List of practice Questions

In the circuit, $V_{in}=100$ mV. The $10$ nF feedback capacitor initially stores $1$ nC with the shown polarity ($+$ at the op-amp output). The switch $S$ toggles with a $1$ kHz square wave ($1$ ms period): position ‘1’ when High, ‘2’ when Low. Find $|V_0|$ at $t=20$ ms (nearest integer, in mV).

A silica-glass fiber has a core refractive index of 1.47 and a cladding refractive index of 1.44. If the cladding is completely stripped out and the core is dipped in water of refractive index 1.33, the numerical aperture (rounded to three decimal places) is ____

In the circuit shown, \(\omega=100\pi\ \text{rad/s}\), \(R_1=R_2=2.2~\Omega\), and \(L=7~\text{mH}\). The capacitance \(C\) for which \(Y_{\text{in}}\) is purely real is _____ mF (rounded to two decimal places).

The R–L circuit with $R=10\,\text{k}\Omega$ and $L=1\,\text{mH}$ is excited by a step current $I_0u(t)$. At $t=0^-$, the inductor current is $i_L=I_0/5$. The minimum time for $i_L(t)$ to reach $99%$ of its final value is _____ $\mu$s (round off to two decimal places)

Consider a standard negative-feedback loop with $G(s)=\dfrac{1}{(s-2)(s-3)}$ and a PID controller $C(s)=K_P+\dfrac{K_I}{s}+K_Ds$. The root-locus of $G(s)C(s)$ (shown) has a double zero at $s=-1$. The gain $|C(j\omega)|=2$ at $\omega=1$ rad/s. The value of $K_D$ is______ (round off to one decimal place).

How many five-digit numbers can be formed using the integers 3, 4, 5 and 6 with exactly one digit appearing twice?

The phase margin of the transfer function $G(s)=\dfrac{2(1-s)}{(1+s)^2}$ is ______ degrees (rounded off to the nearest integer).

A wire-wound `resistive potentiometer type' angle sensor with 72 turns is used. The first turn is connected to ground and the last turn to 3.6 V. The wiper width covers two turns ensuring make-before-break. The output (wiper) voltage when the wiper is on top of both turns 35 and 36 is _____(rounded off to two decimal places).

For the given digital circuit, $A=B=1$. Assume that AND, OR, and NOT gates have propagation delays of $10$ ns, $10$ ns, and $5$ ns respectively (wires have zero delay). Given that $C=1$ at turn–on, the frequency of steady–state oscillation of the output $Y$ is _____.

In the circuit shown, the initial binary content of shift register A is $1101$ and that of shift register B is $1010$. The shift registers are positive–edge triggered, and the gates have no delay. When the shift control is high, what will be the binary content of the shift registers A and B after four clock pulses?

The magnitude and phase plots shown in the figure match with the transfer-function ______.

The simplified form of the Boolean function $F(W,X,Y,Z)=\Sigma(4,5,10,11,12,13,14,15)$ with the minimum number of terms and literals is _____

The full-scale range of the wattmeter shown is 100 W. The turns ratios are as indicated. The RMS source voltage is $V_s=200$ V. The wattmeter reading will be _____ W (rounded off to the nearest integer).

The no-load steady-state output voltage of a DC shunt generator is 200 V when it is driven in the clockwise direction at its rated speed. If the same machine is driven at the rated speed but in the opposite direction, the steady-state output voltage will be ______ V (rounded off to the nearest integer).

The impulse response of an LTI system is $h(t)=\delta(t)+0.5\,\delta(t-4)$. If the input is $x(t)=\cos\!\left(\frac{7\pi}{4}t\right)$, the output is_____

The Laplace transform of the continuous-time signal $x(t)=e^{-3t}\,u(t-5)$ is ____, where $u(t)$ is the unit step.

In a p–i–n photodiode, a pulse with $8\times10^{12}$ incident photons at $\lambda_0=1.55\,\mu$m yields $4\times10^{12}$ electrons collected. The quantum efficiency at this wavelength is _______%.

Let $f(z)=j\,\dfrac{1-z}{1+z}$, where $z$ is complex and $j=\sqrt{-1}$. The inverse function $f^{-1}(z)$ maps the {real axis} to the ______.

Let $y(t)=x(4t)$, where $x(t)$ is a continuous–time periodic signal with fundamental period $100~\text{s}$. The fundamental period of $y(t)$ is _______ s (rounded off to the nearest integer).

When the bridge shown is balanced, the current through the resistor $R_a$ is________ mA (rounded off to two decimal places). The bridge has $R_a=R_b=R_c=10~\mathrm{m}\Omega$ and the detector (galvanometer) is ideal/open at balance; the source is $1~\text{V}$.

In the circuit shown, the Thevenin equivalent resistance $R_{\text{th}}$ across the terminals ‘a’ and ‘b’ is ______ $\Omega$ (rounded off to one decimal place).

$X$ is a discrete random variable taking values $0,1,2$ with $P(X=0)=0.25$, $P(X=1)=0.5$, and $P(X=2)=0.25$. With $E[ . ]$ denoting expectation, compute $E[X]-E[X^2]$ (rounded off to one decimal place).

The diode in the circuit is ideal. The current source $i_s(t)=\pi\sin(3000\pi t)$ mA. The magnitude of the average current flowing through the resistor $R$ is _____ mA (rounded off to two decimal places).

The number of zeros of the polynomial $P(s) = s^3 + 2s^2 + 5s + 80$ in the right-half plane is _____.

The number of times the Nyquist plot of \(G(s)H(s)=\dfrac{1}{2}\,\dfrac{(s-1)(s-2)}{(s+1)(s+2)}\) encircles the origin is ____.