GATE EC question library

In the circuit shown below, $V_{s}$ is a constant voltage source and $I_{L}$ is a constant current load. The value of $I_{L}$ that maximizes the power absorbed by the constant current load is

The switch has been in position $1$ for a long time and abruptly changes to position $2$ at $t = 0$. If time $t$ is in seconds, the capacitor voltage $V_{C}$ (in volts) for $t > 0$ is given by

The figure shown an $RLC$ circuit with a sinusoidal current source. At resonance, the ratio $\mid I_{L} \mid / \mid I_{R} \mid$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________

The $z$-parameter matrix for the two-port network shown is $$\begin{bmatrix} 2j\omega &j\omega \\ j\omega & 3+2j\omega \end{bmatrix},$$ where the entries are in $\Omega$. Suppose $Z_{b}\left ( j\omega \right )=R_{b}+j\omega .$ Then the value of $R_{b}$ (in $\Omega$) equals ________

The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________

The Ebers-Moll model of a $BJT$ is valid

A long-channel $NMOS$ transistor is biased in the linear region with $V_{DS}=50$ $m$ $V$ and is used as a resistance. Which one of the following statement is $NOT$ correct?

Assume that the diode in the figure has $V_{on}=0.7 \:V$, but it otherwise ideal. The magnitude of the current $i_{2}$ in mA) is equal to _________

Resistor $R_{1}$ in the circuit below has been adjusted so that $I_{1}=1$ $mA$. The bipolar transistors $Q1$ and $Q2$ are perfectly matched and have very high current gain, so their base currents are negligible. The supply voltage $V_{cc}$ is $6$ $V$. The thermal voltage $KT/q$ is $26$ $mV$. The value of $R_{2}$ (in $\Omega)$ for …

Which one of the following statements is correct about an ac-coupled common-emitter amplifier operating in the mid-band region?

Transistor geometries in a $CMOS$ inverter have been adjusted to meet the requirement for worst case charge and discharge times for driving a load capacitor $C$. This design is to be converted to that of a $NOR$ circuit in the same technology, so that its worst case charge and discharge times while driving the same capacitor are similar. The channel …

Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor $R=10\Omega$ and the supply voltage is $5\:V$. The $D$ flip-flops $D_{1} \:, D_{2} \:, D_{3} \:, D_{4}$ and $D_{5}$ are initialized with logic values $0,1,0,1$ and $0$, respectively. The clocks has a $30\%$ duty cycle. The average power dissipated (in …

A $4:1$ multiplexer is to be used for generating the output carry of a full adder. $A$ and $B$ are the bits to be added while $C_{in}$ is the input carry and $C_{out}$ is the output carry. $A$ and $B$ are to be used as the select bits with $A$ being the more significant select bit. Which one of the following statements correctly describes the …

The response of the system $G(s)=\frac{s-2}{(s+1)(s+3)}$ to the unit step input $u(t)$ is $y(t)$. The value of $\frac{dy}{dt}$ at $t=0^{+}$ is _________

The number and direction of encirclements around the point $-1+j0$ in the complex plane by the Nyquist plot of $G(s)=\frac{1-s}{4+2s}$ is

A discrete memoryless source has an alphabet $\left \{ a_{1},a_{2}, a_{3},a_{4}\right \}$ with corresponding probabilities $\left \{ \frac{1}{2}, \frac{1}{4},\frac{1}{8},\frac{1}{8}\right \}.$ The minimum required average codeword length in bits to represent this source for error-free reconstruction is _________

A speech signal is sampled at $8$ $kHz$ and encoded into $PCM$ format using $8$ bits/sample. The $PCM$ data is transmitted through a baseband channel via $4$-level $PAM$. The minimum bandwidth (in $kHz$) required for transmission is _________

A uniform and constant magnetic field $\textbf{B}=\hat{z}B$ exists in the $\hat{z}$ direction in vacuum. A particle of mass $m$ with a small charge $q$ is introduced into this region with an initial velocity $\textbf{v}=\hat{x}v_{x}+\hat{z}v_{z}$. Given that $B$, $m$, $q$, $v_{x}$ and $v_{z}$ are all non-zero, which one of the following …

Let the electric field vector of a plane electromagnetic wave propagating in a homogeneous medium be expressed as $\textbf{E}=\hat{x}E_{x}e^{-j(\omega t-\beta z)},$ where the propogation constant $\beta$ is a function of the angular frequency $\omega$. Assume that $\beta (\omega )$ and $E_{x}$ are known and are real. From the information available, …

Light from free space is incident at an angle $\theta _{i}$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are $n _{1}=1.5$ and $n _{2}=1.4$, respectively. The maximum value of $\theta _{i}$ (in degrees) for which the incident light will be guided in the core of the fibre is _________