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GATE2019 EE: 18
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(3,3,2)\rightarrow(2,3,2)\rightarrow(2,6,2) \rightarrow(2,6,1) $ is___________.
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GATE2019 EE: 19
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _________
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GATE2019 EE: 20
A coaxial Cylindrical capacitor is shown in the Figure(i) has dielectric with relative permittivity $\varepsilon_{r1} = 2$. When one – fourth portion of the dielectric is replaced with another dielectric of relative permittivity $\varepsilon_{r2}$, as shown in the Figure(ii), the capacitance is doubled. The value of $\varepsilon_{r2}$ is _________.
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GATE2019 EE: 21
The $Y_{\text{bus}}$ matrix of a twobus power system having two identical parallel lines connected between them in pu is given as $Y_{\text{bus}} = \begin{bmatrix} j8 & j20 \\ j20& j8 \end{bmatrix}$The magnitude of the series reactance of each line in pu (round off upto one decimal place) is__________.
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GATE2019 EE: 22
Five alternators each rated $5$ MVA, $13.2$ kV with $25 \%$ of reactance on its own base are connected in parallel to a busbar. The short circuit level in MVA at the busbar is ____________
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GATE2019 EE: 23
The total impedance of the secondary winding, leads, and burden of a $5$ A CT is $0.01 \: \Omega$. If the fault current is $20$ times the rated primary current of the CT, the VA output of the CT is_________
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GATE2019 EE: 24
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
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GATE2019 EE: 25
The output voltage of a singlephase fullbridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms Component of the output voltage to be $75 \%$ of DC voltage, the required pulse width in degrees (round off up to one decimal place) is ___________.
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GATE2019 EE: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
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GATE2019 EE: 40
The probability of a resistor being deflective is $0.02$. There are $50$ such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is _______________
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GATE2019 EE: 41
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to $1$ V is _________
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GATE2019 EE: 42
The current $I$ flowing in the circuit shown in amperes is ____________
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GATE2019 EE: 43
The voltage across and the current through a load are expressed as follows $v(t)=170 \sin \bigg( 377t \frac{\pi}{6} \bigg) V$ $i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \bigg) A$ The average power in watts (round off to one decimal place) consumed by the load is _________.
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GATE2019 EE: 44
The magnetic circuit shown below has uniform crosssectional area and air gap of $0.2$ cm. The mean path length of the core is $40$ cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the ... to be $1000$ (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is _______
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GATE2019 EE: 45
A singlephase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ________
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GATE2019 EE: 46
A $220$ V DC shunt motor takes $3$ A at noload. It draws $25$ A when running at fullload at $1500$ rpm. The armature and shunt resistance are $0.5 \: \Omega$ and $220 \: \Omega$, respectively. The noload speed in rpm (round off to two decimal places) is _____.
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GATE2019 EE: 47
A deltaconnected, $3.7$ kW, $400$ V(line), threephase, $4$pole, $50$Hz squirrelcage induction moor has the following equivalent circuit parameters per phase referred to the stator: $R_1=5.39 \: \Omega$, $R_2=5.72 \: \Omega$ ... in amperes (round off to two decimal places) when it is connected to a $100$ V(line), $10$ Hz, threephase AC source is _______
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GATE2019 EE: 48
A $220$ V(line), threephase, Yconnected, synchronous motor has a synchronous impedance of $(0.25+j2.5) \: \Omega/\text{phase}$. The motor draws the rated current of $10$ A at $0.8$ pf leading. The rms value of linetoline internal voltage in volts (round off to two decimal places) is _________
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GATE2019 EE: 49
A threephase $50$ Hz, $400$ kV transmission line is $300$ km long. The line inductance is $1$ mH/km per phase, and the capacitance is $0.01 \: \mu F/km$ per phase. The line is under open circuit condition at the receiving end and energized with $400$ kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be _________
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GATE2019 EE: 50
A $30$ kV, $50$ Hz, $50$ MVA generator has the positive, negative, and zero sequence reactances of $0.25$ pu, $0.15$ pu, and $0.05$ pu, respectively. The neutral of the generator is grounded with a reactance so that the fault ... bolted threephase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is ___________
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GATE2019 EE: 51
In the single machine infinite bus system shown below, the generator is delivering the real power of $0.8$ pu at $0.8$ power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is _________
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GATE2019 EE: 52
In a $132$ kV system, the series inductance up to the point of circuit breaker location is $50$ mH. The shunt capacitance at the circuit breaker terminal is $0.05 \: \mu F$. The critical value of resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is ______
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GATE2019 EE: 53
In a DCDC 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 and a very ... converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in $\mu H$) is ________
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GATE2019 EE: 54
A fullycontrolled threephase 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 _______
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GATE2019 EE: 55
A singlephase fullycontrolled thyristor converter is used to obtain an average voltage of $180$ V with $10$ A constant current to feed a DC load. It is fed from singlephase AC supply of $230$ V, $50$ Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is _________
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GATE201854
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 noload, the motor speed can be approximated to the synchronous speed. The noload lagging power factor of the motor is __________ (up to $3$ decimal places).
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GATE201855
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)
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GATE201848
The voltage across the circuit in the figure, and the current through it, are given by the following expressions: $v(t)=510 \cos (\omega t+ 60^{\circ}) \: V$ $i(t)=5 + X \cos (\omega t) \: A$ 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)
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GATE201851
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 $0.02 \: \Omega$. Iron loss of the transformer is $10 \: kW$. The full load $\%$ efficiency of the transformer operated at unity power factor is _______ (up to $2$ decimal places)
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GATE201852
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 same supply voltage, the load torque is increased by $44 \%$. The speed of the motor in r.p.m (rounded to the nearest integer) is _____________
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GATE201850
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 ripple. Both ... average value of $i_{s1}$, the current of switch $S1$ (in Ampere), is ____________ (up to $2$ decimal places).
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GATE201846
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).
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GATE201853
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 $5$ ... state and assuming the diode D to be ideal, the power transferred from $B1$ to $B2$ (in Watt) is ___________ (up to $2$ decimal places)
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GATE201849
A phase controlled single phase rectifier, supplied by an AC source, feeds power to an $RLE$ load as shown in the figure. The rectifier output voltage has an average value given by $V_{\text{o}}= \frac{V_m}{2 \pi} (3+\cos \alpha)$ ... firing angle. If the power delivered to the lossless battery is $1600$ W, $\alpha$ in degree is ___________ (up to $2$ decimal places).
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GATE201847
A threephase load is connected to a threephase balanced supply as shown in the figure. If $V_{\text{an}} = 100 \angle 0^{\circ} \: V$, $V_{\text{bn}}=100 \angle  120 ^{\circ} \: V$ ... positive in the anticlockwise direction), the value of $R$ for zero current in the neutral wire is __________ $\Omega$ (up to $2$ decimal places).
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GATE201843
Let $f(x) = 3x^37x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
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GATE201844
Let $A= \begin{bmatrix} 1 & 0 & 1 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ and $B=A^3A^24A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
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GATE201841
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$. The baseemitter 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)
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GATE201840
The Fourier transform of a continuoustime 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 $e$)
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GATE201845
The capacitance of an airfilled parallelplate 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)
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