Recent questions and answers in Electromagnetics

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1

GATE2020-EC: 13
The impedances $Z=jX,$ for all $X$ in the range $\left ( -\infty ,\infty \right )$, map to the Smith chart as a circle of radius $1$ with centre at $(0, 0)$. a point at the centre of the chart. a line passing through the centre of the chart. a circle of radius $0.5$ with centre at $(0.5, 0)$.

asked Feb 13 in Electromagnetics by jothee (1.4k points)

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2

GATE2020-EC: 21
A transmission line of length $3\lambda /4$ and having a characteristic impedance of $50$ $\Omega$ is terminated with a load of $400 \Omega$. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is __________ $\Omega$.

asked Feb 13 in Electromagnetics by jothee (1.4k points)

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3

GATE2020-EC: 43
For an infinitesimally small dipole in free space, the electric field $E_{\theta }$ in the far field is proportional to $e^{-jkr/r}\sin\theta$, where $k=2\pi /\lambda$. A vertical infinitesimally small electric dipole $\left (\delta l \ll \lambda \right )$ is placed ... far field radiation pattern occurs at $\theta =60^{\circ}$, is $\lambda$ $0.5\lambda$ $0.25\lambda$ $0.75\lambda$

asked Feb 13 in Electromagnetics by jothee (1.4k points)

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4

GATE2020-EC: 45
The magnetic field of a uniform plane wave in vacuum is given by $\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+3x-y-z\right ).$ The value of $b$ is ___________.

asked Feb 13 in Electromagnetics by jothee (1.4k points)

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5

GATE2020-EC: 46
For a $2$-port network consisting of an ideal lossless transformer, the parameter $S_{21}$ (rounded off to two decimal places) for a reference impedance of $10 \Omega$, is __________.

asked Feb 13 in Electromagnetics by jothee (1.4k points)

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6

GATE2019 EC: 12
In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell's equations (in their standard form). Match the left-hand side with the corresponding right-hand side. ... $1-Q,2-R,3-P,4-S$ $1-Q,2-S,3-P,4-R$ $1-R,2-Q,3-S,4-P$

asked Feb 12, 2019 in Electromagnetics by Arjun (1.4k points)

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7

GATE2019 EC: 23
Radiation resistance of a small dipole current element of length $l$ at a frequency of $3$ GHz is $3$ ohms. If the length is changed by $1\%$, then the percentage change in the radiation resistance, rounded off to two decimal places, is ________ $\%.$

asked Feb 12, 2019 in Electromagnetics by Arjun (1.4k points)

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8

GATE2019 EC: 24
In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8\: V$ and $-10\: V$, respectively. Assume that the diode is ideal and $R_{1}=R_{2}=50\: \Omega.$ The average value of $V_{L}$ is _______ volts (rounded off to $1$ decimal place).

asked Feb 12, 2019 in Electromagnetics by Arjun (1.4k points)

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9

GATE2019 EC: 37
The dispersion equation of a waveguide, which relates the wavenumber $k$ to the frequency $\omega$ is $k(\omega)= (1/c) \sqrt{\omega^{2}-\omega_{\circ}^{2}}$ where the speed of light $c= 2 \times 10^{8}\: m/s$ and $\omega_{\circ}$ ... $2 \times 10^{8}\: m/s$ $3 \times 10^{8}\: m/s$ $4.5 \times 10^{8}\: m/s$

asked Feb 12, 2019 in Electromagnetics by Arjun (1.4k points)

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10

GATE2019 EC: 51
A rectangular waveguide of width $w$ and height $h$ has cut-off frequencies for $TE_{10}$ and $TE_{11}$ modes in the ration $1:2$ . The aspect ratio $w/h$, rounded off to two decimal places , is _______.

asked Feb 12, 2019 in Electromagnetics by Arjun (1.4k points)

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11

GATE2016-3-24
If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be right-handed circularly polarized left-handed circularly polarized elliptically polarized with a tilt angle of $45^ \circ$ horizontally polarized

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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12

GATE2016-3-25
Faraday's law of electromagnetic induction is mathematically described by which one of the following equations? $\nabla\ \bullet \overrightarrow{B} = 0$ $\nabla\ \bullet \overrightarrow{D} = \rho_V$ ...

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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13

GATE2016-3-52
Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. At $10 \:GHz$ operating frequency, the value of the propagation constant (per meter) of the corresponding propagation mode is _______

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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14

GATE2016-3-53
Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. The increasing order of the cut-off frequencies for different modes is $TE_{01}<TE_{10}<TE_{11}<TE_{20}$ $TE_{20}<TE_{11}<TE_{10}<TE_{01}$ $TE_{10}<TE_{20}<TE_{01}<TE_{11}$ $TE_{10}<TE_{11}<TE_{20}<TE_{01}$

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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15

GATE2016-3-54
A radar operating at $5\:GHz$ uses a common antenna for transmission and reception. The antenna has a gain of $150$ and is aligned for maximum directional radiation and reception to a target $1\:km$ away having radar cross-section of $3\:m^2$. If it transmits $100\:kW$, then the received power (in $\mu W)$ is _______

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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16

GATE2016-3-55
Consider the charge profile shown in the figure. The resultant potential distribution is best described by

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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17

GATE2016-2-23
A uniform and constant magnetic field $\textbf{B}=\hat{z}B$ exists in the $\hat{z}$ direction in vacuum. A particle of mass $m$ with a small charge $q$ is introduced into this region with an initial velocity $\textbf{v}=\hat{x}v_{x}+\hat{z}v_{z}$. ... $xy$ plane. Linear motion in the $\hat{z}$ direction. Linear motion in the $\hat{x}$ direction.

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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18

GATE2016-2-24
Let the electric field vector of a plane electromagnetic wave propagating in a homogeneous medium be expressed as $\textbf{E}=\hat{x}E_{x}e^{-j(\omega t-\beta z)},$ where the propogation constant $\beta$ is a function of the angular frequency $\omega$. ... polarization of the wave. The group velocity of the wave. The phase velocity of the wave. The power flux through the $z=0$ plane.

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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19

GATE2016-2-25
Light from free space is incident at an angle $\theta _{i}$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are $n _{1}=1.5$ and $n _{2}=1.4$, respectively. The maximum value of $\theta _{i}$ (in degrees) for which the incident light will be guided in the core of the fibre is _________

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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20

GATE2016-2-53
A lossless microstrip transmission line consists of a trace of width $w$. It is drawn over a pratically infinite ground plane and is separated by a dielectric slab of thickness $t$ and relative permittivity $\varepsilon _{r}> 1.$ The inductance per unit length and the characteristic ... $Z_{0}< \sqrt{\frac{Lt}{\varepsilon _{0}\varepsilon _{\gamma}t}}$

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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21

GATE2016-2-54
A microwave circuit consisting of lossless transmission lines $T_{1}$ and $T_{2}$ is shown in the figure. The plot shows the magnitude of the input reflection coefficient $\Gamma$ as a function of frequency $f$. The phase velocity of the signal in the transmission lines is $2\times 10^{8}$ $m/s$. The length $L$ (in meters) of $T_{2}$ is _________

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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22

GATE2016-1-25
The propagation constant of a lossy transmission line is $(2+j5) m^{-1}$ and its characteristic impedance is $(50+j0) \Omega$ at $\omega = 10^6 rad \: s^{-1}$ ... $L = 250 \: \mu H/m, C = 0.2 \: \mu F/m, R=50 \: \Omega /m, \: G=0.04 \: S/m$

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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23

GATE2016-1-52
An antenna pointing in a certain direction has a noise temperature of $50 \: K$. The ambient temperature is $290 \: K$. The antenna is connected to a pre-amplifier that has a noise figure of $2$ dB and an available gain of $40$ dB over an effective bandwidth of $12$ MHz. The effective ... $P_{a0} = 3.85 \times 10^{-10}W$ $T_e = 160.62\thinspace K$ and $P_{a0} = 4.6\times 10^{-10}W$

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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24

GATE2016-1-53
Two lossless X-band horn antennas are separated by a distance of $200 \lambda$. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are $0.15$ and $0.18$,respectively. The maximum directives of the ... antennas are perfectly aligned and polarization matched, the power ( in mW) delivered to the load at the receiver is _________

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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25

GATE2016-1-54
The electric field of a uniform plane wave traveling along the negative $z$ direction is given by the following equation: ${\overrightarrow {E}^i_w= ( \hat {a}_x+ j\hat {a}_y)E_0e^{jkz}}$ This wave is incident upon a receiving antenna placed at the origin and ... ), $-5$dB Circular(clockwise), Linear, $-5$dB Circular(clockwise), Linear, $-3$dB Circular(anti clockwise), Linear, $-3$dB

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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26

GATE2016-1-55
The far-zone power density radiated by a helical antenna is approximated as: ${\overrightarrow W_{rad}= \overrightarrow W_{average} \approx \hat {a_r}C_0\frac{1}{r^2}\cos^4\theta}$ The radiated power density is symmetrical with respect to $\phi$ and exists only ... and the maximum directivity of the antenna, respectively, are $1.5C_0,10dB$ $1.256C_0,10dB$ $1.256C_0,12dB$ $1.5C_0,12dB$

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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27

GATE2015-3-24
The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements improves the radiation efficiency increases the effective area of the antenna results in a better impedance matching allows more power to be transmitted by the antenna

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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28

GATE2015-3-25
A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon $(\varepsilon_{r} = 2.1, \tan \delta = 0).$ Which one of the following circuits can represent the lumped element model of a small piece of this cable having length $\Delta z$?

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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29

GATE2015-3-53
Consider the $3\:m$ long lossless air-filled transmission line shown in the figure. It has a characteristic impedance of $120\pi\: \Omega,$ is terminated by a short circuit, and is excited with a frequency of $37.5\: MHz.$ What is the nature of the input impedance $(Z_{in})?$ Open Short Inductive Capacitive

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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30

GATE2015-2-24
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 _______.

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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31

GATE2015-2-25
The electric field of a uniform plane electromagnetic wave is $\overrightarrow{E} = \left(\overrightarrow{a}_{x} + j 4 \overrightarrow{a}_{y}\right) \text{exp }[j(2\pi \times 10^{7}t – 0.2z)].$ The polarization of the wave is right handed circular right handed elliptical left handed circular left handed elliptical

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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32

GATE2015-2-53
An air-filled rectangular waveguide of internal dimensions $a\: cm \times b\: cm\:(a>b)$ 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 __________.

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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33

GATE2015-2-55
The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expression $\text{E}(z,t) = \textbf{a}_{x} 5 \cos(2\pi \times 10^{9}t + \beta z) + \textbf{a}_{y} 3 \cos\left(2\pi \times 10^{9} t + \beta z – \frac{\pi}{2}\right)$ The type of the polarization is Right Hand Circular Left Hand Elliptical Right Hand Elliptical Linear

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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34

GATE2015-1-21
The polar plot of the transfer function $G(s) = \frac{10(s+1)}{s+10}$ for $0 \leq \omega < \infty$ will be in the first quadrant second quadrant third quadrant fourth quadrant

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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35

GATE2015-1-25
The electric field component of a plane wave traveling in a lossless dielectric medium is given by $\overrightarrow{E}(z,t) = \hat{a}_y 2 \cos \bigg( 10^st-\frac{z}{\sqrt{2}} \bigg) \: V/m$. The wavelength (in m) for the wave is ___________.

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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36

GATE2015-1-37
All the logic gates shown in the figure have a propagation delay of $20$ ns. Let $A=C=0$ and $B=1$ until time $t=0$. At $t=0$, all the inputs flip (i.e., $A=C=1$ and $B=0$) and remain in that state. For $t>0$, output $Z=1$ for a duration (in ns) of ________.

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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37

GATE2015-1-53
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 ... $b=0.033 \: m$. The mode of propagation inside the waveguide is $TM_{12}$ $TM_{21}$ $TE_{21}$ $TE_{12}$

asked Mar 28, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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38

GATE2014-4-8
At $T=300 \:K$, the band gap and the intrinsic carrier concentration of GaAs are $1.42$ eV and $10^6 \: cm^{-3}$, respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength $(\lambda_C)$ ranges of incident radiation, is most suitable? (Given that: Plank's ... $1.62 \: \mu m < \lambda _C < 6.62 \: \mu m$

asked Mar 26, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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39

GATE2014-4-11
If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will reduce both the voltage gain and the input impedance reduce the voltage gain and increase the input impedance increase the voltage gain and reduce the input impedance reduce both the voltage gain and the input impedance

asked Mar 26, 2018 in Electromagnetics by Milicevic3306 (15.8k points)

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40

GATE2014-4-24
For an antenna radiating in free space, the electric field at a distance of $1$ km is found to be $12 \: mV/m$. Given that intrinsic impedance of the free space is $120 \pi \: \Omega$, the magnitude of average power density due to this antenna at a distance of $2$ km from the antenna (in $nW/m^2$) is _________.

asked Mar 26, 2018 in Electromagnetics by Milicevic3306 (15.8k points)