Recent questions tagged numerical-answers

Given that $\vec{F}(x, y, z)=\sin (y) \hat{x}+\cos (x) \hat{y}+5 \hat{z}$, the integral $\oint \oint _{S} \vec{F}(x, y, z) \cdot \overrightarrow{d s}$ over the unit spher...

In the linear regulator circuit shown, the base to emitter voltage $\mathrm{V}_{\mathrm{BE}}$ of the BJT is $0.6$ V. The Zener diode clamps the base voltage to $5.4$ V. I...

Consider the circuit shown. Assume that the diode $D$ is ideal. The supply voltage $v_{s}=325 \sin (2 \pi 50 t) \mathrm{V}, L=500 ~\mu \mathrm{H}$, and $R=10 ~\Omega$. Th...

$A$ is an $m \times m$ skew-symmetric matrix with real-valued entries, and $\boldsymbol{x}$ is an $m$-dimensional column vector with real-valued entries such that $\bolds...

The resistance values of the Wheatstone bridge shown are: $\mathrm{P}=2000 \Omega, \mathrm{Q}=500 \Omega, \mathrm{R}=3000 \Omega$. The battery voltage $\mathrm{E}=50 \mat...

A system with two generators $\text{G1}$ and $\text{G2}$ (without generator limits) is shown.The total load on the system is $1184$ MW. The expressions for the cost of ge...

A balanced three-phase supply is given to a $30 \mathrm{~kW}, 4$-pole, $400 \mathrm{~V}, 50 \mathrm{~Hz}$, wound rotor induction motor with Y-connected stator and rotor w...

Consider the two-port network shown. For maximum power transfer to the resistive load $\left(\mathrm{R}_{\mathrm{L}}\right)$, the value of $\mathrm{R}_{\mathrm{L}}$ shoul...

Consider the circuit shown. Assume that the diode ( $D$ ) is ideal.Given $v_{s}=100 \sin (2 \pi 50 t) \mathrm{V}, V_{d c}=50 \mathrm{~V}$, and $R=10 \Omega$, the average ...

The magnitude of the contour integral\[\oint_{C}\left(\frac{(z+1)^{2}}{(z-i)(z-2)}\right) d z\]over the contour $C:|z-2-i|=3 / 2$ is $\_\_\_\_$(Round off to two decimal p...

A uniform spherical volume charge distribution of radius $2$ m, centered at the origin, has a strength of $\frac{3}{\pi} \times 10^{-6} \mathrm{~C} / \mathrm{m}^{3}$. A p...

Let $\text{X}$ and $\text{Y}$ be two real-valued random variables with $\mathrm{E}(\mathrm{X})=1, \mathrm{E}(\mathrm{Y})=2, \mathrm{E}\left(\mathrm{X}^{2}\right)=4, \math...

Consider discrete random variables $X$ and $Y$ with probabilities as follows:$$ \begin{array}{l} P(X=0 \text { and } Y=0)=\frac{1}{4} \\ P(X=1 \text { and } Y=0)=\frac{1}...

Consider a continuous-time signal$$ x(t)=-t^{2}\{u(t+4)-u(t-4)\}$$where $u(t)$ is the continuous-time unit step function. Let $\delta(t)$ be the continuous-time unit impu...

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of t...

​​Which one of the following figures represents the radial electric field distribution $E_{R}$ caused by a spherical cloud of electrons with a volume charge density, $\rh...

The input voltage $v(t)$ and current $i(t)$ of a converter are given by,$\begin{array}{l} v(t)=300 \sin (\omega t) V \\ i(t)=10 \sin \left(\omega t-\frac{\pi}{6}\right)+2...

A continuous time periodic signal $x(t)$ is$ x(t)=1+2 \cos 2 \pi t+2 \cos 4 \pi t+2 \cos 6 \pi t$If $T$ is the period of $x(t)$, then $\frac{1}{T} \int_{0}^{T} \mid x(t)\...

The maximum percentage error in the equivalent resistance of two parallel-connected resistors of $100 \: \Omega$ and $900 \: \Omega$ with each having a maximum $5 \%$ err...

Consider a distribution feeder, with $R / X$ ratio of $5$. At the receiving end, a $350 \: \mathrm{kVA}$ load is connected. The maximum voltage drop will occur from the s...

A symmetrical fault (through a fault impedance of $j 0.007 \mathrm{pu}$ ) occurs at bus $2$. Neglecting pre-fault loading conditions, the voltage at bus $1$, during the f...

In the circuit with ideal devices, the power MOSFET is operated with a duty cycle of $0.4$ in a switching cycle with $I=10 \mathrm{~A}$ and $V=15 \mathrm{~V}$. The power ...

The induced emf in a $3.3 \: \mathrm{kV}, 4$ pole, $3$-phase star connected synchronous motor is considered to be equal and in phase with the terminal voltage under no lo...

Let continuous-time signals $x_{1}(t)$ and $x_{2}(t)$ be$$x_{1}(t)=\begin{cases} 1, & t \in[0,1] \\ 2-t, & t \in[1,2] \\ 0, & \text { otherwise } \end{cases} \quad \text ...