List of practice Questions

The rank of the matrix $A$ given below is one. The ratio $\dfrac{\alpha}{\beta}$ is ______ (rounded off to the nearest integer). \[ A = \begin{bmatrix} 1 & 4 \\ -3 & \alpha \\ \beta & 6 \end{bmatrix} \]

A 1.999 V True RMS 3-1/2 digit multimeter has an accuracy of $\pm0.1 %$ of reading $\pm 2$ digits. It is used to measure 100 A (RMS) current through a line using a 100:5 ratio Class-1 CT with burden $0.1~\Omega \pm0.5%$. The worst-case absolute error in the multimeter output is _____ V (rounded off to three decimal places).

The voltage source $v_s=10\sqrt{2}\sin(20000\pi t)$ V has an internal resistance of $50~\Omega$. Find the RMS current through the $R=25~\Omega$ resistor (rounded to one decimal place).

An ideal LVDT shows $2\,\text{V}_{\text{RMS}}$ from each secondary at zero displacement. One secondary has a phase deviation of $1^\circ$ from the expected $180^\circ$ opposition; otherwise the LVDT is ideal. If the differential output sensitivity is $1\ \text{mV(RMS)}/\mu\text{m}$, the output for zero displacement is _____(rounded off to one decimal place)} $\mu$m.

Five measurements are made using a weighing machine, and the readings are 80 kg, 79 kg, 81 kg, 79 kg and 81 kg. The sample standard deviation of the measurement is ___________ kg (rounded off to two decimal places).

Four strain gauges $R_A, R_B, R_C, R_D$ (nominal $R$) are in a bridge. Under force: $R_A$ and $R_D$ increase by $\Delta R$, $R_B$ and $R_C$ decrease by $\Delta R$. A potentiometer of total resistance $R_v$ is connected as shown to rebalance the bridge. If $R=100~\Omega$ and $\Delta R=1~\Omega$, the minimum $R_v$ required to balance the bridge is _____ $\Omega$ (rounded off to two decimal places).

Two inductors (4 H with current \(i_1(t)=1\sin(200\pi t)\,\text{mA}\) and 5 H with \(i_2(t)=2\sin(200\pi t)\,\text{mA}\)) are mutually coupled with coupling coefficient \(k=0.6\). Currents enter the dotted ends. Find the {peak} energy stored in the coupled system (in \(\mu\)J).

In the nMOS feedback amplifier (capacitors act as shorts at the signal frequency): \(V_{DD}=5\,\text{V}\), \(R_D=1~\text{k}\Omega\), \(R_S=1~\text{k}\Omega\), \(R_1=200~\text{k}\Omega\), \(R_2=300~\text{k}\Omega\). Given \(\mu_n C_{ox}=1~\text{mA/V}^2\), \(W/L=2\), \(V_T=1~\text{V}\), and the DC drain voltage is \(4~\text{V}\). Find \(V_{\mathrm{out}}/V_{\mathrm{in}}\) (magnitude).

Consider the real-valued function \( g(x)=\max\{(x-2)^2,\,-2x+7\}\), \(x\in(-\infty,\infty)\). The minimum value attained by \(g(x)\) is _____(rounded off to one decimal place).

Short-circuit test on a single-phase transformer at 1 kHz gives: wattmeter \(P=8\) W, primary current \(I=2\) A, primary voltage \(V=6\) V. Assume negligible no-load loss/current and linear core. With the secondary shorted, the primary is now fed from a \(2\) V\(_{\mathrm{RMS}}\), 1 kHz source in series with a capacitor of value \( \dfrac{1}{2\pi\sqrt{5}} \) mF. The primary RMS current is _____A (rounded off to two decimals).

The op-amps are ideal. Inputs: $V_{S1}=3+0.10\sin(300t)\,\text{V}$ and $V_{S2}=-2+0.11\sin(300t)\,\text{V}$. Find the {average} value of $V_0$ (rounded to two decimals).

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).