Recent questions

The current $i(t)$ drawn by a circuit is given as$$i(t)=4+30 \cos (t)-20 \sin (t)+15 \cos (3 t)-10 \sin (3 t) \mathrm{A}$$The root-mean-square value of $i(t)$ is $\_\_\_\...

A linear potentiometer $(0-10 \mathrm{k} \Omega)$ is used to measure the water level as shown in the figure. The resistance between $\mathrm{A}$ and $\mathrm{C}$ varies l...

The switch in the following figure has been closed for a long time $(t<0)$. It is opened at $t=0$ seconds. The value of $d v_{0} / d t$ at $t=0^{+}$is $\_\_\_\_\_\_ ~ \ma...

Consider a system given by the following first order differential equation:$$ \frac{d y}{d t}=y+2 t-t^{2} $$where, $y(0)=1$ and $0 \leq t<\infty$. Using a step size $h=0....

Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have ...

​A wire of circular cross section with radius $a$ is shown in the figure. The current density is given by $\mathbf{J}=k s^{2}$, where $k$ is a constant, $s$ is the radial...

​​​​The measured values from a flow instrument, whose range is between $0$ and $2$ flow units, are shown in the histogram. The systematic error (bias) and the maximum err...

​​​​Consider a discrete-time sequence$x[n]=\begin{cases} (0.2)^{n}, & 0 \leq n \leq 7 \\ 0, & \text { otherwise } \end{cases}$The region of convergence of $X(z)$, the $z$...

​​​​​In the bridge circuit shown in the figure, under balanced condition, the values of $R$ and $C$ respectively, are$1.010 ~\Omega$ and $19.802 ~\mu \mathrm{F}$$9.901 ~\...

​​​​​Laplace transform of a signal $x(t)$ is$$X(s)=\frac{1}{s^{2}+13 s+42}$$Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if t...

​​​​In the figure shown, both the opamps $\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ are ideal, except that the opamp $\mathrm{A}_{1}$ has an offset voltage $\left(\mathrm{V}_{...

​​​​In the figure shown, the positive edge triggered $\mathrm{D}$ flip-flops are initially reset to $Q=0$. The logic gates and the multiplexers have no propagation delay....

​​​In the figure shown, $R=1 \mathrm{~k} \Omega$ and $C=0.1 ~\mu \mathrm{F}$. For a dc gain of $-10$, the $3 \mathrm{~dB}$ cut-off frequency (rounded off to one decimal p...

​​​​Consider the feedback control system shown in the figure. The steady-state error $e_{s s}=\lim _{t \rightarrow \infty}(r(t)-y(t))$ due to unit step reference $r(t)$ i...

​​The transfer function of a system is$$G(s)=\frac{\omega_{n}^{2}}{s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}}$$Choose the range of $\xi$ and $\omega_{n}$ (in $\mathrm{rad} ...

​​Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1...

​​​In the figure shown, assume$\alpha$ is the phase angle between the load current and the load voltage$\beta$ is the phase angle by which pressure coil current lags the ...

​Consider an ultrasonic measurement system shown in the figure. The ultrasonic transmitter $(T)$ sends a continuous wave signal $x(t)=\cos \left(2 \pi f_{1} t\right)$ vol...

​​The complex functions $f(z)=u(x, y)+i ~v(x, y)$ and $\overline{f(z)}=u(x, y)-i~ v(x, y)$ are both analytic in a given domain. Choose the correct option(s) from the foll...

The readings recorded from a $20$ -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04~ x+10.32$. The regression coefficient ...

In the figure shown, $\mathrm{R}=4.5 \mathrm{~k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{~k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance b...

Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched $\mathrm{ON}$ at $\mathrm{t}=0$. Assuming the opamp to be ideal...

The $4$-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the $4$ -point circular...

Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is $\_\_\_\_\_ ~\Omega$ (rounded off to nearest integer).

Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value ...

A shielded cable with $\mathrm{C}_{\text {stray }}=20 \mathrm{~pF}$ and $\mathrm{R}_{\text {wire }}=10 ~\Omega$ is used to connect the inductive sensors as shown in the f...

In the figure shown, the diode current is given by $I_{D}=I_{S} e^{\frac{\alpha V_{D}}{T}} \cdot V_{D}$ is the diode voltage in volts, $T$ is the absolute temperature in ...

An ADC has a full scale voltage of $1.4 \mathrm{~V}$, resolution of $200 ~\mathrm{mV}$, and produces binary output data. The input signal of the ADC has a bandwidth of $5...

In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2 \mathrm{~ms}$ is $\_\_\_\_\_~\mathrm{V}$ ...

In the figure shown, $\mathrm{Sw}$ is a switch whose position changes from 1 to 0 when $\mathrm{Vc}$ changes from logic HIGH to LOW and vice versa. The bandwidth of the p...

A $50 \mathrm{~kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transforme...

A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting...

Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{~mH}$. When connected in series-opposing configurat...

The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is$$y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t...

A random variable $X$ has a probability density function$$f_{X}(x)=\begin{cases} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{cases}$$The probability of $X>2$ is $...