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121
GATE2018IN: 11
An ideal square wave with period of 20ms shown in the figure, is passed through an ideal low pass filter with cut-off frequency 120 Hz. Which of the following is an accurate description of the output? Output is zero Output consists of both 50 Hz and 100 Hz frequency components. Output is a pure sinusoid of frequency 50Hz Output is a square wave of fundamental frequency 50Hz.
An ideal square wave with period of 20ms shown in the figure, is passed through an ideal low pass filter with cut-off frequency 120 Hz. Which of the following is an accur...
gatecse
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122
GATE IN 2022 | Question: 13
The output $\text{F}$ of the digital circuit shown can be written in the form(s) __________ $\overline{A \cdot B}$ $\overline{A} + \overline{B}$ $\overline{A+B}$ $\overline{A} \cdot \overline{B}$
The output $\text{F}$ of the digital circuit shown can be written in the form(s) __________$\overline{A \cdot B}$$\overline{A} + \overline{B}$$\overline{A+B}$$\overline{A...
Lakshman Bhaiya
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Lakshman Bhaiya
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123
GATE IN 2022 | Question: 40
For the complex number $z= \frac{a+jb}{a-jb},$ where $a>0$ and $b>0.$ Which of the following statement(s) is/are true? The phase is $2 \; \tan^{-1}\frac{b}{a}$ The phase is $ \; \tan^{-1}\frac{2b}{a}$ The magnitude is $1$ The magnitude is $\sqrt{\frac{a^{2}+b^{2}}{a^{2}-b^{2}}}$
For the complex number $z= \frac{a+jb}{a-jb},$ where $a>0$ and $b>0.$Which of the following statement(s) is/are true?The phase is $2 \; \tan^{-1}\frac{b}{a}$The phase is ...
Lakshman Bhaiya
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Lakshman Bhaiya
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124
GATE IN 2022 | Question: 43
In a unity-gain feedback control system, the plant $P(s) = \frac{0.001}{s(2s+1)(0.01s+1)}$ is controlled by a lag compensator $C(s) = \frac{s+10}{s+0.1}$ The slope $(\text{in dB/decade})$ of the asymptotic Bode magnitude plot of the loop gain at $\omega = 3 \; \text{rad/s}$ is _________ (in integer)
In a unity-gain feedback control system, the plant$$P(s) = \frac{0.001}{s(2s+1)(0.01s+1)}$$is controlled by a lag compensator$$C(s) = \frac{s+10}{s+0.1}$$The slope $(\tex...
Lakshman Bhaiya
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Lakshman Bhaiya
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125
GATE IN 2022 | Question: 44
Given Circuit $\text{A}$ with currents $I_{1}$ and $I_{2}$ as shown, the current $I_{3}$ in Circuit $\text{B}$ (in amperes), is _________ (round off to one decimal place)
Given Circuit $\text{A}$ with currents $I_{1}$ and $I_{2}$ as shown, the current $I_{3}$ in Circuit $\text{B}$ (in amperes), is _________ (round off to one decimal place)...
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126
GATE IN 2022 | Question: 49
A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air $= 8.854 \times 10^{-12} \; \text{F/m}.)$ The radii of the inner and outer spheres are $a = 10 \; \text{cm}$ and $b = 15 \; \text{cm},$ respectively .The capacitance (in picofarads) is ___________ (round off to $2$ decimal places)
A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air $= 8.854 \times 10^{-12} \; \text{F/m}.)$ The radii of the i...
Lakshman Bhaiya
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127
GATE IN 2022 | Question: 52
In the circuit shown, the capacitance $C_{0}=10 \; \mu \text{F}$ and inductance $\text{L}_{0} = 1 \; \text{mH}$ and the diode is ideal. The capacitor is initially charged to $10 \; \text{V}$ and the current in the inductor is initially zero. If the switch is closed at $t=0 \; \text{s},$ the voltage $V_{c}(t)$ (in volts) across the capacitor at $t=0.5 \; \text{s}$ is (round off to one decimal place)
In the circuit shown, the capacitance $C_{0}=10 \; \mu \text{F}$ and inductance $\text{L}_{0} = 1 \; \text{mH}$ and the diode is ideal. The capacitor is initially charged...
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128
GATE IN 2021 | Question: 19
Given: Density of mercury is $\text{13,600 kg/}$ $m^{3}$ and acceleration due to gravity is $\text{9.81 m/s}^{2}$. Atmospheric pressure is $\text{101 kPa}$. In a mercury $\text{U}$-tube manometer, the difference between the heights of the liquid in the $\text{U}$-tube is $\text{1 cm}$. The differential pressure being measured in pascal is ___________ (rounded off to the nearest integer).
Given: Density of mercury is $\text{13,600 kg/}$ $m^{3}$ and acceleration due to gravity is $\text{9.81 m/s}^{2}$. Atmospheric pressure is $\text{101 kPa}$. In a mercury ...
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129
GATE2012-24
For the circuit shown in the figure, the voltage and current expressions are $v(t)=E_1\sin(\omega t)+E_3\sin(3\omega t)$ and $i(t)=I_1\sin(\omega t-\phi_1)+I_3\sin(3\omega t-\phi_3)+I_5\sin(5\omega t).$ The average power measured by the Wattmeter is $\frac{1}{2}E_1I_1\cos\phi_1$ $\frac{1}{2}[E_1I_1\cos\phi_1+E_1I_3\cos\phi_3+E_1I_5]$ $\frac{1}{2}[E_1I_1\cos\phi_1+E_3I_3\cos\phi_3]$ $\frac{1}{2}[E_1I_1\cos\phi_1+E_3I_1\cos\phi_1]$
For the circuit shown in the figure, the voltage and current expressions are $v(t)=E_1\sin(\omega t)+E_3\sin(3\omega t)$ and $i(t)=I_1\sin(\omega t-\phi_1)+I_3\sin(3\omeg...
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130
GATE2018IN: 52
Assuming ideal opamp, the $RMS$ voltage (in mV) in the output $V{_o}$ only due to the $230V,\; 50\; Hz$ interference is (up to one decimal place) __________.
Assuming ideal opamp, the $RMS$ voltage (in mV) in the output $V{_o}$ only due to the $230V,\; 50\; Hz$ interference is (up to one decimal place) __________.
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131
GATE IN 2022 | Question: 37
In the small circuit shown, the enhancement mode $n$-channel $\text{MOSFET}$ is biased in saturation with a transconductance $g_{m}.$ A small signal low-frequency voltage $v_{d}$ injected at the supply terminal results in a small signal voltage fluctuation $v_{o}$ at the output. If the channel length modulation of the $\text{MOSFET}$ is ignored, the small signal gain ... $\dfrac{-g_{m}R_{o}}{1+2g_{m}R_{o}}$ $\left(\dfrac{g_{m}R_{o}}{2} + \dfrac{3}{2}\right)^{-1}$
In the small circuit shown, the enhancement mode $n$-channel $\text{MOSFET}$ is biased in saturation with a transconductance $g_{m}.$ A small signal low-frequency voltage...
Lakshman Bhaiya
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132
GATE IN 2021 | Question: 15
The transistor $Q_{1}$ has a current gain $\beta _{1}=99$ and the transistor $Q_{2}$ has a current gain $\beta _{2}=49$. The current $I_{B2}$ in microampere is ______________.
The transistor $Q_{1}$ has a current gain $\beta _{1}=99$ and the transistor $Q_{2}$ has a current gain $\beta _{2}=49$. The current $I_{B2}$ in microampere is __________...
Arjun
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133
GATE2020 IN: 54
In the Maxwell-Wien bridge shown, the detector D reads zero when $C_1=100 nF$ and $R_1=100 k\Omega$. The Q factor of the coil is ______
In the Maxwell-Wien bridge shown, the detector D reads zero when $C_1=100 nF$ and $R_1=100 k\Omega$. The Q factor of the coil is ______
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134
GATE2016-3
A voltage $V_1$ is measured $100$ times and its average and standard deviation are $100$ V and $1.5$ V respectively. A second voltage $V_2$, which is independent of $V_1$, is measured $200$ times and its average and standard deviation are $150$ V and $2$ V respectively. $V_3$ is computed as: $V_3$=$V_1$+$V_2$. Then the standard deviation of $V_3$ in volt is_____.
A voltage $V_1$ is measured $100$ times and its average and standard deviation are $100$ V and $1.5$ V respectively. A second voltage $V_2$, which is independent of $V_1...
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135
GATE2018IN: 20
A voltage of 6 cos(100$\pi$t) V is fed as y-input to a CRO. The waveform seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are respectively 1 V/div and 1 ms/div 1 V/div and 2 ms/div 2 V/div and 1 ms/div 2 V/div and 2 ms/div
A voltage of 6 cos(100$\pi$t) V is fed as y-input to a CRO. The waveform seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are r...
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136
GATE IN 2022 | Question: 11
The logic block shown has an output $F$ given by ________ $A + B$ $A \cdot \overline{B}$ $A + \overline{B}$ $\overline{B}$
The logic block shown has an output $F$ given by ________$A + B$$A \cdot \overline{B}$$A + \overline{B}$$\overline{B}$
Lakshman Bhaiya
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137
GATE IN 2021 | Question: 4
The input-output relationship of an $\text{LTI}$ system is given below. For an input $x\left [ n \right ]$ shown below the peak value of the output when $x\left [ n \right ]$ passes through $\text{h}$ is _____________. $2$ $4$ $5$ $6$
The input-output relationship of an $\text{LTI}$ system is given below.For an input $x\left [ n \right ]$ shown belowthe peak value of the output when $x\left [ n \right ...
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138
GATE2017: 54
In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by $A_m(t)=100\cos(\omega_ct) +50\cos(\omega_mt)\cos(\omega_ct)$, where $\omega_c$ is the carrier frequency and $\omega_m$ is the modulation frequency. The power carried by the sidebands in $\%$ of total power is _______________$\%$.
In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by $A_m(t)=100\cos(\omega_ct) +50\cos(\omega_mt)\cos(\omega_ct)$, where $\omega_c...
soujanyareddy13
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139
GATE2015-62
A liquid level measurement system employing a radio-isotope is mounted on a tank as shown in the figure. The absorption coefficient of water for the radiation is $7.7 \;m^{-1}$. If the height of water in the tank is reduced from $100\; mm$ to $90\; mm$, the percentage change in the radiation intensity received by the detector, neglecting absorption of the radiation by air, is ______________ $\%$.
A liquid level measurement system employing a radio-isotope is mounted on a tank as shown in the figure. The absorption coefficient of water for the radiation is $7.7 \;m...
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140
GATE2018IN: 7
The Thevenin equivalent circuit representation across terminals p – q of the circuit shown in the figure is a 1 V source in series with 150k$\Omega$ 1 V source in parallel with 100k$\Omega$ 2 V source in series with 150k$\Omega$ 2 V source in parallel with 200k$\Omega$
The Thevenin equivalent circuit representation across terminals p – q of the circuit shown in the figure is a 1 V source in seri...
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141
GATE2018IN: 10
Consider signal x(t) = . Let $\delta$(t) denote the unit impulse (Dirac-delta) function. The value of the integral $ \int^5_0$ 2x(t- 3)$\delta$(t-4)dt is 2 1 0 3
Consider signal x(t) = . Let $\delta$(t) denote the unit impulse (Dirac-delta) function. The value of the integral $ \int^5_0$ 2x(t- 3)$\delta$(t-4)dt is 2103
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142
GATE IN 2021 | Question: 30
The output $V_{o}$ of the ideal $\text{OpAmP}$ used in the circuit shown below is $\text{5 V}$. Then the value of resistor $R_{L}$ in kilo ohm $(k \Omega)$ is $2.5$ $5$ $25$ $50$
The output $V_{o}$ of the ideal $\text{OpAmP}$ used in the circuit shown below is $\text{5 V}$. Then the value of resistor $R_{L}$ in kilo ohm $(k \Omega)$ is$2.5$$5$$25$...
Arjun
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143
GATE2013-30
The following arrangement consists of an ideal transformer and an attenuator, which attenuates by a factor of 0.8. An ac voltage $V_{WX1}=100V$ is applied across $WX$ to get an open circuit voltage $V_{YZ1}$ across $YZ$. Next, an ac voltage $V_{YZ2}=100V$ is applied across $YZ$ to get an open circuit voltage $V_{WX2}$ across $WX$ ... $125/100\; and\; 80/100$ $100/100\; and\; 80/100$ $100/100\; and\; 100/100$ $80/100\; and\; 80/100$
The following arrangement consists of an ideal transformer and an attenuator, which attenuates by a factor of 0.8. An ac voltage $V_{WX1}=100V$ is applied across $WX$ to ...
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144
GATE IN 2021 | Question: 22
When the movable arm of a Michelson interferometer in vacuum $(n=1)$ is moved by $325\: \mu m$ , the number of fringe crossings is $1000$. The wavelength of the laser used in nanometers is ___________________.
When the movable arm of a Michelson interferometer in vacuum $(n=1)$ is moved by $325\: \mu m$ , the number of fringe crossings is $1000$. The wavelength of the laser use...
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145
GATE2016-38
The transfer function $G(s)$ of a system which has the asymptotic Bode plot shown below is $10^4 \frac {(s-1)^2}{(s+100)^2}$ $10^4 \frac {(s+1)^2}{(s+100)^2}$ $10^4 \frac {(s+1)}{(s+100)^2}$ $10^4 \frac {(s-1)^2}{(s-100)^2}$
The transfer function $G(s)$ of a system which has the asymptotic Bode plot shown below is $10^4 \frac {(s-1)^2}{(s+100)^2}$$10^4 \frac {(s+1)^2}{(s+100)^2}$$10^4 \frac {...
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146
GATE2014-55
For the given low-pass circuit shown in the figure, the cutoff frequency in Hz will be ____________.
For the given low-pass circuit shown in the figure, the cutoff frequency in Hz will be ____________.
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147
GATE2018IN: 39
Unit step response of a linear time invariant $(LTI)$ system is given by $y(t) = (1 – e^{-2t})u(t)$. Assuming zero initial condition, the transfer function of the system is $\frac{1}{s+1}$ $\frac{2}{(s+1)(s+2)}$ $\frac{1}{s+2}$ $\frac{2}{s+2}$
Unit step response of a linear time invariant $(LTI)$ system is given by $y(t) = (1 – e^{-2t})u(t)$. Assuming zero initial condition, the transfer function of the syste...
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148
GATE IN 2022 | Question: 46
The circuit shown is driven by a sinusoidal input voltage, $V_{in},$ resulting in the output voltage, $V_{out}.$ The frequency (in kilohertz) at which the voltage gain is $0$ dB is _________ (round off to two decimal places)
The circuit shown is driven by a sinusoidal input voltage, $V_{in},$ resulting in the output voltage, $V_{out}.$ The frequency (in kilohertz) at which the voltage gain is...
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149
GATE IN 2022 | Question: 47
A conducting semi-circular loop of radius $R=0.1 \; \text{m}, $ with its diameter centered at the origin, rotates in the $x-y$ plane about the origin with a constant angular velocity, $\omega= 20 \; \text{rad/s},$ as shown. A magnetic field of magnitude $B=2T$ and normal to $x-y$ plane exists in ... loop has a resistance of $2 \; \Omega,$ and negligible inductance, the peak-to-peak current (in milliamperes) in the loop is ___________ (round off to one decimal place)
A conducting semi-circular loop of radius $R=0.1 \; \text{m}, $ with its diameter centered at the origin, rotates in the $x-y$ plane about the origin with a constant angu...
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150
GATE IN 2022 | Question: 53
The bridge shown is balanced when $R_{1}=100 \; \Omega , R_{2}=210 \; \Omega, C_{2}=2.9 \; \mu\text{F},$ and $R_{4}=50 \; \Omega.$ The $2\;\text{kHz}$ sine-wave generator supplies a voltage of $10 \; \text{V}_{\text{p-p}}.$ The value of $\text{L}_{3}$ (in millihenry) is __________ (round off to two decimal places)
The bridge shown is balanced when $R_{1}=100 \; \Omega , R_{2}=210 \; \Omega, C_{2}=2.9 \; \mu\text{F},$ and $R_{4}=50 \; \Omega.$ The $2\;\text{kHz}$ sine-wave generator...
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151
GATE2020 IN: 23
A $\text{200 mV}$ full-scale dual-slope analog to digital converter $\text{(DS-ADC)}$ has a reference voltage of $\text{100 mV}$. The first integration time is set as $\text{100 ms.}$ The $\text{DS-ADC}$ is operated in the continuous conversion mode. The conversion time of the $\text{DS-ADC}$ for an input voltage of $\text{123.4 mV (in ms, rounded off to one decimal place)}$ is _____.
A $\text{200 mV}$ full-scale dual-slope analog to digital converter $\text{(DS-ADC)}$ has a reference voltage of $\text{100 mV}$. The first integration time is set as $\t...
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152
GATE2019 IN: 31
The forward path transfer function L(s) of the control system shown in Figure(a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d(t) is given by d(t) = 0.1 sin($\omega$t) where $\omega$ = 5 rad/s, the steady-state amplitude of the output y(t) is 1.00x10$^{-3}$ 2.50x10$^{-3}$ 5.00x10$^{-3}$ 10.00x10$^{-3}$
The forward path transfer function L(s) of the control system shown in Figure(a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d(t) is given by d(t...
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153
GATE2019 IN: 37
A differential capacitive sensor with a distance between the extreme plates $100\;mm$ is shown in figure below. The difference voltage $\Delta V=V_1-V_2,$ where $V_1$ and $V_2$ are the rms values, for a downward displacement of $10\;mm$ of the intermediate plate from the central position, in volts, is __________. $0.9$ $1.0$ $1.1$ $2$
A differential capacitive sensor with a distance between the extreme plates $100\;mm$ is shown in figure below. The difference voltage $\Delta V=V_1-V_2,$ where $V_1$ and...
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154
GATE2015-18
A p-type semiconductor strain gauge has a nominal resistance of $1000\;\Omega$ and a gauge factor of $+200$ at $25\;^\circ C$. The resistance of the strain gauge in ohms when subjected to a strain of $+10^{-4}$ m/m at the same temperature is __________ $\Omega$.
A p-type semiconductor strain gauge has a nominal resistance of $1000\;\Omega$ and a gauge factor of $+200$ at $25\;^\circ C$. The resistance of the strain gauge in ohms ...
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155
GATE IN 2022 | Question: 10
The resistance of a pure copper wire of length $10 \; \text{cm}$ and diameter $1 \; \text{mm}$ is to be measured. The most suitable method from amongst the choices given below is _________ Two wire method Three wire method Four wire method Ellipsometry
The resistance of a pure copper wire of length $10 \; \text{cm}$ and diameter $1 \; \text{mm}$ is to be measured. The most suitable method from amongst the choices given ...
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156
GATE IN 2022 | Question: 42
In the circuit shown, the load is driven by a sinusoidal ac voltage source $V_{1} =100 \; \angle 0^{\circ} \; \text{V}$ at $50 \; \text{Hz}.$ Given $R_{1}=20 \; \Omega, C_{1} = \left(\frac{1000}{\pi}\right) \mu \text{F, L}_{1} = \left(\frac{20}{\pi}\right) \; \text{mH} $ and $R_{2} = 4 \; \Omega,$ the power factor is _________ (round off to one decimal place)
In the circuit shown, the load is driven by a sinusoidal ac voltage source $V_{1} =100 \; \angle 0^{\circ} \; \text{V}$ at $50 \; \text{Hz}.$ Given $R_{1}=20 \; \Omega, ...
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157
GATE IN 2022 | Question: 50
A $1 \; \text{kHz}$ sine-wave generator having an internal resistance of $50 \; \Omega$ generates an open-circuit voltage of $10 \; \text{V}_{\text{p-p}}.$ When a capacitor is connected across the output terminals, the voltage drops to $8 \; \text{V}_{\text{p-p}}$. The capacitance of the capacitor (in microfarads) is _________________ (round off to two decimal places)
A $1 \; \text{kHz}$ sine-wave generator having an internal resistance of $50 \; \Omega$ generates an open-circuit voltage of $10 \; \text{V}_{\text{p-p}}.$ When a capacit...
Lakshman Bhaiya
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Lakshman Bhaiya
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158
GATE2016-7
An air cored coil has a $Q$ of $5$ at a frequency of $100$ kHz. The $Q$ of the coil at $20$ kHz (neglecting skin effect) will be ________.
An air cored coil has a $Q$ of $5$ at a frequency of $100$ kHz. The $Q$ of the coil at $20$ kHz (neglecting skin effect) will be ________.
Milicevic3306
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Milicevic3306
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GATE2016-15
The diode $D$ used in the circuit below is ideal. The voltage drop $V_{ab}$ across the $1\;k\Omega$ resistor in $\text{volt}$ is $\_\_\_\_\_\_\_\_.$
The diode $D$ used in the circuit below is ideal. The voltage drop $V_{ab}$ across the $1\;k\Omega$ resistor in $\text{volt}$ is $\_\_\_\_\_\_\_\_.$
Milicevic3306
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Milicevic3306
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160
GATE2016-48
The comparators (output=$’1’$, when input $\underline{>}$ and output=$’0’$, when input$<0$), exclusive-OR gate and the unity gain low-pass filter given in the circuit are ideal. The logic output voltages of the exclusive-OR gate are $\text{0 V}$ and $\text{5 V}$. The cutoff frequency of the low-pass filter is $\text{0.1 Hz}$. For $V_1=1 \sin (3000t+36^0)V$ and $V_2=1 \sin (3000t)V$, the value of $V_0$ in $volt$ is $\_\_\_\_\_\_\_\_.$
The comparators (output=$’1’$, when input $\underline{>}$ and output=$’0’$, when input$<0$), exclusive-OR gate and the unity gain low-pass filter given in the cir...
Milicevic3306
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Milicevic3306
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