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881
GATE Electrical 2015 Set 2 | Question: 52
The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables $x$ and $y$. The integration time step is $h$. $\dfrac{x_{k+1}-x_{k}}{h}=y_{k}$ ... $\dfrac{1}{2\pi}<h<\dfrac{1}{\pi}$
The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables ...
makhdoom ghaya
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882
GATE Electrical 2015 Set 2 | Question: 53
The unit step response of a system with the transfer function $G(s)=\dfrac{1-2s}{1+s}$ is given by which one of the following waveforms?
The unit step response of a system with the transfer function $G(s)=\dfrac{1-2s}{1+s}$ is given by which one of the following waveforms?
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883
GATE Electrical 2015 Set 2 | Question: 54
An open loop transfer function $G(s)$ of a system is $G(s)=\dfrac{k}{s(s+1)(s+2)}$ For a unity feedback system, the breakaway point of the root loci on the real axis occurs at, $−0.42$ $−1.58$ $−0.42$ and $−1.58$ None of the above
An open loop transfer function $G(s)$ of a system is$G(s)=\dfrac{k}{s(s+1)(s+2)}$For a unity feedback system, the breakaway point of the root loci on the real axis occurs...
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884
GATE Electrical 2015 Set 2 | Question: 55
For the system governed by the set of equations: $dx_{1}/dt=2x_{1}+x_{2}+u$ $dx_{2}/dt=-2x_{1}+u$ $y=3 x_{1}$ the transfer function $Y(s)/U(s)$ is given by $3(s+1)/(s^{2}-2s+2)$ $3(2s+1)/(s^{2}-2s+1)$ $(s+1)/(s^{2}-2s+1)$ $3(2s+1)/(s^{2}-2s+2)$
For the system governed by the set of equations:$dx_{1}/dt=2x_{1}+x_{2}+u$$dx_{2}/dt=-2x_{1}+u$$y=3 x_{1}$the transfer function $Y(s)/U(s)$ is given by$3(s+1)/(s^{2}-2s+2...
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885
GATE Electrical 2015 Set 2 | Question: 39
The saturation voltage of the ideal op-amp shown below is $\pm 10$ V. The output voltage $v_{o}$ of the following circuit in the steady-state is Square wave of period $0.55$ ms. Triangular wave of period $0.55$ ms. square Square wave of period $0.25$ ms. Triangular wave of period $0.25$ ms
The saturation voltage of the ideal op-amp shown below is $\pm 10$ V. The output voltage $v_{o}$ of the following circuit in the steady-state isSquare wave of period $0.5...
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886
GATE Electrical 2015 Set 2 | Question: 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 $\dfrac{dC_{1}}{dP_{1}}=0.2P_{1}+50$ ... $dC_{2}/dP_{2} = 68.8$ Rs/MWh. If the generations are rescheduled to minimize the total cost, then $P_{2}$ is ________.
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$\dfrac{dC_{...
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887
GATE Electrical 2015 Set 2 | Question: 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 __________.
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 compos...
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888
GATE Electrical 2015 Set 2 | Question: 42
A 3-phase transformer rated for $33 kV/11 kV$ is connected in delta/star as shown in figure. The current transformers ($CTs$) on low and high voltage sides have a ratio of $500/5$. Find the currents $i_{1}$ and $i_{2}$, if the fault current is $300$ ... $i_{1}=0A, i_{2}=1\sqrt{3}A$ $i_{1}=1\sqrt{3}A, i_{2}=1\sqrt{3}A$
A 3-phase transformer rated for $33 kV/11 kV$ is connected in delta/star as shown in figure. The current transformers ($CTs$) on low and high voltage sides have a ratio o...
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889
GATE Electrical 2015 Set 2 | Question: 43
A balanced (positive sequence) three-phase $AC$ voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. The line-to-line voltage rating is $230$ V on the star side, and $115$ V on the delta ... Ampere? $50\angle 30^\circ$ $50\angle- 30^\circ$ $50\sqrt{3}\angle 30^\circ$ $200\angle 30^\circ$
A balanced (positive sequence) three-phase $AC$ voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. Th...
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890
GATE Electrical 2015 Set 2 | Question: 44
In the given network $V_{1}=100\angle 0^{\circ}V, V_{2}=100\angle -120^{\circ}V, V_{3}=100\angle +120^{\circ}V$. The phasor current $i$ (in Ampere) is $173.2\angle -60^{\circ}$ $173.2\angle 120^{\circ}$ $100.0\angle -60^{\circ}$ $100.0\angle 120^{\circ}$
In the given network $V_{1}=100\angle 0^{\circ}V, V_{2}=100\angle -120^{\circ}V, V_{3}=100\angle +120^{\circ}V$. The phasor current $i$ (in Ampere) is$173.2\angle -60^{\c...
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891
GATE Electrical 2015 Set 2 | Question: 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 ______.
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 $...
makhdoom ghaya
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numerical-answers
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892
GATE Electrical 2015 Set 2 | Question: 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 ________.
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...
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numerical-answers
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893
GATE Electrical 2015 Set 2 | Question: 47
A three-winding transformer is connected to an $AC$ voltage source as shown in the figure. The number of turns are as follows: $N_{1} = 100, N_{2} = 50, N_{3} = 50$ ... in Ampere? $1\angle 90^{\circ}$ $1\angle 270^{\circ}$ $4\angle 90^{\circ}$ $4\angle 270^{\circ}$
A three-winding transformer is connected to an $AC$ voltage source as shown in the figure. The number of turns are as follows: $N_{1} = 100, N_{2} = 50, N_{3} = 50$. If t...
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894
GATE Electrical 2015 Set 2 | Question: 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 ... rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to $500$ rpm is _________.
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...
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makhdoom ghaya
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895
GATE Electrical 2015 Set 2 | Question: 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 ... torque is increased so that the stator current is $120$ A, then the load angle (in degrees) at this load is __________.
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 $5...
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896
GATE Electrical 2015 Set 2 | Question: 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 ... resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is _________.
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 c...
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897
GATE Electrical 2015 Set 2 | Question: 27
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $H$ represents head and $T$ represents tail. Which one of the ... is TRUE? The coin tosses are independent. $R$ is fair, $S$ is not. $S$ is fair, $R$ is not. The coin tosses are dependent.
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $...
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Probability & Statistics
gate2015-ee-2
probability-and-statistics
probability
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898
GATE Electrical 2015 Set 2 | Question: 28
A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
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Differential Equations
gate2015-ee-2
differential-equations
numerical-answers
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899
GATE Electrical 2015 Set 2 | Question: 29
Consider a signal defined by $x(t)= \begin{cases} e^{j10 t} & \text{for } \mid t \mid \leq 1 \\ 0& \text{for } \mid t \mid > 1\end{cases}$ Its Fourier Transform is $\dfrac{2 \sin (\omega -10)}{\omega - 10}\\$ ... $\dfrac{2 \sin \omega}{\omega - 10} \\$ $e^{j10 \omega }\dfrac{2 \sin\omega }{\omega }$
Consider a signal defined by$x(t)= \begin{cases} e^{j10 t} & \text{for } \mid t \mid \leq 1 \\ 0& \text{for } \mid t \mid 1\end{cases}$Its Fourier Transform is$\dfrac...
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Signals and Systems
gate2015-ee-2
fourier-analysis
causal-system
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900
GATE Electrical 2015 Set 2 | Question: 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 ________.
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 measu...
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Electric Circuits
gate2015-ee-2
power-measurement
coils
power-factor
numerical-answers
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901
GATE Electrical 2015 Set 2 | Question: 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 $V_{o}$ is $36$ V. Assume that all the components are ideal ... is ripple-free. The value of $R$ (in Ohm) that will make the inductor current ($i_{L}$) just continuous is _________.
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 ...
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Analog and Digital Electronics
gate2015-ee-2
step-down-converter
ripple-voltages
numerical-answers
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902
GATE Electrical 2015 Set 2 | Question: 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 ________.
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 positi...
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Analog and Digital Electronics
gate2015-ee-2
steady-state-operation
reverse-current
numerical-answers
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903
GATE Electrical 2015 Set 2 | Question: 33
In the given rectifier, the delay angle of the thyristor $T_{1}$ measured from the positive going zero crossing of $V_{s}$ is $30^\circ$. If the input voltage $V_{s}$ is $100 \sin(100 \pi t) V$, the average voltage across $R$ (in Volt) under steady-state is _________.
In the given rectifier, the delay angle of the thyristor $T_{1}$ measured from the positive going zero crossing of $V_{s}$ is $30^\circ$. If the input voltage $V_{s}$ is ...
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Analog and Digital Electronics
gate2015-ee-2
bridge-rectifier
diodes
thyrister
numerical-answers
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904
GATE Electrical 2015 Set 2 | Question: 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
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, bu...
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Signals and Systems
gate2015-ee-2
impulse-response
unit-step-response
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905
GATE Electrical 2015 Set 2 | Question: 35
The $z$-Transform of a sequence $x[n]$ is given as $X(z)=2z+4-4/z+3/z^{2}$. If $y[n]$ is the first difference of $x[n]$, then $Y(z)$ is given by $2z+2-8/z+7/z^{2}-3/z^{3}$ $-2z+2-6/z+1/z^{2}-3/z^{3}$ $-2z-2+8/z-7/z^{2}+3/z^{3}$ $4z-2-8/z-1/z^{2}+3/z^{3}$
The $z$-Transform of a sequence $x[n]$ is given as $X(z)=2z+4-4/z+3/z^{2}$. If $y[n]$ is the first difference of $x[n]$, then $Y(z)$ is given by$2z+2-8/z+7/z^{2}-3/z^{3}$...
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Signals and Systems
gate2015-ee-2
sequence
complex-frequency-domain-representation
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906
GATE Electrical 2015 Set 2 | Question: 36
Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of $+Q$ is placed at a distance of $d$ from both sheets. The net force on the charge is $\dfrac{Q^{2}}{4\pi \in_{0}} \frac{Q}{d^{2}}$, where $K$ is ... $\dfrac{1-2\sqrt{2}}{8\sqrt{2}} \hat{t}+\dfrac{1-2\sqrt{2}}{8\sqrt{2}} \hat{j}$
Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of $+Q$ is placed at a distance of $d$ from both sheet...
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907
GATE Electrical 2015 Set 2 | Question: 37
In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is $Q_{1}Q_{0}=00$. The state $(Q_{1}Q_{0})$, immediately after the $333^{rd}$ clock pulse is $00$ $01$ $10$ $11$
In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is $Q_{1}Q_{0}=00$. The state $(Q_{1}Q_{0})$, immediately after the $...
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Analog and Digital Electronics
gate2015-ee-2
analog-and-digital-electronics
sequential-circuit
counters
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908
GATE Electrical 2015 Set 2 | Question: 15
When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE about the state of its collector-base $(CB)$ and the base-emitter $(BE)$ junctions? The $CB$ ... . Both the $CB$ and $BE$ junctions are forward biased. Both the $CB$ and $BE$ junctions are reverse biased.
When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE about the state of its collector-base $(CB)$ and the...
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Analog and Digital Electronics
gate2015-ee-2
bjt-as-switch
common-emitter
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909
GATE Electrical 2015 Set 2 | Question: 16
The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude $E$ are ... . Which one of the following waveforms of the rotor angle $\delta$ shows the transient correctly?
The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. T...
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makhdoom ghaya
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Power Systems
gate2015-ee-2
power-system-protection
source-of-reactive-power
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910
GATE Electrical 2015 Set 2 | Question: 17
A $3$-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is $\begin{bmatrix} -j6 &j3 &j4 \\ j3&-j7 &j5 \\ j4& j5 & -j8 \end{bmatrix}$ pu. If the shunt ... $−j7.0$ $−j8.5$ $−j7.5$ $−j9.0$
A $3$-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is$\begin{bmatrix}-j6 &j3 &j4 \\ j3&-j7 &j5 \\ ...
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makhdoom ghaya
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Feb 11, 2017
Power Systems
gate2015-ee-2
bus-admittance-matrix
self-admittance
mutual
admittance
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911
GATE Electrical 2015 Set 2 | Question: 18
A series $RL$ circuit is excited at $t = 0$ by closing a switch as shown in the figure. Assuming zero initial conditions, the value of $\dfrac{d^{2}i}{dt^{2}}$ at $t=0^{+}$ is $\dfrac{V}{L} \\$ $\dfrac{-V}{R} \\$ $0 \\$ $\dfrac{-RV}{L^{2}}$
A series $RL$ circuit is excited at $t = 0$ by closing a switch as shown in the figure. Assuming zero initial conditions, the value of $\dfrac{d^{2}i}{dt^{2}}$ at $t=0^{+...
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9.4k
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makhdoom ghaya
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Feb 11, 2017
Electric Circuits
gate2015-ee-2
switching
rl-circuit
zero-initial-condition
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0
votes
0
answers
912
GATE Electrical 2015 Set 2 | Question: 19
The current $i$ (in Ampere) in the $2 \Omega$ resistor of the given network is ________.
The current $i$ (in Ampere) in the $2 \Omega$ resistor of the given network is ________.
makhdoom ghaya
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Electric Circuits
gate2015-ee-2
electric-circuit-reduction
nodal-analysis
numerical-answers
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0
votes
0
answers
913
GATE Electrical 2015 Set 2 | Question: 20
Find the transformer ratios $a$ and $b$ such that the impedance ($Z_{in}$) is resistive and equals $2.5 \Omega$ when the network is excited with a sine wave voltage of angular frequency of $5000$ rad/s. $a = 0.5, b = 2.0$ $a = 2.0, b = 0.5$ $a = 1.0, b = 1.0$ $a = 4.0, b = 0.5$
Find the transformer ratios $a$ and $b$ such that the impedance ($Z_{in}$) is resistive and equals $2.5 \Omega$ when the network is excited with a sine wave voltage of an...
makhdoom ghaya
9.4k
points
makhdoom ghaya
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Feb 11, 2017
Power Systems
gate2015-ee-2
turn-ratio
transformer-core
eddy-current
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0
votes
0
answers
914
GATE Electrical 2015 Set 2 | Question: 21
A shunt-connected $DC$ motor operates at its rated terminal voltage. Its no-load speed is $200$ radian/second. At its rated torque of $500$ Nm, its speed is $180$ radian/second. The motor is used to directly drive a load whose ... . Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is _________.
A shunt-connected $DC$ motor operates at its rated terminal voltage. Its no-load speed is $200$ radian/second. At its rated torque of $500$ Nm, its speed is $180$ radian/...
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9.4k
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makhdoom ghaya
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Feb 11, 2017
Electrical Machines
gate2015-ee-2
no-load-speed
rotational-losses
numerical-answers
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0
votes
0
answers
915
GATE Electrical 2015 Set 2 | Question: 22
The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at $50$ Hz. The “air-gap” voltage, $V_{g}$ across the magnetizing inductance, is $210$ V rms, and the slip, $s$, is $0.05$. The torque (in Nm) produced by the motor is _________.
The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at $50$ Hz. The “air-gap” voltage, $V_{g}$ across the magnetizin...
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9.4k
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makhdoom ghaya
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Feb 11, 2017
Electrical Machines
gate2015-ee-2
slip-speed
motor
winding
numerical-answers
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0
votes
0
answers
916
GATE Electrical 2015 Set 2 | Question: 23
A $4$-pole, separately excited, wave wound $DC$ machine with negligible armature resistance is rated for $230$ V and $5$ kW at a speed of $1200$ rpm. If the same armature coils are reconnected to form a lap winding, what is the rated voltage (in volts) and ... field circuit is left unchanged ? $230$ and $5$ $115$ and $5$ $115$ and $2.5$ $230$ and $2.5$
A $4$-pole, separately excited, wave wound $DC$ machine with negligible armature resistance is rated for $230$ V and $5$ kW at a speed of $1200$ rpm. If the same armature...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Electrical Machines
gate2015-ee-2
lap-winding
armature-core
revolution-per-minute
+
–
0
votes
0
answers
917
GATE Electrical 2015 Set 2 | Question: 24
An open loop control system results in a response of $e^{-2t}(\sin 5t+\cos 5t)$ for a unit impulse input. The $DC$ gain of the control system is ________.
An open loop control system results in a response of $e^{-2t}(\sin 5t+\cos 5t)$ for a unit impulse input. The $DC$ gain of the control system is ________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Control Systems
gate2015-ee-2
open-loop-system
independant-system
numerical-answers
+
–
0
votes
0
answers
918
GATE Electrical 2015 Set 2 | Question: 25
Nyquist plots of two functions $G_{1}(s)$ and $G_{2}(s)$ are shown in figure. Nyquist plot of the product of $G_{1}(s)$ and $G_{2}(s)$ is
Nyquist plots of two functions $G_{1}(s)$ and $G_{2}(s)$ are shown in figure.Nyquist plot of the product of $G_{1}(s)$ and $G_{2}(s)$ is
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Control Systems
gate2015-ee-2
stability
real-roots
imaginary-roots
+
–
0
votes
0
answers
919
GATE Electrical 2015 Set 2 | Question: 26
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2015-ee-2
calculus
volume-integral
numerical-answers
+
–
0
votes
0
answers
920
GATE Electrical 2015 Set 2 | Question: 3
Match the following. ... $P-4; Q-1; R-3; S-2$ $P-4; Q-3; R-1; S-2$ $P-3; Q-4; R-2; S-1$
Match the following.$\begin{array}{|l|l|l|l|} \hline P. & \text{Stokes’s Theorem} & 1. & ∯ D.ds = Q \\ \hline Q. & \text{Gauss’s Theorem} & 2. & \oint f(z) dz =0 \\...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2015-ee-2
calculus
divergence
+
–
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