Recent questions tagged gate2016-ee-2

The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function $G(s)=\frac{Ks}{(s-1)(s-4)}$ is$1$$2$ $5$$9$

Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedances of $j0....

An energy meter, having meter constant of $1200$ revolutions/kWh, makes $20$ revolutions in $30$ seconds for a constant load. The load, in $kW$, is __________.

A rotating conductor of $1$ m length is placed in a radially outward (about the $z$-axis) magnetic flux density $(B)$ of $1$ Tesla as shown in figure below. Conductor is ...

Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ co...

A single-phase bi-directional voltage source converter $(VSC)$ is shown in the figure below. All devices are ideal. It is used to charge a battery at $400$ V with power o...

A second-order real system has the following properties:a) the damping ratio $\zeta=0.5$ and undamped natural frequency $\omega _{n}=10$ rad/sb) the steady state value of...

Three single-phase transformers are connected to form a delta-star three-phase transformer of $110$ kV/ $11$ kV. The transformer supplies at $11$ kV a load of $8$ MW at $...

A full-bridge converter supplying an $RLE$ load is shown in figure. The firing angle of the bridge converter is $120$°. The supply voltage $v_{m}(t) =200\pi \sin (100\pi ...

A $DC-DC$ boost converter, as shown in the figure below, is used to boost $360$ V to $400$ V, at a power of $4$ kW. All devices are ideal. Considering continuous inductor...

A three-phase Voltage Source Inverter $(VSI)$ as shown in the figure is feeding a delta connected resistive load of $30 \Omega$/phase. If it is fed from a $600$ V battery...

A single-phase, $2$ kVA, $100/200$ V transformer is reconnected as an auto-transformer such that its $kVA$ rating is maximum. The new rating, in $kVA$, is ______.

The starting line current of a $415$ V, $3$-phase, delta connected induction motor is $120$ A, when the rated voltage is applied to its stator winding. The starting line ...

The power consumption of an industry is $500$ kVA, at $0.8$ p.f. lagging. A synchronous motor is added to raise the power factor of the industry to unity. If the power in...

At no load condition, a $3$-phase, $50$ Hz, lossless power transmission line has sending-end and receiving-end voltages of $400$ kV and $420$ kV respectively. Assuming th...

In the balanced $3$-phase, $50$ Hz, circuit shown below, the value of inductance $(L)$ is $10$ mH. The value of the capacitance $(C)$ for which all the line currents are ...

The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and $1.0$ p.u. The p.u. reactan...

In the circuit shown below, the initial capacitor voltage is $4 V$. Switch $S_{1}$ is closed at $t=0$. The charge (in $\mu C$) lost by the capacitor from $t=25 \mu s$ to ...

The open loop transfer function of a unity feedback control system is given by$G(s)=\frac{k(s+1)}{s(1+Ts)(1+2S)'}, K 0, T 0.$The closed loop system will be stable if$0 ...

Let the probability density function of a random variable, $X$, be given as:$f_{x}(x)=\frac{3}{2}e^{-3x}u(x)+ae^{4x}u(-x)$where u(x) is the unit step function.Then the va...

The $z$-parameters of the two port network shown in the figure are $z_{11}=40\Omega, z_{12}=60\Omega, z_{21}=80\Omega$ and $z_{22}=100\Omega$. The average power delivered...

The driving point input impedance seen from the source $V_{s}$ of the circuit shown below, in $\Omega$, is ______.

Let $P=\begin{bmatrix} 3&1 \\ 1 & 3\end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix}x\\ y\end{pmatrix}$ such that $a^{2}+b^{2}=1$ where $\begin{pmatrix}...

Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then...

The value of the integral $2\int_{-\infty}^{\infty} (\frac{\sin2\pi t}{\pi t}) \text{d}t$ is equal to$0$$0.5$ $1$$2$

The line integral of the vector field $F=5xz \hat{i}+(3x^{2}+2y)\hat{j}+x^{2}z\hat{k}$ along a path from $(0,0,0)$ to $(1,1,1)$ parametrized by $(t, t^{2}, t)$ is _______...

The Boolean expression $\overline{(a+\bar{b}+c+\bar{d})+(b+\bar{c})}$ simplifies to$1$$\overline{a.b}$$a.b$$0$

Let $x_{1}(t)\leftrightarrow X_{1}(\omega )$ and $x_{2}(t)\leftrightarrow X_{2}(\omega )$ be two signals whose Fourier Transforms are as shown in the figure below. In the...

For the circuit shown below, taking the opamp as ideal, the output voltage $V_{out}$ in terms of the input voltages $V_{1}, V_{2}$ and $V_{3}$ is$1.8V_{1} + 7.2V_{2} -V_{...