. The unit step response will be absolutely integrable. The unit step response will be bounded

retagged 1 day ago in Signals and Systems by jothee (100 points)

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28

GATE2015-2-51
Two three-phase transformers are realized using single-phase transformers as shown in the figure. The phase difference (in degree) between voltages $V_{1}$ and $V_{2}$ is _______.

retagged 1 day ago in new by jothee (100 points)

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29

GATE2015-2-50
A $220$ V, $3$-phase, $4$-pole, $50$ Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is $225$ % of ... of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is _________.

retagged 1 day ago in new by jothee (100 points)

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30

GATE2015-2-49
A three-phase, $11$ kV, $50$ Hz, $2$ pole, star connected, cylindrical rotor synchronous motor is connected to an $11$ kV, $50$ Hz source. Its synchronous reactance is $50 \Omega$ per phase, and its stator resistance is negligible. The motor has a ... the load torque is increased so that the stator current is $120$ A, then the load angle (in degrees) at this load is __________.

retagged 1 day ago in new by jothee (100 points)

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31

GATE2015-2-48
With an armature voltage of $100$ V and rated field winding voltage, the speed of a separately excited $DC$ motor driving a fan is $1000$ rpm, and its armature current is $10$ A. The armature resistance is $1 \Omega$. The load torque of the ... speed. Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to $500$ rpm is _________.

retagged 1 day ago in new by jothee (100 points)

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32

GATE2015-2-46
Two identical coils each having inductance $L$ are placed together on the same core. If an overall inductance of $\alpha L$ is obtained by interconnecting these two coils, the minimum value of $\alpha$ is ________.

retagged 1 day ago in new by jothee (100 points)

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33

GATE2015-2-45
A symmetrical square wave of $50$% duty cycle has amplitude of $\pm15$ V and time period of $0.4\pi$ ms. This square wave is applied across a series $RLC$ circuit with $R = 5 \Omega$, $L = 10$ mH, and $C = 4 \mu F$. The amplitude of the $5000$ rad/s component of the capacitor voltage (in Volt) is ______.

retagged 1 day ago in new by jothee (100 points)

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34

GATE2015-2-41
A composite conductor consists of three conductors of radius $R$ each. The conductors are arranged as shown below. The geometric mean radius $(GMR)$ (in cm) of the composite conductor is $kR$. The value of $k$ is __________.

edited 1 day ago in new by jothee (100 points)

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35

GATE2015-2-40
The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers $P_{1}$ and $P_{2}$ in $MW$, and are given by $\frac{dC_{1}}{dP_{1}}=0.2P_{1}+50$ $\frac{dC_{2}}{dP_{2}}=0.24P_{2}+40$ ... Rs/MWh and $dC_{2}/dP_{2} = 68.8$ Rs/MWh. If the generations are rescheduled to minimize the total cost, then $P_{2}$ is ________.

retagged 1 day ago in new by jothee (100 points)

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36

GATE2015-2-33
In the given rectifier, the delay angle of the thyristor $T_{1}$ measured from the positive going zero crossing of $V_{s}$ is $30$°. If the input voltage $V_{s}$ is $100 \sin(100 \pi t) V$, the average voltage across $R$ (in Volt) under steady-state is _________.

retagged 1 day ago in Analog and Digital Electronics by jothee (100 points)

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37

GATE2015-2-32
For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is $T_{s}$. If the voltage $V_{L}$ is as shown, the duty cycle of the switch $S$ is ________.

retagged 1 day ago in Analog and Digital Electronics by jothee (100 points)

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38

GATE2015-2-31
A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch $S$ is $100$ kHz and the duty ratio is $0.6$. The output voltage $V_{0}$ is $36$ V. Assume that all the components are ideal, and that the output voltage is ripple-free. The value of $R$ (in Ohm) that will make the inductor current ($i_{L}$) just continuous is _________.

retagged 1 day ago in Analog and Digital Electronics by jothee (100 points)

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39

GATE2015-2-30
The coils of a wattmeter have resistances $0.01 \Omega$ and $1000 \Omega$; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws $25 A$ at power factor $0.8$. The voltage across the load terminals is $30 V$. The percentage error on the wattmeter reading is ________.

retagged 1 day ago in Electrical Circuits by jothee (100 points)

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40

GATE2015-2-28
A differential equation $\frac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.

retagged 1 day ago in Differential Equations by jothee (100 points)