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201
GATE Electrical 2021 | Question: 23
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{2}$ is __________ $k \Omega$. (Round off to $2$ decimal places.)
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{...
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202
GATE Electrical 2021 | Question: 42
Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity $5$. The plates are initially charged to a potential difference of $V$ volts and then disconnected from the source ... of the new electric field $E_{2}$ in the gap to the original electric field $E_{1}$ is ________.
Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity $5$. The plates are initi...
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203
GATE Electrical 2021 | Question: 44
A belt-driven $\text{DC}$ shunt generator running at $300\: \text{RPM}$ delivers $100 \:\text{kW}$ to a $200 \:V\: \text{DC}$ grid. It continues to run as a motor when the belt breaks, taking $10 \:\text{kW}$ from the $\text{DC}$ grid ... drop is $2 \:V$. Ignoring armature reaction, the speed of the motor is _____ $\text{RPM}$. (Round off to $2$ decimal places.)
A belt-driven $\text{DC}$ shunt generator running at $300\: \text{RPM}$ delivers $100 \:\text{kW}$ to a $200 \:V\: \text{DC}$ grid. It continues to run as a motor when th...
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204
GATE Electrical 2021 | Question: 52
A $\text{CMOS}$ Schmitt-trigger inverter has a low output level of $\text{0 V}$ and a high output level of $\text{5 V}$. It has input thresholds of $\text{1.6 V}$ and $\text{2.4 V}$. The input capacitance and output resistance of the Schmitt-trigger are negligible. The frequency of the oscillator shown is ____________$\text{Hz}$.(Round off to $2$ decimal places.)
A $\text{CMOS}$ Schmitt-trigger inverter has a low output level of $\text{0 V}$ and a high output level of $\text{5 V}$. It has input thresholds of $\text{1.6 V}$ and $\t...
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205
GATE Electrical 2021 | Question: 18
The power input to a $\text{500 V, 50 Hz, 6-pole, 3-phase}$ induction motor running at $975 \text{RPM}$ is $40 \text{ kW}$ . The total stator losses are $1 \text{ kW}$. If the total friction and windage losses are $2.025\text{ kW}$, then the efficiency is _____________$\%$.
The power input to a $\text{500 V, 50 Hz, 6-pole, 3-phase}$ induction motor running at $975 \text{RPM}$ is $40 \text{ kW}$ . The total stator losses are $1 \text{ kW}$. I...
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206
GATE Electrical 2021 | Question: 46
Consider a closed-loop system as shown. $G_{P}\left ( s \right )=\dfrac{14.4}{s\left ( 1+0.1s \right )}$ is the plant transfer function and $G_{c}(S)=1$ is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is ___________________ $\text{rad/s}$. (Round off to $2$ decimal places.)
Consider a closed-loop system as shown. $G_{P}\left ( s \right )=\dfrac{14.4}{s\left ( 1+0.1s \right )}$ is the plant transfer function and $G_{c}(S)=1$ is the compensato...
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207
GATE Electrical 2021 | Question: 17
A $1\;\mu C$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10\;\mu C$ is moved from $\left ( 0,10,0 \right )$ to $\left ( 5,5,5\right )$ and subsequently to $\left ( 5,0,0\right )$, ... decimal places). Take $\dfrac{1}{4\pi \varepsilon _{0}}=9\times 10^{9}$ in $\text{SI}$ units. All coordinates are in meters.
A $1\;\mu C$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10\;\mu C$ is moved from $\left ( 0,10,0 \right )$ to $\lef...
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208
GATE Electrical 2021 | Question: 55
A single-phase full-bridge inverter fed by a $\text{325 V DC}$ produces a symmetric quasi-square waveform across '$ab$' as shown. To achieve a modulation index of $0.8$, the angle $\theta$ expressed in degrees should be _______________. ( ... is defined as the ratio of the peak of the fundamental component of $V_{ab}$ to the applied $\text{DC}$ value.)
A single-phase full-bridge inverter fed by a $\text{325 V DC}$ produces a symmetric quasi-square waveform across '$ab$' as shown. To achieve a modulation index of $0.8$, ...
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209
GATE Electrical 2021 | Question: 10
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are $\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$ $\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}$ They need to deliver a combined load of $260$ $\text{MW}$. Ignoring the network losses, for ... $P_{1}=P_{2}=130$ $P_{1}=160, P_{2}=100$ $P_{1}=140, P_{2}=120$ $P_{1}=120, P_{2}=140$
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are$\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$$\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}...
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210
GATE Electrical 2021 | Question: 29
In the circuit, switch '$S$' is in the closed position for a very long time. If the switch is opened at time $t = 0$, then in $i_{L} (t)$ amperes, for $t\geq0$ is $8e^{-10t}$ $10$ $8+2e^{-10t}$ $10\left ( 1-e^{-2t} \right )$
In the circuit, switch '$S$' is in the closed position for a very long time. If the switch is opened at time $t = 0$, then in $i_{L} (t)$ amperes, for $t\geq0$ is$8e^{-10...
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211
GATE Electrical 2021 | Question: 54
Consider the buck-boost converter shown. Switch $Q$ is operating at $\text{25 kHz}$ and $0.75$ duty-cycle. Assume diode and switch to be ideal. Under steady-state condition, the average current flowing through the indicator is ____________$A$.
Consider the buck-boost converter shown. Switch $Q$ is operating at $\text{25 kHz}$ and $0.75$ duty-cycle. Assume diode and switch to be ideal. Under steady-state conditi...
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212
GATE Electrical 2021 | Question: 12
Inductance is measured by Schering bridge Maxwell bridge Kelvin bridge Wien bridge
Inductance is measured bySchering bridgeMaxwell bridgeKelvin bridgeWien bridge
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213
GATE Electrical 2021 | Question: 27
Suppose the probability that a coin toss shows "head" is $p$, where $0<p<1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is $p/\left ( 1-p \right )$ $\left ( 1-p \right )/p$ $1/p$ $1/p^{2}$
Suppose the probability that a coin toss shows "head" is $p$, where $0<p<1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses r...
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214
GATE Electrical 2021 | Question: 40
In the given circuit, for maximum power to be delivered to $R_{L}$, its value should be ______________ $\Omega$. (Round off to $2$ decimal places.)
In the given circuit, for maximum power to be delivered to $R_{L}$, its value should be ______________ $\Omega$.(Round off to $2$ decimal places.)
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215
GATE Electrical 2021 | Question: 41
One coulomb of point charge moving with a uniform velocity $10\:\hat{X}$ $\text{m/s}$ enters the region $x\geq 0$ having a magnetic flux density $\overrightarrow{B}=\left ( 10y\:\hat{X} + 10x\:\hat{Y}+10\:\hat{Z}\right )T$. The magnitude of force on the ... ($\hat{X}$, $\hat{Y}$, and $\hat{Z}$ are unit vectors along $x$-axis, $y$-axis and $z$-axis, respectively.)
One coulomb of point charge moving with a uniform velocity $10\:\hat{X}$ $\text{m/s}$ enters the region $x\geq 0$ having a magnetic flux density $\overrightarrow{B}=\left...
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216
GATE Electrical 2021 | Question: 34
In the figure shown, self-impedances of the two transmission lines are $1.5j\:p.u$ each, and $Z_{m}=0.5j \:p.u$ is the mutual impedance. Bus voltages shown in the figure are in $p.u$. Given that $\delta>0$, the maximum steady-state real power that can be transferred ... $2\left | E \right |\left | V \right |$ $\frac{3\left | E \right |\left | V \right |}{2}$
In the figure shown, self-impedances of the two transmission lines are $1.5j\:p.u$ each, and $Z_{m}=0.5j \:p.u$ is the mutual impedance. Bus voltages shown in the figure ...
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217
GATE Electrical 2021 | Question: 45
An $8$-pole, $50 \:Hz$, three-phase, slip-ring induction motor has an effective rotor resistance of $0.08\:\Omega$ per phase. Its speed at maximum torque is $650 \text{ RPM}$. The additional resistance per ... Round off to $2$ decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.
An $8$-pole, $50 \:Hz$, three-phase, slip-ring induction motor has an effective rotor resistance of $0.08\:\Omega$ per phase. Its speed at maximum torque is $650 \text{ R...
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218
GATE Electrical 2021 | Question: 47
In the given figure, plant $G_{P}\left ( s \right )=\dfrac{2.2}{\left ( 1+0.1s \right )\left ( 1+0.4s \right )\left ( 1+1.2s \right )}$ ... is a unit step, the steady-state error should not exceed $0.1$ unit. The minimum value of $K$ is _____________. (Round off to $2$ decimal places.)
In the given figure, plant $G_{P}\left ( s \right )=\dfrac{2.2}{\left ( 1+0.1s \right )\left ( 1+0.4s \right )\left ( 1+1.2s \right )}$ and compensator $G_{C}\left ( s \r...
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219
GATE Electrical 2021 | Question: 49
The state space representation of a first-order system is given as $\overset{\bullet }{x}=-x+u$ $y=x$ where,$x$ is the state variable, $u$ is the control input and $y$ is the controlled output. Let $u=-Kx$ be the control law, where $K$ is the controller gain. To place a closed-loop pole at $-2$, the value of $K$ is ___________________.
The state space representation of a first-order system is given as $\overset{\bullet }{x}=-x+u$$y=x$where,$x$ is the state variable, $u$ is the control input and $y$ is t...
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220
GATE Electrical 2021 | Question: 31
The casual signal with $z$-transformer $Z^{2}\left ( Z-a \right )^{-2}$ is ($u[n]$ is the unit step signal) $a^{2n}u\left [ n \right ]$ $\left ( n+1 \right )a^{n}u\left [ n \right ]$ $n^{-1}a^{n}u\left [ n \right ]$ $n^{2}a^{n}u\left [ n \right ]$
The casual signal with $z$-transformer $Z^{2}\left ( Z-a \right )^{-2}$ is ($u[n]$ is the unit step signal)$a^{2n}u\left [ n \right ]$$\left ( n+1 \right )a^{n}u\left [ n...
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