The points $P$, $Q$, and $R$ shown on the Smith chart (normalized impedance chart) in the following figure represent:
A lossy transmission line has resistance per unit length $ R=0.05\Omega$/m . The line is distortionless and has characteristic impedance of $ 50\Omega $ . The attenuation constant (in Np/m, correct to three decimal places) of the line is _______.
The distance (in meters) a wave has to propagate in a medium having a skin depth of 0.1 m so that the amplitude of the wave attenuates by 20 dB, is
The cutoff frequency of $ TE_{01} $ mode of an air filled rectangular waveguide having inner dimensions $a$ cm $\times$ $b$ cm $ \left(a>b\right) $ is twice that of the dominant $ TE_{10} $ mode. When the waveguide is operated at a frequency which is 25% higher than the cutoff frequency of the dominant mode, the guide wavelength is found to be 4 cm. The value of $b$ (in cm, correct to two decimal places) is _______.
A uniform plane wave traveling in free space and having the electric field
$ \overrightarrow E=\left(\sqrt2{\widehat a}_x-{\widehat a}_z\right)\cos\left[6\sqrt3\pi\times10^8t-2\pi\left(x+\sqrt2z\right)\right]\;V/m $
is incident on a dielectric medium (relative permittivity $>$ 1, relative permeability = 1) as shown in the figure and there is no reflected wave.
The relative permittivity (correct to two decimal places) of the dielectric medium is ___________.
The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $V\left(l\right)={e}^{-\gamma l+j\omega t}$ Volts, where l is the distance along the length of the cable in meters,$\gamma =(0.1+j40){m}^{-1}$ is the complex propagation constant, and $\omega =2\pi \times {10}^{9}$ rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/metre is__________.
Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link
An optical fiber is kept along the $\hat{z}$ direction. The refractive indicates for the electric fields along $\hat{x}$ and $\hat{y}$ directions in the fiber are n_{x}=1.5000 and n_{y}=1.5001, respectively ($ n_x\neq n_y $ due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5 µm. If the lightwave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeters, is____________.
The expression for an electric field in free space is $E={E}_{0}(\hat{x}+\hat{y}+j2\hat{z}){e}^{-j(\omega t-kx+ky)}$, where x, y, z represent the special coordinates, t represent time, and ω, k are constant. This electric field
A half wavelength dipole is kept in the x-y plane and oriented along 45° from the x –axis. Determine the direction of null in the radiation pattern for $ 0\leq\mathrm\phi\leq\pi $, Here the angle $ \theta\left(0\leq\mathrm\theta\leq\pi\right) $ is measured from the z-axis, and the angle $ \mathrm\phi\left(0\leq\mathrm\phi\leq2\pi\right) $ is measured from the x-axis in the x-y plane.
Two conducting spheres S1 and S2 of radii $a$ and $b (b > a)$ respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.
For some charge placed on this structure, the potential and surface electric field on S1 are V_{a }and E_{a} and that on S2 are V_{b} and E_{b}, respectively. Then, which of the following is CORRECT?
A two-wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power that is reflected from the television set is___________
If the vector function $\overrightarrow{F}=\hat{{a}_{x}}(3y-{k}_{1}z)+\hat{{a}_{y}}({k}_{2}x-2z)-\hat{{a}_{z}}({k}_{3}y+z)$ is irrotational, then the values of the constant k_{1, }k_{2} and k_{3} , respectively, are
An electron (q_{1}) is moving in free space with velocity 10^{5} m/s towards a stationary electron (q_{2}) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is___________ ×10^{-8} m.
[Given, mass of electron m = 9.11×10^{-31} kg, charge of electron e = 1.6 ×10^{-19} C, and permittivity $ \varepsilon_0=\left(1/36\pi\right)\times10^{-9\;}\mathrm F/\mathrm m $]
Standard air-filled rectangular waveguides of dimension a = 2.29 cm and b = 1.02 cm are designed for radar application. It is desired that these waveguides operate only in the dominant TE_{10} mode but not higher than 95% of the next cutoff frequency. The range of the allowable operating frequency f is
The permittivity of water at optical frequencies is 1.75 $\varepsilon_0$. It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5 m, as shown in the figure. The critical angle is $\theta_c$ .
The value of d (in meter) is___________
The current density in a medium is given by
$\overrightarrow J=\frac{400\;\sin\theta}{2\mathrm\pi\left(\mathrm r^2+4\right)}{\widehat a}_r\mathrm{Am}^{-2}$
${\overrightarrow{E}}_{w}^{i}=\left({\hat{a}}_{x}+j{\hat{a}}_{y}\right){E}_{0}{e}^{jkz}$
${\overrightarrow{E}}_{a}=\left({\hat{a}}_{x}+2{\hat{a}}_{y}\right){E}_{I}\frac{1}{r}{e}^{-jkr}$
The far-zone power density radiated by a helical antenna is approximated as:
${\overrightarrow W}_{rad}={\overrightarrow W}_{average}\approx\widehat{a_r}C_0\frac1{r^2}\cos^4\theta$
At this new plate separation, what is the energy stored in the capacitor, neglecting fringing effects?
Which one of the following inequalities is always satisfied?
${Z}_{0}\sqrt{\frac{Lt}{{\epsilon}_{0}{\epsilon}_{r}w}}$
The length L (in meters) of T_{2} is ________
A positive charge q is placed at x=0 between two infinite metal plates placed at x=-d and at x=+d respectively. The metal plates lie in the yz plane
The electric field component of a plane wave traveling in a lossless dielectric medium is given by $\overrightarrow{E}\left(z,t\right)={\hat{a}}_{y}2\mathrm{cos}\left({10}^{8}t-\frac{z}{\sqrt{2}}\right)\mathrm{V}/\mathrm{m}$. Thewavelength (in m) for the wave is_______.
A vector $\overrightarrow{P}$ is given by $\overrightarrow{P}={x}^{3}y{\overrightarrow{a}}_{x}-{x}^{2}{y}^{2}{\overrightarrow{a}}_{y}-{x}^{2}yz{\overrightarrow{a}}_{z}$. Which one of the following statements is TRUE?
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression
${H}_{z}\left(x,y,z,t\right)=0.1\mathrm{cos}\left(25\pi \mathrm{x}\right)\mathrm{cos}\left(30.3\pi y\right)\mathrm{cos}\left(12\pi \times {10}^{9}t-\beta z\right)\left(A/m\right)$
The cross-sectional dimensions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is
The electric field intensity of a plane wave traveling in free space is given by the following expression
$ \boldsymbol E(x,t)={\boldsymbol a}_y\;24\mathrm\pi\;\cos(\mathrm{ωt}-{\mathrm k}_0\mathrm x)(\mathrm V/\mathrm m). $
In this field, consider a square area 10 cm X 10 cm on a plane $ \mathrm x+\mathrm y=1. $ The total time-averaged power (in mW) passing through the square area is _______.
Consider a uniform plane wave with amplitude (E_{0}) of 10 V/m and 1.1 GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity (${\mathrm{\epsilon}}_{\mathrm{r}}$) and permeability (${\mathrm{\mu}}_{\mathrm{r}}$) as shown in the figure.
The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of 10 cm inside the dielectric region is_______.
In a source free region in vacuum, if the electrostatic potential $ \varphi=2x^2+y^2+cz^2 $, the value of constant $ c $ must be _______.
The electric field of a uniform plane electromagnetic wave is
$\overrightarrow{E}=\left({\overrightarrow{a}}_{x}+j4{\overrightarrow{a}}_{y}\right)\mathrm{exp}\left[j\left(2\mathrm{\pi}\times {10}^{7}t-0.2z\right)\right]$
The polarization of the wave is
An air-filled rectangular waveguide of internal dimension a cm X b cm (a > b) has a cutoff frequency of 6 GHz for the dominant TE_{10} mode. For the same waveguide, if the cutoff frequency of the TM_{11} mode is 15 GHz, the cutoff frequency of the TE_{01} mode in GHz is __________.
Two half –wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency 3 MHz and phase shift of $\mathrm{\pi}$/2 between them (the element at the origin leads in phase) . If the maximum radiated E –field at the point P in the x-y plane occurs at an azimuthal angle of 60^{o}, the distance d (in meters) between the antennas is________.
The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expression
$\mathrm{E}\left(z,t\right)={\mathrm{a}}_{x}5\mathrm{cos}\left(2\pi \times {10}^{9}t+\beta z\right)+{\mathrm{a}}_{y}3\mathrm{cos}\left(2\pi \times {10}^{9}t+\beta z-\frac{\pi}{2}\right)$
The type of the polarization is
The directivity of an antenna array can be increased by adding more antenna, as a larger number of elements
A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon (${\epsilon}_{r}$ = 2.1, tan $\delta $ = 0). Which one of the following circuits can represent the lumped element model of a small piece of this cable having length $\bigtriangleup$z ?
A vector field $\mathbf{D}=2{\rho}^{2}{\mathbf{a}}_{\rho}+z{\mathbf{a}}_{z}$ exists inside a cylindrical region enclosed by the surfaces ρ = 1, z = 0 and z=5. Let S be the surface bounding this cylindrical region. The surface integral of this field on $\left({\u222f}_{s}\mathbf{D}\mathbf{\xb7}\mathbf{ds}\right)$ is______.
Consider the 3 m long lossless air-filled transmission line shown in the figure. It has a characteristic impedance of 120 $\mathrm{\pi \Omega}$, is terminated by a short circuit, and is excited with a frequency of 37.5 MHz. What is the nature of the input impedance (Z_{in})?
A 200 m long transmission line having parameters shown in the figure is terminated into a load R_{L}. The line is connected to a 400 V source having source resistance R_{S} Through a switch, which is closed at t=0. The transient response of the circuit at the input of the line (z=0) is also drawn in the figure. The value of R_{L} (in Ω) is_______.
A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172 pF/m. If the ratio of outer radius to inner radius is doubled, the capacitance per unit length (in pF/m) is ________.
A two-port network has scattering parameters given by $\left[S\right]=\left[\begin{array}{cc}{s}_{11}& {s}_{12}\\ {s}_{21}& {s}_{22}\end{array}\right]$. If the port-2 of the two- port is short circuited , the ${s}_{11}$ parameter for the resultant one-port network is
The force on a point charge +q kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity $\in $ is
In spherical coordinates, let ${\widehat a}_\theta,{\widehat a}_\phi$; denote unit vectors along the $\theta,\phi$ directions
$E=\frac{100}r\sin\theta\;\cos\;\left(\omega t-\beta r\right){\widehat a}_\theta V/m$
and
$H=\frac{0.265}r\sin\theta\;\cos\;\left(\omega t-\beta r\right){\widehat a}_\phi A/m$
represent the electric and magnetic field components of the EM wave at large distances r from a dipole antenna, in free space. The average power (W) crossing the hemispherical shell located at $r=1km,0\le \theta \le \raisebox{1ex}{$\mathrm{\pi}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ is _______.
For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in
The input impedance of a $\frac{\lambda}{8}$ section of a lossless transmission line of characteristic impedance 50Ω is found to be real when the other end is terminated by a load ${Z}_{L}\left(=R+jx\right)\Omega $ If X is 30Ω, the value of R (in Ω) is_________
To maximize power transfer, a lossless transmission line is to be matched to a resistive load impedance via a $\lambda /4$ transformer as shown.
The characteristic impedance (in Ω) of the $\lambda /4$ transformer is _________.
Which one of the following field patterns represents a TEM wave travelling in the positive x direction?
if $\overrightarrow r=x{\widehat a}_x+y{\widehat a}_y+z{\widehat a}_z\;and\;\left|\overrightarrow r\right|=r$ then div $\left(r^2\nabla\left(\ln\;r\right)\right)$ = ______ .
If the electric field of a plane wave is
$\overrightarrow{\mathrm E}\left(z,t\right)=\widehat x3\cos\left(\omega t-kz+30^\circ\right)-\widehat y4\sin\left(\omega t-kz+45^\circ\right)\left(mV/m\right)$
the polarization state of the plane wave is
In the transmission line shown, the impedance Z_{in} (in ohms) between node A and the ground is _________.
For a rectangular waveguide of internal dimensions a × b (a>b), the cut-off frequency for the TE_{11 }mode is the arithmetic mean of the cut-off frequencies for TE_{10} mode and TE_{20} mode. If $a=\sqrt{5}$cm, the value of b (in cm) is _____.
Consider an air filled rectangular waveguide with a cross-section of 5 cm × 3 cm. For this waveguide, the cut-off frequency (in MHz) of TE_{21} mode is _________.
In the following figure, the transmitter Tx sends a wideband modulated RF signal via a coaxial cable to the receiver Rx. The output impedance Z_{T} of Tx, the characteristic impedance Z_{0} of the cable and the input impedance Z_{R} of Rx are all real.
Which one of the following statements is TRUE about the distortion of the received signal due to impedance mismatch?