Recent questions tagged numerical-answers / GO Electrical

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121

GATE Electrical 2019 | Question: 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 ... operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in $\mu H$) is ________

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 switch...

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122

GATE Electrical 2019 | Question: 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 _______

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 l...

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123

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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Arjun asked Feb 19, 2018

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124

GATE Electrical 2018 | Question: 54
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S$ is the slip. At no-load, the motor speed can be approximated to the synchronous speed. The no-load lagging power factor of the motor is __________ (up to $3$ decimal places).

The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S...

Arjun

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125

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 ...

Arjun

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126

GATE Electrical 2018 | Question: 52
A $200$ V DC series motor, when operating from rated voltage while driving a certain load, draws $10$ A current and runs at $1000$ r.p.m. The total series resistance is $1 \: \Omega$. The magnetic circuit is assumed to be linear. At the ... the load torque is increased by $44 \%$. The speed of the motor in r.p.m (rounded to the nearest integer) is _____________

A $200$ V DC series motor, when operating from rated voltage while driving a certain load, draws $10$ A current and runs at $1000$ r.p.m. The total series resistance is $...

Arjun

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Arjun asked Feb 19, 2018

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127

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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128

GATE Electrical 2018 | Question: 50
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of identical value. The load resistance is $1 \: \Omega$. The capacitor voltage has negligible ... of $i_{s1}$, the current of switch $S1$ (in Ampere), is ____________ (up to $2$ decimal places).

The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of ide...

Arjun

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129

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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130

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 \...

Arjun

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131

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...

Arjun

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Arjun asked Feb 19, 2018

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132

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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133

GATE Electrical 2018 | Question: 44
Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).

Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$...

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134

GATE Electrical 2018 | Question: 43
Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).

Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).

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135

GATE Electrical 2018 | Question: 42
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).

As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$...

Arjun

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136

GATE Electrical 2018 | Question: 40
The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{-1}$ and $\omega$ denoes frequency. Then the value of $\mid \text{ln } x(t) \mid$ at $t=1$ is _________ (up to $1$ decimal place). ($\text{ln}$ denotes the logarithm base $e$)

The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{-1}$ and $\om...

Arjun

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137

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 ...

Arjun

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138

GATE Electrical 2018 | Question: 41
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$. The base-emitter voltage drop is a constant, $V_{BE}=0.7 \: V$. The value of the Thevenin equivalent resistance $R_{Th}$ (in $\Omega$) as shown in the figure is _________ (up to $2$ decimal places)

In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$. The base-emitter voltage drop is a constant, $V_{BE}=0.7 \: V$...

Arjun

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139

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...

Arjun

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140

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...

Arjun

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141

GATE Electrical 2018 | Question: 18
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).

Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0...

Arjun

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142

GATE Electrical 2018 | Question: 17
Consider a non-singular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textbf{A}$ is _________ (up to $1$ decimal place).

Consider a non-singular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textb...

Arjun

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143

GATE Electrical 2018 | Question: 23
The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If $I_0=20$ A, the rms value of fundamental component of the current is ________ A (up to $2$ decimal places).

The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If $I_0=20$ A, the rms value of fundamental component of...

Arjun

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144

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)...

Arjun

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Arjun asked Feb 19, 2018

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145

GATE Electrical 2018 | Question: 21
The positive, negative and zero sequence impedances of a $125$ MVA, three-phase, $15.5$ kV, star-gounded, $50$ Hz generator are $j0.1$ pu, $j0.05$ pu and $j0.01$ pu respectively on the machine rating base. The machine is unloaded and working ... then the magnitude of fault current for a $b$-phase to ground fault (in kA) is __________ (up to $2$ decimal places).

The positive, negative and zero sequence impedances of a $125$ MVA, three-phase, $15.5$ kV, star-gounded, $50$ Hz generator are $j0.1$ pu, $j0.05$ pu and $j0.01$ pu respe...

Arjun

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146

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...

Arjun

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Arjun asked Feb 19, 2018

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147

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).

Arjun

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148

GATE Electrical 2017 Set 2 | Question: 49
For the synchronous sequential circuit shown below, the output $Z$ is zero for the initial conditions $Q_{A}, Q_{B}, Q_{C}= Q'_{A}, Q'_{B}, Q'_{C}=100$ The minimum number of clock cycles after which the output $Z$ would again become zero is _________.

For the synchronous sequential circuit shown below, the output $Z$ is zero for the initial conditions $Q_{A}, Q_{B}, Q_{C}= Q'_{A}, Q'_{B}, Q'_{C}=100$The minimum number ...

Arjun

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149

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...

Arjun

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150

GATE Electrical 2017 Set 2 | Question: 54
A $3$-phase, $2$-pole, $50$Hz, synchronous generator has a rating of $250$ MVA, $0.8$ pf lagging. The kinetic energy of the machine at synchronous speed is $1000$MJ. The machine is running steadily at synchronous speed ... assuming the acceleration is constant for $10$ cycles, the value of the power angle after $5$ cycles is __________ electrical degrees.

A $3$-phase, $2$-pole, $50$Hz, synchronous generator has a rating of $250$ MVA, $0.8$ pf lagging. The kinetic energy of the machine at synchronous speed is $1000$MJ. The ...

Arjun

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151

GATE Electrical 2017 Set 2 | Question: 53
Two generating units rated $300$MW and $400$MW have governor speed regulation of $6 \%$ and $4 \%$ respectively from no load to full load. Both the generating units are operating in parallel to share a load of $600$MW. Assuming free governor action, the load shared by the larger unit is _________ MW.

Two generating units rated $300$MW and $400$MW have governor speed regulation of $6 \%$ and $4 \%$ respectively from no load to full load. Both the generating units are o...

Arjun

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152

GATE Electrical 2017 Set 2 | Question: 52
A $3$-phase, $50$Hz generator supplies power of $3$MW at $17.32$kV to a balanced $3$-phase inductive load through an overhead line. The per phase line resistance and reactance are $0.25 \Omega$ and $3.925 \Omega$ respectively. If the voltage at the generator terminal is $17.87$kV, the power factor of the load is ________.

A $3$-phase, $50$Hz generator supplies power of $3$MW at $17.32$kV to a balanced $3$-phase inductive load through an overhead line. The per phase line resistance and reac...

Arjun

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153

GATE Electrical 2017 Set 2 | Question: 51
Consider an overhead transmission line with $3$-phase, $50$ Hz balanced system with conductors located at the vertices of an equilateral triangle of length $D_{ab}=D_{bc}=D_{ca}=1m$ as shown in figure below. The resistance of the ... of ground, the magnitude of positive sequence reactance in $\Omega/km$ (rounded off to three decimal places) is _________.

Consider an overhead transmission line with $3$-phase, $50$ Hz balanced system with conductors located at the vertices of an equilateral triangle of length $D_{ab}=D_{bc}...

Arjun

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154

GATE Electrical 2017 Set 2 | Question: 50
In the circuit shown all elements are ideal and the switch $S$ is operated at $10$kHz and $60 \%$ duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the $50$ V DC source is _______.(Give the answer up to one decimal place.)

In the circuit shown all elements are ideal and the switch $S$ is operated at $10$kHz and $60 \%$ duty ratio. The capacitor is large enough so that the ripple across it i...

Arjun

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155

GATE Electrical 2017 Set 2 | Question: 48
In the circuit shown in the figure, the diode used is ideal. The input power factor is ________. (Give the answer up to two decimal places).

In the circuit shown in the figure, the diode used is ideal. The input power factor is ________. (Give the answer up to two decimal places).

Arjun

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156

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...

Arjun

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157

GATE Electrical 2017 Set 2 | Question: 46
Consider the system described by the following state space representation ... $y(t)$ at $t=1$ sec (rounded off to three decimal places) is ___________.

Consider the system described by the following state space representation$\begin{bmatrix}\dot{x}_{1}(t)\\\dot{x}_{2}(t)\end{bmatrix}=\begin{bmatrix}0 &1 \\0 & -2\end{bmat...

Arjun

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158

GATE Electrical 2017 Set 2 | Question: 45
If the primary line voltage rating is $3.3$kV (Y side) of a $25$kVA, $Y-\Delta$ transformer (the per phase turns ratio is $5:1$), then the line current rating of the secondary side (in Ampere) is _______.

If the primary line voltage rating is $3.3$kV (Y side) of a $25$kVA, $Y-\Delta$ transformer (the per phase turns ratio is $5:1$), then the line current rating of the seco...

Arjun

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159

GATE Electrical 2017 Set 2 | Question: 44
A $25$ kVA, $400$ V, $\Delta$-connected, $3$-phase, cylindrical rotor synchronous generator requires a field current of $5$ A to maintain the rated armature current under short-circuit condition. For the same field current, the open ... terminal voltage), when the generator delivers the rated load at $0.8$ pf leading, at rated terminal voltage is _________.

A $25$ kVA, $400$ V, $\Delta$-connected, $3$-phase, cylindrical rotor synchronous generator requires a field current of $5$ A to maintain the rated armature current under...

Arjun

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160

GATE Electrical 2017 Set 2 | Question: 43
A star-connected, $12.5$kW, $208$ V (line), $3$-phase, $60$ ... starting current (in Ampere) for this motor when connected to an $80$ V (line), $20$ Hz, $3$-phase AC source is _________.

A star-connected, $12.5$kW, $208$ V (line), $3$-phase, $60$Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: ...

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