Recent questions without answers

Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}.$ If $C$ is a counterclockwise path in the $z$-plane such that $|z+1|=1,$ the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is$-2$$-1$$...

The average power delivered to an impedance $(4-j3)\Omega$ by a current $5\cos(100\pi t+100)\text{A}$ is $44.2\;\text{W}$ $50\;\text{W}$ $62.5\;\text{W}$ $125\;\text{W}$

In the circuit shown below, the current through the inductor is $\frac{2}{1+j}\text{A}$$\frac{-1}{1+j}\text{A}$$\frac{1}{1+j}\text{A}$$0\text{A}$

In the following figure, $\text{C}_1$ and $\text{C}_2$ are ideal capacitors. $\text{C}_1$ has been charged to $12\;\text{V}$ before the ideal switch $\text{S}$ is closed ...

The impedance looking into nodes $1$ and $2$ in the given circuit is$50\;\Omega$$100\;\Omega$$5\;k\Omega$$10.1\;k\Omega$

The $i-v$ characteristics of the diode in the circuit given below are $$i=\left\{ \begin{array}{rcl} \frac{\text{v}-0.7}{500}\text{A},& \text{v}\geq0.7\text{v}\\ 0\;\text...

A system with transfer function $$G(s)=\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$$is excited by $\sin(\omega t).$ The steady-state output of the system is zero at $\omega =1\;...

With initial condition $x(1)=0.5$, the solution of the differential equation,$t\frac{dx}{dt}+x=t$ is $x=t-\frac{1}{2}$$x=t^2-\frac{1}{2}$$x=\frac{t^2}{2}$$x=\frac{t}{2}$

Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$...

The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}.$ The unilateral Laplace transform of $tf(t)$ is$-\frac{s}{(s^2+s+1)^2}$$-\frac{2s+1}{(s^2+s+1)^2}$$\frac...

If $x=\sqrt{-1},$ then the value of $x^x$ is $e^{-\pi/2}$$e^{\pi/2}$$x$$1$

A multi-mode optical fiber with a large core diameter has a core refractive index $n_1 = 1.5$ and cladding refractive index $n_2 = 1.4142.$ The maximum value of $\theta_A...

A high $Q$ coil having distributed (self) capacitance is tested with a Q-meter. First resonance at $\omega_1$ = $10^6$ rad/s is obtained with a capacitance of $990\; pF$....

The inductance of a coil is measured using the bridge shown in the figure. Balance $(D = 0)$ is obtained with $C_1= 1\; nF, R_1 = 2.2\; M\Omega, R_2 = 22.2\; k\Omega, R...

The average velocity $v$ of flow of clear water in a $100\; cm$ (inner) diameter tube is measured using the ultrasonic flow meter as shown in the figure. The angle $\thet...

A $1000\;\Omega$ strain gage $(R_g$) has a gage factor of $2.5$. It is connected in the bridge as shown in figure. The strain gage is subjected with a positive strain of ...

Assuming ideal opamp, the $RMS$ voltage (in mV) in the output $V{_o}$ only due to the $230V,\; 50\; Hz$ interference is (up to one decimal place) __________.

The sampling rate for Compact Discs $(CDs)$ is $44,000\; samples/s$. If the samples are quantized to $256$ levels and binary coded, the corresponding bit rate (in bits pe...

A Michelson Interferometer using a laser source of wavelength $\lambda_0 = 500\; nm$, with both the mirrors $(M_1$ & $M_2)$ fixed and positioned equidistant from the spl...

Unit step response of a linear time invariant $(LTI)$ system is given by $y(t) = (1 – e^{-2t})u(t)$. Assuming zero initial condition, the transfer function of the system ...

In the given relaxation oscillator, the opamps and the zener diodes are ideal. The frequency (in $kHz$) of the square wave output $v_{\circ}$ is $\_\_\_\_\_\_$.

An opamp that is powered from a $\pm\; 5V$ supply is used to build a non-inverting amplifier having a gain of $15$. The slew rate of the opamp is $0.5 \times 10^6 \;V/s.$...

The circuit given uses ideal opamps. The current $I$ (in $\mu$A) drawn from the source v$_s$ is (up to two decimal places) $\_\_\_\_\_$.

The product of sum expression of a Boolean function F(A, B, C) of three variables is given by$F(A, B, C) = (A + B + \overline{C}) \cdot(A + \overline{B} + \overline{C}) \...

A 2-bit synchronous counter using two $J-K$ flip flops is shown. The expressions for the inputs to the $J-K$ flip flops are also shown in the figure. The output sequence ...

A portion of an assembly language program written for an 8-bit microprocessor is given below along with explanations. The code is intended to introduce a software time de...

The Boolean function $F(X, Y)$ realized by the given circuit is $\overline{X} Y + X \overline{Y}$$\overline{X} \;\overline{Y}+ ...

The voltage and current drawn by a resistive load are measured with a $300\; V$ voltmeter of accuracy $\pm1\%$ of full scale and a $5 \;A$ ammeter of accuracy $\pm 0.5\%$...

In the given circuit, superposition is applied.When V$_2$ is set to 0 V, the current I$_2$ is -6 A. When V$_1$ is set to 0 v, the current I$_1$ is + 6A. Current I$_3$ (in...

In the figure, an RLC load supplied by a 230 V, 50 Hz single phase source. The magnitude of the reactive power (in VAr) supplied by the source is $\_\_\_\_\_$.

In the given circuit, the mesh currents $I{_1}$,$I{_2}$ and $I{_3}$ are $I{_1}$ = 1 A, $I{_2}$ =2 A and $I{_3}$ ...

The Fourier transform of a signal x(t), denoted by X(j$\omega$), is shown in the figure Let y(t) = x(t) + e$^{jt}...

Let y[n] = x[n] * h[n], where * denotes convolution and x[n] and h[n] are two discrete time sequences, Given that the z-transform of y[n] is y(z) = 2+ 3z$^{-1}$ + z$^{-2}...

For the sequence $x[n] = \{1, -1,1, -1\},$ with $n = 0,1,2,3,$ the DFT is computed as $X(k) = \displaystyle{}\Sigma^3_{n=0}x[n]e^{-j\frac {2\pi}{4}nk}$, for $k = 0,1,2,3....

Consider the standard negative feedback configuration with G(s) = $\frac{s^2+0.2s+100}{s^2 – 0.2s +100}$ and H(s) = $\frac{1}{2}$. The number of clockwise encirclements o...

Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for...

Consider a standard negative feedback configuration with G(s) = $\frac{1}{(s+1)(s+2)}$ and H(s) = $\frac{s+a}{s}$, For the closed loop system to have poles on the imagina...

A 300 V, 5A, 0.2 pf low power factor wattmeter is used to measure the power consumed by a load. The wattmeter scale has 150 divisions and the pointer is on the 100$^{th}$...

As shown in the figure, temperature $\theta$ is measured using a $K$ type thermocouple. It has a sensitivity of 40 $\mu V/^{\circ}C$. The gain $(G)$ of the ideal instrume...

A piezoelectric pressure sensor has a bandpass characteristic with cut-off frequencies of 0.1 Hz and 1 MHz, and a sensitivity of 100 mV/kPa. The sensor is subjected to a ...