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361
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 ...
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362
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...
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363
GATE Electrical 2018 | Question: 39
The signal energy of he continuous-time signal $x(t)=[(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)]$ is $11/3$ $7/3$ $1/3$ $5/3$
The signal energy of he continuous-time signal $x(t)=[(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)]$ is$11/3$$7/3$$1/3$$5/3$
Arjun
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364
GATE Electrical 2018 | Question: 1
A single-phase $100$ kVA, $1000$ V / $100$ V, $50$ Hz transformer has a voltage has a voltage drop of $5 \%$ across its series impedance at full load. Of this, $3\%$ is due to resistance. The percentage regulation of the transformer at full load with $0.8$ lagging power factor is $4.8$ $6.8$ $8.8$ $10.8$
A single-phase $100$ kVA, $1000$ V / $100$ V, $50$ Hz transformer has a voltage has a voltage drop of $5 \%$ across its series impedance at full load. Of this, $3\%$ is d...
Arjun
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365
GATE Electrical 2018 | Question: 24
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produces a torque of $500$ Nm at zero speed. Neglecting all mechanical losses, the no- ... motor (in $\text{radian /s}$) for an armature voltage of $150$ V is ____________ (up to $2$ decimal places).
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produ...
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366
GATE Electrical 2018 | Question: 25
Consider a unity feedback system with forward transfer function given by $G(s) = \frac{1}{(s+1)(s+2)}$ The steady-state error in the output of the system for a unit-step input is _______ (up to $2$ decimal places).
Consider a unity feedback system with forward transfer function given by $$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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367
GATE Electrical 2018 | Question: 28
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$, the fault current is $I_{f1}= kI_f$, where $I_f$ is the fault current with zero fault impedance. The relation ... $Z_f=\frac{(Z_1+Z_2)k}{1-k} \\$ $Z_f=\frac{(Z_1+Z_2)k}{1+k}$
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$,...
Arjun
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368
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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369
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 ...
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370
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)...
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371
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 \...
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372
GATE Electrical 2018 | Question: 2
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is $0$ $45$ $60$ $90$
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is$0$$45$$60$$90$
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373
GATE Electrical 2018 | Question: 30
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, $P=1.4 \sin \delta + 0.15 \sin 2 \delta$, where $\delta$ is the load angle. Newton-Raphson method is used to calculate the value of $\delta$ ... at the end of the first iteration is $15^{\circ}$ $28.28^{\circ}$ $28.74^{\circ}$ $31.20^{\circ}$
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, $P=1.4 \sin \delta + 0.15 \sin 2 \delta$, where $...
Arjun
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374
GATE Electrical 2018 | Question: 31
A DC voltage source is connected to a series $L-C$ circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the following circular loci represents the plot of $i(t)$ versus $v(t)$?
A DC voltage source is connected to a series $L-C$ circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the fo...
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375
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...
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376
GATE Electrical 2018 | Question: 3
A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current? $v_o \geq 0$ & $i_o<0$ $v_o < 0$ & $i_o <0$ $v_o \geq 0$ & $i_o \geq 0$ $v_0 < 0$ & $i_o\geq 0$
A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the foll...
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377
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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378
GATE Electrical 2018 | Question: 10
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85 \times 10^{-12}$ F/m. The $Z$ component of the E field at $(0,0,0.1)$ is closest to $899.18$ V/m $-899.18$ V/m $999.09$ V/m $-999.09$ V/m
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85...
Arjun
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379
GATE Electrical 2018 | Question: 15
The op-amp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by $Z \frac{R_1}{R_2}$ $ – Z \frac{R_2}{R_1}$ $Z$ $ – Z \frac{R_1}{R_1 + R_2}$
The op-amp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by$Z \frac{R_1}{R_2}$$ – Z \frac{R_2}{R_1}$$Z$$ – Z \frac{...
Arjun
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380
GATE Electrical 2018 | Question: 16
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is $k \: x(t)$, where $k$ is an eigenvalue $k \: e^{j \omega t} \: x(t)$, where $k$ is an eigenvalue and $e^{j \omega t}$ is a complex ... $k \: H(\omega)$, where $k$ is an eigenvalue and $H(\omega)$ is a frequency response of the system
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is$k \: x(t)$, where $k$ is an eigenvalue$k \: e^{j \omega t} \: x(t)$, where $k...
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