List of top Questions asked in GATE Electrical Engineering

In the figure, the electric field \(E\) and the magnetic field \(B\) point to \(z\) and \(x\) directions, respectively, and have constant magnitudes. A positive charge \(q\) is released from rest at the origin. Which of the following statement(s) is/are true? \begin{center} \includegraphics[width=0.45\textwidth]{20.jpeg} \end{center}

Consider the OP AMP based circuit shown in the figure. Ignore the conduction drops of diodes \(D_1\) and \(D_2\). All the components are ideal and the breakdown voltage of the Zener is 5 V. Which of the following statements is true? \begin{center} \includegraphics[width=0.55\textwidth]{16.jpeg} \end{center}

Consider a lead compensator of the form \[ K(s) = \frac{1 + \tfrac{s}{a}}{1 + \tfrac{s}{\beta a}}, \beta > 1, \, a > 0 \] The frequency at which this compensator produces maximum phase lead is \(4 \, \text{rad/s}\). At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of \(K(s)\), is \(6 \, \text{dB}\). The values of \(a, \beta\), respectively, are:

A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is –400 W and the line current is \(I_R = 2 \, \text{A (rms)}\), then the power factor of the load per phase is: \begin{center} \includegraphics[width=0.65\textwidth]{17.jpeg} \end{center}

A 50 Hz, 275 kV line of length 400 km has the following parameters: Resistance, $R = 0.035 \,\Omega/\text{km}$
Inductance, $L = 1 \,\text{mH}/\text{km}$
Capacitance, $C = 0.01 \,\mu\text{F}/\text{km}$
The line is represented by the nominal-$\pi$ model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by $V_S$ and $V_R$, respectively) maintained at 275 kV, the phase angle difference $(\theta)$ between $V_S$ and $V_R$ required for maximum possible active power to be delivered to the receiving end, in degree is \underline{\hspace{2cm}} (Round off to 2 decimal places).

In the following differential equation, the numerically obtained value of $y(t)$ at $t=1$ is \underline{\hspace{3cm}} (Round off to 2 decimal places). \[ \frac{dy}{dt} = \frac{e^{-\alpha t}}{2 + \alpha t}, \alpha = 0.01, \, y(0)=0 \]

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is: \begin{center} \includegraphics[width=0.45\textwidth]{15.jpeg} \end{center}

For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t) = x(t) * y(t)$ is maximum at $t = T_{1$. Then $T_{1}$ in seconds is \underline{\hspace{1cm}} (Round off to the nearest integer).} \begin{center} \includegraphics[width=0.5\textwidth]{13.jpeg} \end{center}

For the circuit shown in the figure, $V_{1 = 8$ V, DC and $I_{1} = 8$ A, DC. The voltage $V_{ab}$ in Volts is \underline{\hspace{1cm}} (Round off to 1 decimal place).} \begin{center} \includegraphics[width=0.5\textwidth]{14.jpeg} \end{center}

The bus admittance ($Y_{\text{bus}}$) matrix of a 3-bus power system is given below. \[ Y_{\text{bus}} = \begin{bmatrix} -j15 & j10 & j5 \\ j10 & -j13.5 & j4 \\ j5 & j4 & -j8 \end{bmatrix} \] Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?

The value of parameters of the circuit shown in the figure are $R_{1 = 2\Omega, R_{2} = 2\Omega, R_{3} = 3\Omega, L = 10 \,\text{mH}, C = 100 \,\mu\text{F}$. For time $t < 0$, the circuit is at steady state with the switch $K$ in closed condition. If the switch is opened at $t = 0$, the value of the voltage across the inductor ($V_{L}$) at $t = 0^{+}$ in Volts is \underline{\hspace{3cm}} (Round off to 1 decimal place).} \begin{center} \includegraphics[width=0.5\textwidth]{12.jpeg} \end{center}

One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $\sigma_{0$. The $\sigma_{0}$ is estimated by randomly drawing out 10,000 samples $(x_{n})$. The estimates $\hat{\sigma}_{1}, \hat{\sigma}_{2}$ are computed in the following two ways:} \[ \hat{\sigma}_{1}^{2} = \frac{1}{10000}\sum_{n=1}^{10000} x_{n}^{2}, \hat{\sigma}_{2}^{2} = \frac{1}{9999}\sum_{n=1}^{10000} x_{n}^{2} \] Which of the following statements is true?

A semiconductor switch needs to block voltage $V$ of only one polarity ($V > 0$) during OFF state as shown in figure (i) and carry current in both directions during ON state as shown in figure (ii). Which of the following switch combination(s) will realize the same? \begin{center} \includegraphics[width=0.5\textwidth]{10.jpeg} \end{center}

The expressions of fuel cost of two thermal generating units as a function of the respective power generation $P_{G1$ and $P_{G2}$ are given as} \[ F_{1}(P_{G1}) = 0.1aP_{G1}^2 + 40P_{G1} + 120 \; \text{Rs/hour}, 0 \leq P_{G1} \leq 350 \, MW \] \[ F_{2}(P_{G2}) = 0.2P_{G2}^2 + 30P_{G2} + 100 \; \text{Rs/hour}, 0 \leq P_{G2} \leq 300 \, MW \] where $a$ is a constant. For a given value of $a$, optimal dispatch requires the total load of $290 \, MW$ to be shared as $P_{G1} = 175 \, MW$ and $P_{G2} = 115 \, MW$. With the load remaining unchanged, the value of $a$ is increased by $10%$ and optimal dispatch is carried out. The changes in $P_{G1}$ and in the total cost of generation, $F = F_{1} + F_{2}$, will be as follows:

The four stator conductors (A, A$'$, B and B$'$) of a rotating machine are carrying DC currents of the same value, the directions of which are shown in the figure (i). The rotor coils $a$–$a'$ and $b$–$b'$ are formed by connecting the back ends of conductors $a$ and $a'$, and $b$ and $b'$, respectively, as shown in figure (ii). The e.m.f. induced in coil $a$–$a'$ and coil $b$–$b'$ are denoted by $E_{a\text{–a'}$ and $E_{b\text{–}b'}$, respectively. If the rotor is rotated at uniform angular speed $\omega \, \text{rad/s}$ in the clockwise direction then which of the following correctly describes the $E_{a\text{–}a'}$ and $E_{b\text{–}b'}$?} \begin{center} \includegraphics[width=0.5\textwidth]{07.jpeg} \end{center}

The chopper circuit shown in figure (i) feeds power to a 5 A DC constant current source. The switching frequency of the chopper is $100 \,\text{kHz$. All the components can be assumed to be ideal. The gate signals of switches $S_{1}$ and $S_{2}$ are shown in figure (ii). The average voltage across the 5 A current source is:} \begin{center} \includegraphics[width=0.5\textwidth]{08.jpeg} \end{center}

In the figure, the vectors $\mathbf{u$ and $\mathbf{v}$ are related as: $A\mathbf{u} = \mathbf{v}$ by a transformation matrix $A$. The correct choice of $A$ is:} \begin{center} \includegraphics[width=0.5\textwidth]{09.jpeg} \end{center}

A continuous-time system that is initially at rest is described by: \[ \frac{dy(t)}{dt} + 3y(t) = 2x(t), \] where \(x(t)\) is the input voltage and \(y(t)\) is the output voltage. The impulse response of the system is:

The Fourier transform \(X(\omega)\) of the signal \(x(t)\) is given by \[ X(\omega) = \begin{cases} 1, & |\omega| < W_0
0, & |\omega| > W_0 \end{cases} \] Which one of the following statements is true?

The Z-transform of a discrete signal \(x[n]\) is \[ X(z) = \frac{4z}{\left(z-\tfrac{2}{3}\right)(z-3)}, \text{with ROC} = R. \] Which one of the following statements is true?

For the three-bus power system shown in the figure, the trip signals to the circuit breakers $B_{1$ to $B_{9}$ are provided by overcurrent relays $R_{1}$ to $R_{9}$, respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the R--L loads with isolation of minimum portion of the network using minimum number of directional relays is:} \begin{center} \includegraphics[width=0.5\textwidth]{06.jpeg} \end{center}

Consider a unity-gain negative feedback system consisting of the plant \(G(s)\) and a proportional-integral (PI) controller. \[ G(s) = \frac{1}{s-1} \] PI controller: \(C(s) = K_p + \frac{K_i}{s} = \frac{K_p s + K_i}{s}\). Given \(K_p = 3, K_i = 1\). For a unit step reference input, the final values of the controller output and the plant output are asked.