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1

GATE Electrical 2015 Set 1 | Question: 54
Find the transfer function $\dfrac{Y(s)}{X(s)}$ of the system given below $\dfrac{G_{1}}{1-HG_{1}} + \dfrac{G_{2}}{1-HG_{2}} \\$ $\dfrac{G_{1}}{1+HG_{1}} + \dfrac{G_{2}}{1+HG_{2}} \\$ $\dfrac{G_{1}+G_{2}}{1+H (G_{1}+G_{2})} \\$ $\dfrac{G_{1}+G_{2}}{1-H (G_{1}+G_{2})}$

Find the transfer function $\dfrac{Y(s)}{X(s)}$ of the system given below$\dfrac{G_{1}}{1-HG_{1}} + \dfrac{G_{2}}{1-HG_{2}} \\$$\dfrac{G_{1}}{1+HG_{1}} + \dfrac{G_{2}}{1+...

Lakshman Bhaiya

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Lakshman Bhaiya recategorized Mar 8, 2021

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GATE Electrical 2014 Set 3 | Question: 19
An $LPF$ wattmeter of power factor $0.2$ is having three voltage settings $300 V$, $150 V$ and $75 V$, and two current settings $5 A$ and $10 A$. The full scale reading is $150$. If the wattmeter is used with $150 V$ voltage setting and $10 A$ current setting, the multiplying factor of the wattmeter is _________.

An $LPF$ wattmeter of power factor $0.2$ is having three voltage settings $300 V$, $150 V$ and $75 V$, and two current settings $5 A$ and $10 A$. The full scale reading i...

Lakshman Bhaiya

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Lakshman Bhaiya recategorized Mar 8, 2021

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GATE Electrical 2014 Set 2 | Question: 47
Suppose that resistors $R_1$ and $R_2$ are connected in parallel to give an equivalent resistor $R$. If resistors $R_1$ and $R_2$ have tolerance of $1 \%$ each, the equivalent resistor $R$ for resistors $R_1=300\: \Omega$ and $R_2 = 200 \: \Omega$ will have tolerance of $0.5 \%$ $1 \%$ $1.2 \%$ $2 \%$

Suppose that resistors $R_1$ and $R_2$ are connected in parallel to give an equivalent resistor $R$. If resistors $R_1$ and $R_2$ have tolerance of $1 \%$ each, the equiv...

Lakshman Bhaiya

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Lakshman Bhaiya recategorized Mar 8, 2021

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4

GATE Electrical 2016 Set 1 | Question: 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 ... more than that of the inductance per conductor of the single-phase system. The distance $D$, in meters, is _________.

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 con...

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go_editor edited Oct 3, 2020

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GATE Electrical 2016 Set 1 | Question: 42
If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage, then $V_{AB}$ leads $V_{ab}$ by $60^\circ$ $V_{AB}$ lags $V_{ab}$ by $60^\circ$ $V_{AB}$ leads $V_{ab}$ by $30^\circ$ $V_{AB}$ lags $V_{ab}$ by $30^\circ$

If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage, then$V_{AB}$ leads $V_{ab}$ by $60^\circ$$V_{AB}$ lags $V_{a...

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go_editor edited Oct 3, 2020

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GATE Electrical 2016 Set 1 | Question: 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 ... The value of $X_{n}$ (in p.u.) that will limit the positive sequence generator current to $4270 \: A$ is ________.

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...

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go_editor edited Oct 3, 2020

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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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go_editor edited Oct 2, 2020

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GATE Electrical 2015 Set 1 | Question: 41
Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below: ... $200 \: MW$ is _______.

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are give...

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go_editor edited Sep 25, 2020

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9

GATE Electrical 2015 Set 1 | Question: 43
A $50 \text{ Hz}$ generating unit has H-constant of $2 \text{ MJ/MVA}$. The machine is initially operating in steady state at synchronous speed, and producing $1 \:pu$ of real power. The initial value of the rotor angle $\delta$ ... power to remain at $1 \: pu$, the value of $\delta$ in degrees, $0.02$ second after the fault is _________.

A $50 \text{ Hz}$ generating unit has H-constant of $2 \text{ MJ/MVA}$. The machine is initially operating in steady state at synchronous speed, and producing $1 \:pu$ of...

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go_editor edited Sep 25, 2020

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GATE Electrical 2015 Set 1 | Question: 42
Determine the correctness or otherwise of the following Assertion $[a]$ and the Reason $[r]$ ... $[a]$ and $[r]$ are false. $[a]$ is false and $[r]$ is true.

Determine the correctness or otherwise of the following Assertion $[a]$ and the Reason $[r]$.Assertion: Fast decoupled load flow method gives approximate load flow soluti...

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go_editor edited Sep 25, 2020

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GATE Electrical 2015 Set 1 | Question: 16
Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of $750$ MW from System $1$ to System $2$ ... $V_{1} = −500 \text{ kV} , V_{2} = −485 \text{ kV} $ and $I = −1.5 \text{ kA}$

Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of $750$ MW from System $1$ to System $2$, the voltage...

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go_editor edited Sep 25, 2020

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12

GATE Electrical 2015 Set 1 | Question: 12
A steady current $I$ is flowing in the $-x$ direction through each of two infinitely long wires at $y = \pm \dfrac{L}{2}$ as shown in the figure. The permeability of the medium is $\mu_{0}$. The $\overrightarrow{B}$-field at $(0,L,0)$ ... $+\dfrac{4\mu _{0}I}{3\Pi L} \hat{Z} \\$ $0 \\$ $-\dfrac{3\mu _{0}I}{4\Pi L} \hat{Z}$

A steady current $I$ is flowing in the $-x$ direction through each of two infinitely long wires at $y = \pm \dfrac{L}{2}$ as shown in the figure. The permeability of the ...

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go_editor edited Sep 25, 2020

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13

GATE Electrical 2014 Set 3 | Question: 53
A three-phase fully controlled bridge converter is fed through star-delta transformer as shown in the figure. The converter is operated at a firing angle of $300$. Assuming the load current $(I_0)$ to be virtually constant at $1 \: p.u$. and transformer to be an ideal one, the input phase current waveform is

A three-phase fully controlled bridge converter is fed through star-delta transformer as shown in the figure.The converter is operated at a firing angle of $300$. Assumin...

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go_editor edited Sep 25, 2020

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14

GATE Electrical 2014 Set 3 | Question: 43
The figure shows the single line diagram of a single machine infinite bus system. The inertia constant of the synchronous generator $H = 5 \: MW-s/MVA$. Frequency is $50 \: Hz$. Mechanical power is $1 \: pu$. The system is operating at the stable ... $3.762 \text{ radian/s}$ respectively, then $P_{\text{max}}$ (in $pu$) is _______.

The figure shows the single line diagram of a single machine infinite bus system.The inertia constant of the synchronous generator $H = 5 \: MW-s/MVA$. Frequency is $50 \...

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go_editor edited Sep 24, 2020

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15

GATE Electrical 2014 Set 3 | Question: 42
The complex power consumed by a constant-voltage load is given by $(P_1+jQ_1)$, where, $1 \: kW \leq P_1 \leq 1.5 \text{ kW}$ and $0.5 \: \text{kVAR} \leq Q_1 \leq 1 \text{ kVAR}$. A compensating shunt ... is the net reactive power consumed by the capacitor-load combination. The reactive power (in $\text{kVAR}$) supplied by the capacitor is _________.

The complex power consumed by a constant-voltage load is given by $(P_1+jQ_1)$, where, $1 \: kW \leq P_1 \leq 1.5 \text{ kW}$ and $0.5 \: \text{kVAR} \leq Q_1 \leq 1 \te...

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go_editor edited Sep 24, 2020

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16

GATE Electrical 2014 Set 3 | Question: 6
The line $A$ to neutral voltage is $10\angle 15^\circ$ for a balanced three phase star-connected load with phase sequence $ABC$. The voltage of line $B$ with respect to line $C$ is given by $10\sqrt{3}\angle 105^\circ$ $10\angle 105^\circ$ $10\sqrt{3}\angle -75^\circ$ $-10\sqrt{3}\angle 90^\circ$

The line $A$ to neutral voltage is $10\angle 15^\circ$ for a balanced three phase star-connected load with phase sequence $ABC$. The voltage of line $B$ with respect to ...

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go_editor edited Sep 24, 2020

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17

GATE Electrical 2016 Set 2 | Question: 53
Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedances of $j0.4$ p.u., $j0.3$ p.u. and $j0.15$ p.u., respectively. If the pre-fault ... a line-to-ground $(L-G)$ fault at the terminals of the generators, the fault current, in p.u., is ___________.

Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedances of $j0....

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go_editor retagged Dec 6, 2019

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18

GATE Electrical 2016 Set 2 | Question: 54
An energy meter, having meter constant of $1200$ revolutions/kWh, makes $20$ revolutions in $30$ seconds for a constant load. The load, in $kW$, is __________.

An energy meter, having meter constant of $1200$ revolutions/kWh, makes $20$ revolutions in $30$ seconds for a constant load. The load, in $kW$, is __________.

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go_editor retagged Dec 6, 2019

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19

GATE Electrical 2016 Set 2 | Question: 44
A single-phase, $2$ kVA, $100/200$ V transformer is reconnected as an auto-transformer such that its $kVA$ rating is maximum. The new rating, in $kVA$, is ______.

A single-phase, $2$ kVA, $100/200$ V transformer is reconnected as an auto-transformer such that its $kVA$ rating is maximum. The new rating, in $kVA$, is ______.

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go_editor retagged Dec 6, 2019

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20

GATE Electrical 2016 Set 2 | Question: 41
The power consumption of an industry is $500$ kVA, at $0.8$ p.f. lagging. A synchronous motor is added to raise the power factor of the industry to unity. If the power intake of the motor is $100$ kW, the p.f. of the motor is ___________.

The power consumption of an industry is $500$ kVA, at $0.8$ p.f. lagging. A synchronous motor is added to raise the power factor of the industry to unity. If the power in...

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go_editor retagged Dec 6, 2019

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21

GATE Electrical 2016 Set 2 | Question: 40
At no load condition, a $3$-phase, $50$ Hz, lossless power transmission line has sending-end and receiving-end voltages of $400$ kV and $420$ kV respectively. Assuming the velocity of traveling wave to be the velocity of light, the length of the line, in km, is ____________.

At no load condition, a $3$-phase, $50$ Hz, lossless power transmission line has sending-end and receiving-end voltages of $400$ kV and $420$ kV respectively. Assuming th...

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22

GATE Electrical 2016 Set 2 | Question: 38
The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and $1.0$ p.u. The p.u. reactances of different components in the system are ... transferred during the pre-fault condition to the maximum real power that can be transferred under the faulted condition is _________.

The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and $1.0$ p.u. The p.u. reactan...

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go_editor retagged Dec 6, 2019

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23

GATE Electrical 2016 Set 2 | Question: 36
In the balanced $3$-phase, $50$ Hz, circuit shown below, the value of inductance $(L)$ is $10$ mH. The value of the capacitance $(C)$ for which all the line currents are zero, in millifarads, is ___________.

In the balanced $3$-phase, $50$ Hz, circuit shown below, the value of inductance $(L)$ is $10$ mH. The value of the capacitance $(C)$ for which all the line currents are ...

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go_editor retagged Dec 6, 2019

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GATE Electrical 2016 Set 2 | Question: 35
The $z$-parameters of the two port network shown in the figure are $z_{11}=40\Omega, z_{12}=60\Omega, z_{21}=80\Omega$ and $z_{22}=100\Omega$. The average power delivered to $R_{L}=20\Omega$, in watts, is ________.

The $z$-parameters of the two port network shown in the figure are $z_{11}=40\Omega, z_{12}=60\Omega, z_{21}=80\Omega$ and $z_{22}=100\Omega$. The average power delivered...

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25

GATE Electrical 2016 Set 2 | Question: 12
The voltage $(V)$ and current $(A)$ across a load are as follows. $v(t)=100\sin$ (ωt), $i(t)=10\sin(ωt-60°) + 2\sin(3ωt)+5\sin(5ωt)$ The average power consumed by the load, in $W$, is _________.

The voltage $(V)$ and current $(A)$ across a load are as follows.$v(t)=100\sin$ (ωt),$i(t)=10\sin(ωt-60°) + 2\sin(3ωt)+5\sin(5ωt)$The average power consumed by the l...

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go_editor retagged Dec 6, 2019

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GATE Electrical 2016 Set 1 | Question: 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- ... voltage is $3.3 kV$, $50 Hz$, the capacitance per phase of the bank, expressed in microfarads, is ________.

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 wi...

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go_editor retagged Dec 4, 2019

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27

GATE Electrical 2016 Set 1 | Question: 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 ... $0.8$ pu. The voltage magnitude at bus $A$ during a three-phase fault at bus $B$, in pu, is __________.

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 conside...

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go_editor retagged Dec 4, 2019

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GATE Electrical 2015 Set 1 | Question: 51
Two single-phase transformers $T_{1}$ and $T_{2}$ each rated at $500$ kVA are operated in parallel. Percentage impedances of $T_{1}$ and $T_{2}$ are $(1 + j6)$ and $(0.8 + j4.8)$, respectively. To share a load of $1000$ kVA at $0.8$ lagging power factor, the contribution of $T_{2}$ (in kVA) is _______.

Two single-phase transformers $T_{1}$ and $T_{2}$ each rated at $500$ kVA are operated in parallel. Percentage impedances of $T_{1}$ and $T_{2}$ are $(1 + j6)$ and $(0.8 ...

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go_editor retagged Dec 4, 2019

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29

GATE Electrical 2014 Set 3 | Question: 41
For a $400$ $km$ long transmission line, the series impedance is ($0.0$ + $j0.5$) $Ω/km$ and the shunt admittance is ($0.0$ + $j5.0$) $μmho$/$km$. The magnitude of the series impedance (in $\Omega$) of the equivalent $\pi$ circuit of the transmission line is ________.

For a $400$ $km$ long transmission line, the series impedance is ($0.0$ + $j0.5$) $Ω/km$ and the shunt admittance is ($0.0$ + $j5.0$) $μmho$/$km$. The magnitude of the ...

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go_editor retagged Dec 3, 2019

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GATE Electrical 2014 Set 3 | Question: 16
A $183$-bus power system has $150$ $PQ$ buses and $32$ $PV$ buses. In the general case, to obtain the load flow solution using Newton-Raphson method in polar coordinates, the minimum number of simultaneous equations to be solved is ___________.

A $183$-bus power system has $150$ $PQ$ buses and $32$ $PV$ buses. In the general case, to obtain the load flow solution using Newton-Raphson method in polar coordinates,...

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go_editor retagged Dec 3, 2019

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31

GATE Electrical 2014 Set 2 | Question: 43
Three phase $100$ $MVA$ ,$25$ $kV$ generator has solidly grounded neutral. The positive, negative, and the zero sequence reactances of the generator are $0.2$ $pu$, $0.2$ $pu$, and $0.05$ $pu$, respectively, at ... phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is _________.

Three phase $100$ $MVA$ ,$25$ $kV$ generator has solidly grounded neutral. The positive, negative, and the zero sequence reactances of the generator are $0.2$ $pu$, $0.2$...

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go_editor retagged Dec 2, 2019

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32

GATE Electrical 2014 Set 2 | Question: 41
There are two generators in a power system. No-load frequencies of the generators are $51.5$ $Hz$ and $51$ $Hz$, respectively, and both are having droop constant of $1$ $Hz$/$MW$. Total load in the system is ... are operating under their respective droop characteristics, the frequency of the power system in $Hz$ in the steady state is ___________.

There are two generators in a power system. No-load frequencies of the generators are $51.5$ $Hz$ and $51$ $Hz$, respectively, and both are having droop constant of $1$ $...

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go_editor retagged Dec 2, 2019

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33

GATE Electrical 2014 Set 2 | Question: 40
A synchronous generator is connected to an infinite bus with excitation voltage $E_f$ = $1.3$ $pu$. The generator has a synchronous reactance of $1.1$ $pu$ and is delivering real power $(P)$ of $0.6$ $pu$ to the bus. ... Neglect stator resistance. The reactive power $(Q)$ in $pu$ supplied by the generator to the bus under this condition is _________.

A synchronous generator is connected to an infinite bus with excitation voltage $E_f$ = $1.3$ $pu$. The generator has a synchronous reactance of $1.1$ $pu$ and is deliver...

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go_editor retagged Dec 2, 2019

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34

GATE Electrical 2014 Set 2 | Question: 6
Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are $380$ $μH$ and $240$ $μH$. Their mutual inductance in $μH$ is ________

Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are $380$ $μH$ and $240$ $μH$. Their mutual in...

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go_editor retagged Dec 2, 2019

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35

GATE Electrical 2014 Set 2 | Question: 20
While measuring power of a three-phase balanced load by the two-wattmeter method, the readings are $100$ $W$ and $250$ $W$. The power factor of the load is ______.

While measuring power of a three-phase balanced load by the two-wattmeter method, the readings are $100$ $W$ and $250$ $W$. The power factor of the load is ______.

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go_editor retagged Dec 2, 2019

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36

GATE Electrical 2014 Set 2 | Question: 15
A three phase star-connected load is drawing power at a voltage of $0.9$ $pu$ and $0.8$ power factor lagging. The three phase base power and base current are $100$ $MVA$ and $437.384$ $A$ respectively. The line-to-line load voltage in $kV$ is ________.

A three phase star-connected load is drawing power at a voltage of $0.9$ $pu$ and $0.8$ power factor lagging. The three phase base power and base current are $100$ $MVA$ ...

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go_editor retagged Dec 2, 2019

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37

GATE Electrical 2014 Set 2 | Question: 12
A single phase, $50$ $kVA$, $1000V$/$100V$ two winding transformer is connected as an autotransformer as shown in the figure. The $kVA$ rating of the autotransformer is _____________.

A single phase, $50$ $kVA$, $1000V$/$100V$ two winding transformer is connected as an autotransformer as shown in the figure.The $kVA$ rating of the autotransformer is __...

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GATE Electrical 2014 Set 1 | Question: 16
A $2$-bus system and corresponding zero sequence network are shown in the figure. The transformers $T_1$and $T_2$ are connected as

A $2$-bus system and corresponding zero sequence network are shown in the figure. The transformers $T_1$and $T_2$ are connected as

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go_editor edited Dec 2, 2019

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39

GATE Electrical 2014 Set 1 | Question: 45
The Bode magnitude plot of the transfer function $G(s)=\dfrac{K(1+0.5s)(1+as)}{s(1+\frac{s}{8})(1+bs)(1+\frac{s}{36})}$ is shown below: Note that $-6dB/octave = -20 dB/decade.$ The value of $\dfrac{a}{bK}$ is ________.

The Bode magnitude plot of the transfer function $G(s)=\dfrac{K(1+0.5s)(1+as)}{s(1+\frac{s}{8})(1+bs)(1+\frac{s}{36})}$ is shown below:Note that $-6dB/octave = -20 dB/dec...

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40

GATE Electrical 2014 Set 1 | Question: 43
The overcurrent relays for the line protection and loads connected at the buses are shown in the figure. The relays are $IDMT$ ... relay $R_B$ to be $0.1$ and $5A$ respectively, the operating time of $R_B$ (in seconds) is ______________

The overcurrent relays for the line protection and loads connected at the buses are shown in the figure.The relays are $IDMT$ in nature having the characteristic$t_{op}=\...

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go_editor retagged Dec 2, 2019

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