Test 1 - Electromagnetics | Electronics and Communication (ECE)
Topic wise test for Electromagnetics of Electronics and Communication (ECE
Questions
If the scattering matrix [S] of a two port network is [S] = $
\left[
\begin{array}
\ 0.2\angle0^\circ & 0.9 \angle90^\circ \\
0.9\angle90^\circ & 0.1 \angle 90^\circ
\end{array}
\right]
$ then the network is
- lossless and reciprocal
- lossless but not reciprocal
- not lossless but reciprocal
- neither lossless nor reciprocal
A plane wave propagating in air with $\dot E = (8\widehat a_x + 6 \widehat a_y + 5 \widehat a_z) e^{ot + 3y -4y}$V/m is incident on a perfectly conducting slab positioned at x $\le$ 0. The $\vec E$field of the reflected wave is
- $(-8\widehat a_x - 6 \widehat a_y - 5 \widehat a_z) e^{j(ot + 3y +4y)}$ V/m
- $(-8\widehat a_x + 6 \widehat a_y - 5 \widehat a_z) e^{j(ot + 3y +4y)}$ V/m
- $(-8\widehat a_x - 6 \widehat a_y - 5 \widehat a_z) e^{j(ot - 3y -4y)}$ V/m
- $(-8\widehat a_x + 6 \widehat a_y - 5 \widehat a_z) e^{j(ot - 3y -4y)}$ V/m
Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel to the y−axis. The other wire is in the x-y plane and parallel to the x−axis. Which components of the resulting magnetic field are non-zero at the origin?
- x, y, z components
- x, y components
- y, z components
- x, z components
The electric field of an electromagnetic wave propagating in the positive z - direction is given by
$E = \widehat a_x sin(\omega t - \beta z) + \widehat a_y sin(\omega t - \beta z + \pi / 2)$
The wave is
- linearly polarized in the z-direction
- elliptically polarized
- left-hand circularly polarized
- right-hand circularly polarized
The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the TE10 mode is
- equal to its group velocity
- less than the velocity of light in free space
- equal to the velocity of light in free space
- greater than the velocity of light in free space
A transmission line with a characteristic impedance of 100 $\Omega$is used to match a 50 $\Omega$section to a 200 $\Omega$section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately
- 82.5 cm
- 1.05 m
- 1.58 m
- 1.75 m
A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in TE11 mode. The minimum operating frequency is
- 6.25 GHz
- 6.0 GHz
- 5.0 GHz
- 3.75 GHz
Which one of the following represents the electric field lines for the TE02 mode in the cross-section of a hollow rectangular metallic waveguide?
A parallel plate air-filled capacitor has plate area of 10-4 m2 and plate separation of 10-3 m. It is connected to a 0.5 V, 3.6 GHz source. The magnitude of the displacement current is ($\epsilon$= $\dfrac{1}{36\pi} 10^{-9}$F/m)
- 10 mA
- 100 mA
- 10 A
- 1.59 mA
The $\vec E$ field in a rectangular waveguide of inner dimensions a$\times$b is given by
$\vec E$= $\dfrac{\omega \mu}{h^2} \left( \dfrac{\pi}{a} \right)$H0 sin $\left( \dfrac{2\pi x}{a} \right)^2$sin ($\omega t - \beta z$$\widehat y$
Where H0 is a constant, and a and b are the dimensions along the x-axis and the y-axis respectively. The mode of propagation in the waveguide is
- TE20
- TM11
- TM20
- TE10
A transmission line has a characteristic impedance of 50$\Omega$ and a resistance of 0.1$\Omega$ /m. if the line is distortion less, the attenuation constant (in Np/m) is
- 500
- 5
- 0.014
- 0.002
The unit of $\nabla$$\times$ H is
- Ampere
- Ampere/metre
- Ampere/metre2
- Ampere-metre
The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by $\dot E = 10(\widehat a_y + j\widehat a_z) e^{-j25x}$. The frequency and polarization of the wave, respectively, are
- 1.2 GHz and left circular
- 4 Hz and left circular
- 1.2 GHz and right circular
- 4 Hz and right circular
For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is
- 360o
- 180o
- 90o
- 45o
The magnetic field intensity vector of a plane wave is given by $\bar H (x,y,z,t)$ = 10 sin (50000t + 0.004x + 30)$\widehat a_y$ where $\widehat a_y$denotes the unit vector in y direction. The wave is propagating with a phase velocity
- 5 x 104 m/s
- - 3 x 108 m/s
- - 1.25 x 107 m/s
- 3 x 108 m/s
One end of a loss-less transmission line having the characteristic impedance of 75 $\Omega$ and length of 1 cm is short-circuited. At 3 GHz, the input impedance at the other end of transmission line is
- 0
- Resistive
- Capacitive
- Inductive
Medium 1 has the electrical permittivity $\xi_1$= 1.5 $\xi_0$ farad/m and occupies the region to the left of x = 0 plane. Medium 2 has the electrical permittivity $\xi_2$ = 2.5 $\xi_0$ farad/m and occupies the region to the right of x = 0 plane. If E1 in medium 1 is
E1 = (2ux -3uy + 1uz) volt/m, then E2 in medium 2 is
- (2.0ux - 7.5uy + 2.5uz) volt/m
- (2.0ux - 2.0uy + 0.6uz) volt/m
- (1.2ux - 3.0uy + 1.0uz) volt/m
- (1.2ux - 2.0uy + 0.6uz) volt/m
A transmission line of characteristic impedance 50W is terminated in a load impedance ZL. The VSWR of the line is measured as 5 and the first of the voltage maxima in the line is observed at a distance of $\dfrac{\lambda}{4}$from the load. The value of ZL is
- 10$\Omega$
- 250$\Omega$
- (19.23 + j46.15)$\Omega$
- (19.23) - j46.15)$\Omega$
A load of 50$\Omega$is connected in shunt in a 2-wire transmission line of Z0 = 50 $\Omega$as shown in the figure. The 2-port scattering parameter matrix (S-matrix) of the shunt element is
- $ \left[ \begin{array} \ -\dfrac{1}{2} & \dfrac{1}{2} \\\\ \dfrac{1}{2} & -\dfrac{1}{2} \end{array} \right] $
- $ \left[ \begin{array} \ 0 & 0 \\\\ 1 & 1 \end{array} \right] $
- $ \left[ \begin{array} \ -\dfrac{1}{3} & \dfrac{2}{3} \\\\ \dfrac{2}{3} & -\dfrac{1}{3} \end{array} \right] $
- $ \left[ \begin{array} \ \dfrac{1}{4} & -\dfrac{3}{4} \\\\ -\dfrac{3}{4} & -\dfrac{1}{4} \end{array} \right] $
When a plane wave traveling in free-space is incident normally on a medium having $\epsilon_r$ = 4.0 the fraction of power transmitted into the medium is given by
- $\dfrac{8}{9}$
- $\dfrac{1}{2}$
- $\dfrac{1}{3}$
- $\dfrac{5}{6}$
