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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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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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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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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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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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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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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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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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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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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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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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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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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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GATE201842
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).
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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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GATE201825
Consider a unity feedback system with forward transfer function given by $G(s) = \frac{1}{(s+1)(s+2)}$ The steadystate error in the output of the system for a unitstep input is _______ (up to $2$ decimal places).
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GATE201824
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 noload speed of the motor (in $\text{radian /s}$) for an armature voltage of $150$ V is ____________ (up to $2$ decimal places).
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GATE201823
The waveform of the current drawn by a semiconverter 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).
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GATE201822
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ nonzero elements. The minimum number of branches (transmission lines and transformers) in this system are _________ (up to $2$ decimal places).
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GATE201821
The positive, negative and zero sequence impedances of a $125$ MVA, threephase, $15.5$ kV, stargounded, $50$ 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 at the rated ... $b$phase to ground fault (in kA) is __________ (up to $2$ decimal places).
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GATE201820
The series impedance matrix of a short threephase transmission line in phase coordinates is $\begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{bmatrix}$. If the positive sequence impedance is $(1+j \: 10) \Omega$, and the ... $(4+j \: 31) \Omega$, then the imaginary part of $Z_m$ (in $\Omega$) is ___________ (up to $2$ decimal places).
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GATE201819
In the twoport 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).
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GATE201818
Let $f$ be a realvalued 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).
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GATE201817
Consider a nonsingular $2 \times 2$ square matrix $\textbf{A}$. If $\textit{trace}(\textbf{A})=4$ and $\textit{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textbf{A}$ is _________ (up to $1$ decimal place).
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GATE2017126
A function $f(x)$ is defined as $f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$ Which one of the following statement is TRUE? $f(x)$ is NOT differentiable at $x=1$ for any values of $a$ ... $x=1$ for all values of $a$ and $b$ such that $a+b=e$. $f(x)$ is differentiable at $x=1$ for all values of $a$ and $b$.
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GATE2017255
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 of a soap (assuming ... , of the resulting single spherical drop with respect to the same reference point at infinity is _________. (Give the answer up to two decimal places.)
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GATE2017254
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 and delivering $60$ ... removed, assuming the acceleration is constant for $10$ cycles, the value of the power angle after $5$ cycles is __________ electrical degrees.
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GATE2017253
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.
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GATE2017252
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 ________.
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GATE2017251
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 conductors are ... the effect of ground, the magnitude of positive sequence reactance in $\Omega/km$ (rounded off to three decimal places) is _________.
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GATE2017250
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.)
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GATE2017249
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 _________.
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GATE2017248
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).
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GATE2017247
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 _______.
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GATE2017246
Consider the system described by the following state space representation ... $y(t)$ at $t=1$ sec (rounded off to three decimal places) is ___________.
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GATE2017245
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 _______.
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GATE2017244
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 shortcircuit condition. For the same field current, the opencircuit voltage is ... to terminal voltage), when the generator delivers the rated load at $0.8$ pf leading, at rated terminal voltage is _________.
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GATE2017243
A starconnected, $12.5$kW, $208$ V (line), $3$phase, $60$Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: $R_{1}=0.3 \Omega, R_{2}=0.3\Omega, X_{1}=0.41\Omega, X_{2}=0.41\Omega$. Neglect ... . The starting current (in Ampere) for this motor when connected to an $80$ V (line), $20$ Hz, $3$phase AC source is _________.
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GATE2017242
A $120$ V DC shunt motor takes $2$A at no load. It takes $7$A on full load while running at $1200$ rpm. The armature resistance is $0.8 \Omega$, and the shunt field resistance is $240 \Omega$. The no load speed, in rpm, is _________.
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