Recent questions tagged gate2015-ee-2

An open loop transfer function $G(s)$ of a system is$G(s)=\dfrac{k}{s(s+1)(s+2)}$For a unity feedback system, the breakaway point of the root loci on the real axis occurs...

The unit step response of a system with the transfer function $G(s)=\dfrac{1-2s}{1+s}$ is given by which one of the following waveforms?

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables ...

Two three-phase transformers are realized using single-phase transformers as shown in the figure.The phase difference (in degree) between voltages $V_{1}$ and $V_{2}$ is ...

For the system governed by the set of equations:$dx_{1}/dt=2x_{1}+x_{2}+u$$dx_{2}/dt=-2x_{1}+u$$y=3 x_{1}$the transfer function $Y(s)/U(s)$ is given by$3(s+1)/(s^{2}-2s+2...

A three-winding transformer is connected to an $AC$ voltage source as shown in the figure. The number of turns are as follows: $N_{1} = 100, N_{2} = 50, N_{3} = 50$. If t...

The saturation voltage of the ideal op-amp shown below is $\pm 10$ V. The output voltage $v_{o}$ of the following circuit in the steady-state isSquare wave of period $0.5...

A $220$ V, $3$-phase, $4$-pole, $50$ Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and c...

The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers $P_{1}$ and $P_{2}$ in $MW$, and are given by$\dfrac{dC_{...

A symmetrical square wave of $50\%$ duty cycle has amplitude of $\pm15$ V and time period of $0.4\pi$ ms. This square wave is applied across a series $RLC$ circuit with $...

A balanced (positive sequence) three-phase $AC$ voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. Th...

A three-phase, $11$ kV, $50$ Hz, $2$ pole, star connected, cylindrical rotor synchronous motor is connected to an $11$ kV, $50$ Hz source. Its synchronous reactance is $5...

With an armature voltage of $100$ V and rated field winding voltage, the speed of a separately excited $DC$ motor driving a fan is $1000$ rpm, and its armature current is...

Two identical coils each having inductance $L$ are placed together on the same core. If an overall inductance of $\alpha L$ is obtained by interconnecting these two coils...

A composite conductor consists of three conductors of radius $R$ each. The conductors are arranged as shown below. The geometric mean radius $(GMR)$ (in cm) of the compos...

In the given network $V_{1}=100\angle 0^{\circ}V, V_{2}=100\angle -120^{\circ}V, V_{3}=100\angle +120^{\circ}V$. The phasor current $i$ (in Ampere) is$173.2\angle -60^{\c...

A 3-phase transformer rated for $33 kV/11 kV$ is connected in delta/star as shown in figure. The current transformers ($CTs$) on low and high voltage sides have a ratio o...

In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is $Q_{1}Q_{0}=00$. The state $(Q_{1}Q_{0})$, immediately after the $...

Consider a signal defined by$x(t)= \begin{cases} e^{j10 t} & \text{for } \mid t \mid \leq 1 \\ 0& \text{for } \mid t \mid 1\end{cases}$Its Fourier Transform is$\dfrac...

Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $...

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of $+Q$ is placed at a distance of $d$ from both sheet...

A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.

In the given rectifier, the delay angle of the thyristor $T_{1}$ measured from the positive going zero crossing of $V_{s}$ is $30^\circ$. If the input voltage $V_{s}$ is ...

A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch $S$ is $100$ kHz and the duty ratio is $0.6$. The output ...

For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE?The impulse response will be integrable, bu...

For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positi...

The coils of a wattmeter have resistances $0.01 \Omega$ and $1000 \Omega$; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measu...

The $z$-Transform of a sequence $x[n]$ is given as $X(z)=2z+4-4/z+3/z^{2}$. If $y[n]$ is the first difference of $x[n]$, then $Y(z)$ is given by$2z+2-8/z+7/z^{2}-3/z^{3}$...

Nyquist plots of two functions $G_{1}(s)$ and $G_{2}(s)$ are shown in figure.Nyquist plot of the product of $G_{1}(s)$ and $G_{2}(s)$ is