Recent activity in Electromagnetics

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1

GATE ECE 2019 | Question: 48
A Germanium sample of dimensions $1\: cm \times 1\: cm$ is illuminated with a $20\:mW,$ $600\: nm$ laser light source as shown in the figure. The illuminated sample surface has a $100\: nm$ of loss-less Silicon dioxide layer that reflects one-fourth ... bandgap is $0.66\: eV,$ the thickness of the Germanium layer, rounded off to $3$ decimal places, is ________ $\mu m.$

A Germanium sample of dimensions $1\: cm \times 1\: cm$ is illuminated with a $20\:mW,$ $600\: nm$ laser light source as shown in the figure. The illuminated sample surfa...

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GATE ECE 2017 Set 1 | Question: 9
A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true? Silicon atoms act as $p$-type dopants in Arsenic sites and ... Arsenic sites as well as Gallium sites Silicon atoms act as $n$-type dopants in Arsenic sites as well as Gallium sites

A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statem...

Lakshman Bhaiya

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GATE ECE 2018 | Question: 49
A uniform plane wave traveling in free space and having the electric field ... ) as shown in the figure and there is no reflected wave. The relative permittivity (correct to two decimal places) of the dielectric medium is __________.

A uniform plane wave traveling in free space and having the electric field$$\overrightarrow{E} =\left ( \sqrt{2}\:\hat{a}_{x} -\hat{a}_{z}\right )cos\left [ 6\sqrt{3}\: \...

soujanyareddy13

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GATE ECE 2014 Set 4 | Question: 55
If $\overrightarrow{E} = -(2y^3 – 3yz^2)\hat{x} – (6xy^2-3xz^2) \hat{y}+(6xyz) \hat{z}$ is the electric field in a source free region, a valid expression for the electrostatic potential is $xy^3 – yz^2$ $2xy^3-xyz^2$ $y^3+xyz^2$ $2xy^3-3xyz^2$

If $\overrightarrow{E} = -(2y^3 – 3yz^2)\hat{x} – (6xy^2-3xz^2) \hat{y}+(6xyz) \hat{z}$ is the electric field in a source free region, a valid expression for the ele...

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GATE ECE 2017 Set 1 | Question: 25
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 ... factor of $2$ Decreases by a factor of $2$ Remains unchanged Decreases by a factor of $\sqrt{2}$

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 t...

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GATE ECE 2017 Set 1 | Question: 54
The expression for an electric field in free space is , $\textbf{E}=E_{0}( \hat{x}+\hat{y}+j2 \hat{z} )e^{-j( \omega t-kx+ky)}$ where $x,y,z$ represent the special coordinates, $t$ represents time, and ... normal to the $z$-axis represents an elliptically polarized plane wave propagating along the $x - y$ plane represents a linearly polarized plane wave

The expression for an electric field in free space is , $\textbf{E}=E_{0}( \hat{x}+\hat{y}+j2 \hat{z} )e^{-j( \omega t-kx+ky)}$ where $x,y,z$ represent the special coordi...

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GATE ECE 2017 Set 2 | Question: 55
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 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 c...

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GATE ECE 2019 | Question: 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 _______.

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...

soujanyareddy13

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GATE ECE 2018 | Question: 3
A good transimpedance amplifier has low input impedance and high output impedance high input impedance and high output impedance high input impedance and low output impedance low input impedance and low output impedance

A good transimpedance amplifier haslow input impedance and high output impedancehigh input impedance and high output impedancehigh input impedance and low output impedanc...

soujanyareddy13

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GATE ECE 2015 Set 1 | Question: 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 ___________.

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}{\sqr...

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GATE ECE 2019 | Question: 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).

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_{...

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GATE ECE 2019 | Question: 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 ________ $\%.$

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 ...

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GATE ECE 2016 Set 3 | Question: 25
Faraday's law of electromagnetic induction is mathematically described by which one of the following equations? $\nabla\ \bullet \overrightarrow{B} = 0$ $\nabla\ \bullet \overrightarrow{D} = \rho_V$ ...

Faraday’s law of electromagnetic induction is mathematically described by which one of the following equations?$\nabla\ \bullet \overrightarrow{B} = 0$$\nabla\ \bulle...

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GATE ECE 2016 Set 2 | Question: 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 $\beta$ ... of the wave. The group velocity of the wave. The phase velocity of the wave. The power flux through the $z=0$ plane.

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...

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GATE ECE 2014 Set 4 | Question: 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 _________.

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 \...

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GATE ECE 2015 Set 3 | Question: 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

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 circu...

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GATE ECE 2014 Set 4 | Question: 33
For the two-port network shown in the figure, the impedance (Z) matrix (in $\Omega$) is $\begin{bmatrix} 6 & 24 \\ 42 & 9 \end{bmatrix}$ $\begin{bmatrix} 9 & 8 \\ 8 & 24 \end{bmatrix}$ $\begin{bmatrix} 9 & 6 \\ 6 & 24 \end{bmatrix}$ $\begin{bmatrix} 42 & 6 \\ 6 & 60 \end{bmatrix}$

For the two-port network shown in the figure, the impedance (Z) matrix (in $\Omega$) is$\begin{bmatrix} 6 & 24 \\ 42 & 9 \end{bmatrix}$$\begin{bmatrix} 9 & 8 \\ 8 & 24 \e...

soujanyareddy13

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GATE ECE 2014 Set 1 | Question: 11
A good current buffer has low input impedance and low output impedance low input impedance and high output impedance high input impedance and low output impedance high input impedance and high output impedance

A good current buffer haslow input impedance and low output impedancelow input impedance and high output impedancehigh input impedance and low output impedancehigh input ...

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GATE ECE 2013 | Question: 23
A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\Omega$ should be $3$ $4$ $5$ $7$

A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum powe...

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GATE ECE 2013 | Question: 15
In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain $k$ is increased? The input impedance increases and output impedance decreases The input impedance increases and output ... also increases The input impedance decreases and output impedance also decreases The input impedance decreases and output impedance increases

In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain $k$ is increased? The input impedance increases and output impedan...

soujanyareddy13

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GATE ECE 2016 Set 1 | Question: 25
The propagation constant of a lossy transmission line is $(2+j5) m^{-1}$ and its characteristic impedance is $(50+j0) \Omega$ at $\omega = 10^6 rad \: s^{-1}$ ... $L = 250 \: \mu H/m, C = 0.2 \: \mu F/m, R=50 \: \Omega /m, \: G=0.04 \: S/m$

The propagation constant of a lossy transmission line is $(2+j5) m^{-1}$ and its characteristic impedance is $(50+j0) \Omega$ at $\omega = 10^6 rad \: s^{-1}$. The values...

soujanyareddy13

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GATE ECE 2016 Set 1 | Question: 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 ... $-5$dB Circular(clockwise), Linear, $-3$dB Circular(anti clockwise), Linear, $-3$dB

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 {...

soujanyareddy13

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GATE ECE 2016 Set 2 | Question: 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 ... $Z_{0}< \sqrt{\frac{Lt}{\varepsilon _{0}\varepsilon _{\gamma}t}}$

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 thi...

soujanyareddy13

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GATE ECE 2020 | Question: 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 ___________.

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+...

soujanyareddy13

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GATE ECE 2020 | Question: 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 $(0.5, 0)$.

The impedances $Z=jX,$ for all $X$ in the range $\left ( -\infty ,\infty \right )$, map to the Smith chart asa circle of radius $1$ with centre at $(0, 0)$.a point at the...

soujanyareddy13

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GATE ECE 2020 | Question: 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 __________ $\Omega$.

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 t...

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GATE ECE 2020 | Question: 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 $\left (\delta l \ll \lambda \right )$ ... field radiation pattern occurs at $\theta =60^{\circ}$, is $\lambda$ $0.5\lambda$ $0.25\lambda$ $0.75\lambda$

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...

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GATE ECE 2020 | Question: 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 __________.

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 $10 \Omega$, i...

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GATE ECE 2019 | Question: 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. ... $1-Q,2-R,3-P,4-S$ $1-Q,2-S,3-P,4-R$ $1-R,2-Q,3-S,4-P$

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 fo...

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GATE ECE 2019 | Question: 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 $\omega_{\circ}$ ... $2 \times 10^{8}\: m/s$ $3 \times 10^{8}\: m/s$ $4.5 \times 10^{8}\: m/s$

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 sp...

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GATE ECE 2018 | Question: 48
The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a\:\text{cm} \: \times \: b\: \text{cm}\:\left ( a> b \right )$ is twice that of the dominant $TE_{10}$ mode. When the waveguide is operated ... the guide wavelength is found to be $4\:\text{cm}$. The value of $b$ (in cm, correct to two decimal places) is ________.

The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a\:\text{cm} \: \times \: b\: \text{cm}\:\left ( a b \right )$ is t...

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GATE ECE 2018 | Question: 21
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 $\text{Np/m}$, correct to three decimal places) of the line is ________.

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 ...

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GATE ECE 2018 | Question: 10
The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: $\text{P: Open Circuit, Q: Short Circuit, R: Matched Load}$ $\text{P: Open Circuit, Q: Matched Load, R: Short Circuit}$ $\text{P: Short Circuit, Q: Matched Load, R: Open Circuit}$ $\text{P: Short Circuit, Q: Open Circuit, R: Matched Load}$

The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: $\text{P: Open Circu...

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GATE ECE 2016 Set 3 | Question: 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

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will beright-handed circularly polarizedleft-handed...

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GATE ECE 2016 Set 3 | Question: 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 _______

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 (pe...

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GATE ECE 2016 Set 3 | Question: 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 $TE_{01}<TE_{10}<TE_{11}<TE_{20}$ $TE_{20}<TE_{11}<TE_{10}<TE_{01}$ $TE_{10}<TE_{20}<TE_{01}<TE_{11}$ $TE_{10}<TE_{11}<TE_{20}<TE_{01}$

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_{...

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GATE ECE 2016 Set 3 | Question: 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 _______

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 r...

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GATE ECE 2016 Set 3 | Question: 55
Consider the charge profile shown in the figure. The resultant potential distribution is best described by

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

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GATE ECE 2016 Set 2 | Question: 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 $q$ ... . Circular motion in the $xy$ plane. Linear motion in the $\hat{z}$ direction. Linear motion in the $\hat{x}$ direction.

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...

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GATE ECE 2016 Set 2 | Question: 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 _________

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 ...

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