The current i_{b} through the base of a silicon npn transistor is 1+0.1 cos(10000$\pi t$) mA. At 300 K, the r_{$\pi $} in the small signal model of the transistor is
The power spectral density of a real process X(t) for positive frequencies is shown below. The values of E[X^{2}(t)] and |E[X(t)]| , respectively, are
In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is
A plane wave propagating in air with $\overrightarrow{E}=\left(8{\hat{a}}_{x}+6{\hat{a}}_{y}+5{\hat{a}}_{z}\right){e}^{j\left(wt+3x-4y\right)}\mathrm{V}/\mathrm{m}$ is incident on a perfectly conducting slab positioned at $x\le 0$.The $\overrightarrow{E}$ field of the reflected wave is
The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\overrightarrow{E}=10\left({\hat{a}}_{y}+j{\hat{a}}_{z}\right){e}^{-j25x}$.The frequency and polarization of the wave, respectively, are
Consider the given circuit.
In this circuit, the race around
The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is
The i-v characteristics of the diode in the circuit given below are
$i=\left\{\begin{array}{ll}\frac{v-0.7}{500}A,& v\ge 0.7v\\ 0A,& v0.7v\end{array}\right.$
The current in the circuit is
In the following figure, C_{1} and C_{2} are ideal capacitors. C_{1} has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is
The average power delivered to an impedance (4-j3)$\Omega $ by a current $5\mathrm{cos}\left(100\pi t+100\right)A$ is
The unilateral Laplace transform of f (t) is $\frac{1}{{s}^{2}+s+1}$. The unilateral Laplace transform of t f (t) is
With initial condition $x\left(1\right)=0.5$ , the solution of the differential equation,
$t\frac{dx}{dt}+x=t$ is
The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D1 is
In the circuit shown
A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount $\epsilon $ and decreases that of the second by $\epsilon $. After encoding, the entropy of the source
A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given ${\mu}_{0}=4\pi \times {10}^{-7}H/m,{\epsilon}_{0}=\frac{{10}^{-9}}{36\pi}F/m$, the characteristic impedance of the cable is
The radiation pattern of an antenna in spherical co-ordinates is given by
$F\left(\theta \right)={\mathrm{cos}}^{4}\theta ;0\le \theta \le \mathrm{\pi}/2$
The directivity of the antenna is
If $x\left[n\right]={\left(1/3\right)}^{\left|n\right|}-{\left(1/2\right)}^{n}u\left[n\right]$, then the region of convergence (ROC) of its Z-transform in the Z-plane will be
In the sum of products function f(X,Y,Z)=$\sum \left(2,3,4,5\right)$,the prime implicants are
A system with transfer function
G(s)=$\frac{\left({s}^{2}+9\right)\left(s+2\right)}{\left(s+1\right)\left(s+3\right)\left(s+4\right)}$
is excited by $\mathrm{sin}\left(\omega t\right)$. The steady-state output of the system is zero at