Sinusoidal Steady State Analysis · Electric Circuits · GATE EE

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Marks 1

1

The value of parameters of the circuit shown in the figure are

$${R_1} = 2\Omega ,{R_2} = 2\Omega ,{R_3} = 3\Omega ,L = 10$$ mH, $$C = 100$$ $$\mu$$F

For time t < 0, the circuit is at steady state with the switch 'K' in closed condition. If the switch is opened at t = 0, the value of the voltage across the inductor (V$$_L$$) at t = 0$$^+$$ in Volts is ___________ (Round off to 1 decimal place).

GATE EE 2023 Electric Circuits - Sinusoidal Steady State Analysis Question 2 English

GATE EE 2023
2

An inductor having a Q-factor of 60 is connected in series with a capacitor having a Q-factor of 240. The overall Q-factor of the circuit is ________. (round off to nearest integer).

GATE EE 2022
3

The network shown below has a resonant frequency of 150 kHz and a bandwidth of 600 Hz. The Q-factor of the network is _______. (round off to nearest integer).

GATE EE 2022 Electric Circuits - Sinusoidal Steady State Analysis Question 4 English

GATE EE 2022
4
The mean square value of the given periodic waveform f(t) is_________. GATE EE 2017 Set 2 Electric Circuits - Sinusoidal Steady State Analysis Question 61 English
GATE EE 2017 Set 2
5
An inductor is connected in parallel with a capacitor as shown in the figure. GATE EE 2015 Set 1 Electric Circuits - Sinusoidal Steady State Analysis Question 59 English As the frequency of current i is increased, the impedance (Z) of the network varies as
GATE EE 2015 Set 1
6
Find the transformer ratios a and b that the impedance (Zin) is resistive and equal 2.5 Ω when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s. GATE EE 2015 Set 2 Electric Circuits - Sinusoidal Steady State Analysis Question 60 English
GATE EE 2015 Set 2
7
The average power delivered to an impedance $$\left(4-j3\right)$$ Ω by a current $$5\cos\left(100\mathrm{πt}+100\right)\;A$$ is
GATE EE 2012
8
A two phase load draws the following phase currents: $$i_1\left(t\right)=I_m\sin\left(\omega t-\phi_1\right)$$, $$i_2\left(t\right)=I_m\cos\left(\omega t-\phi_2\right)$$. These currents are balanced if $$\phi_1$$ is equal to
GATE EE 2012
9
The r.m.s value of the current i(t) in the circuit shown below is GATE EE 2011 Electric Circuits - Sinusoidal Steady State Analysis Question 55 English
GATE EE 2011
10
The voltage applied to a circuit is $$100\sqrt2\cos\left(100\mathrm{πt}\right)$$ volts and the circuit draws a current of $$10\sqrt2\;\sin\left(100\mathrm{πt}+\mathrm\pi/4\right)$$ amperes. Taking the voltage as the reference phasor, the phasor representation of the current in amperes is
GATE EE 2011
11
The value of $$Z$$ in Fig., which is most appropriate to cause parallel resonance at $$500$$ $$Hz$$ is GATE EE 2004 Electric Circuits - Sinusoidal Steady State Analysis Question 27 English
GATE EE 2004
12
In a series $$RLC$$ circuit at resonance, the magnitude of the voltage developed across the capacitor
GATE EE 2001
13
The $$RMS$$ value of half $$-$$ wave rectified symmetrical square wave current of $$2A$$ is
GATE EE 1999
14
A series $$R-L-C$$ circuit when excited by a $$10$$ $$V$$ sinusoidal voltage source of variable frequency, exhibits resonance at $$100$$ $$Hz$$ and has a $$3$$ $$dB$$ bandwidth of $$5$$ $$Hz.$$ The voltage across the inductor $$L$$ at resonace is

GATE EE 1999
15
The current in the circuit shown in figure is GATE EE 1999 Electric Circuits - Sinusoidal Steady State Analysis Question 29 English
GATE EE 1999
16
A sinusoidal source of voltage $$V$$ and frequency $$f$$ is connected to a series circuit of variables resistance, $$R$$ and a fixed reactance, $$X.$$ The locus of the tip of the current phasor, $$I$$, as $$R$$ is varied from $$0$$ to $$\infty $$ is
GATE EE 1998
17
A circuit with a resistor, inductor and capacitor in series is resonant at $${f_0}\,\,Hz.$$ If all the component values are now doubled, the new resonant frequency is
GATE EE 1998
18
In the circuit shown in Fig. $$X$$ $$-$$ is an element which always absorbs power. During a particular operation, it sets up a current of $$1$$ $$amp$$ in the direction shown and absorbs a power $${P_{x}}.$$ It is possible that $$X$$ can absorb the same power $${P_x}$$ for another current $$i.$$ Then the value of this current is GATE EE 1996 Electric Circuits - Sinusoidal Steady State Analysis Question 34 English
GATE EE 1996
19
A series $$R-L-C$$ circuit has the following parameter values:
$$R = 10\Omega ,\,\,L = 0.01\,H,\,\,C = 100\,\,m\,\,F.$$
The $$Q$$ factor of the circuit at resonance is
GATE EE 1995
20
In the circuit of Figure, Ammeter $${A_2}$$ reads $$12$$ $$A$$ and $${A_3}$$ reads $$9$$ $$A.$$ $${A_1}$$ will read ______ GATE EE 1995 Electric Circuits - Sinusoidal Steady State Analysis Question 35 English
GATE EE 1995
21
At resonance, the given parallel circuit constituted by an iron - cored coil and a capacitor behaves like GATE EE 1994 Electric Circuits - Sinusoidal Steady State Analysis Question 37 English
GATE EE 1994
22
In the following circuit (Fig.) $$i(t)$$ under steady state is GATE EE 1993 Electric Circuits - Sinusoidal Steady State Analysis Question 39 English
GATE EE 1993
23
The following circuit (Fig.) resonates at GATE EE 1993 Electric Circuits - Sinusoidal Steady State Analysis Question 38 English
GATE EE 1993

Marks 2

1

For the circuit shown in the figure, the source frequency is 5000 rad/sec. The mutual inductance between the magnetically coupled inductors is 5 mH with their self inductances being 125 mH and 1 mH. The Thevenin’s impedance, $Z_{th}$, between the terminals P and Q in $\Omega$ is ______________ (rounded off to 2 decimal places).

GATE EE 2024 Electric Circuits - Sinusoidal Steady State Analysis Question 1 English
GATE EE 2024
2
A 0.1 μF capacitor charged to 100 V is discharged through a 1 kΩ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to 1 V is ___________.
GATE EE 2019
3
In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is GATE EE 2017 Set 2 Electric Circuits - Sinusoidal Steady State Analysis Question 54 English
GATE EE 2017 Set 2
4
The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the admittance of the circuit becomes a pure conductance at all frequencies is ________. GATE EE 2016 Set 1 Electric Circuits - Sinusoidal Steady State Analysis Question 53 English
GATE EE 2016 Set 1
5
In the circuit shown below, the supply voltage is 10sin(1000t) volts. The peak value of the steady state current through the 1Ω resistor, in amperes, is _________. GATE EE 2016 Set 1 Electric Circuits - Sinusoidal Steady State Analysis Question 52 English
GATE EE 2016 Set 1
6
The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volt) is given by v(t) = 12sint. If the circuit is in steady-state, then the rms value of the current (in Ampere) flowing in the circuit is ______. GATE EE 2015 Set 1 Electric Circuits - Sinusoidal Steady State Analysis Question 48 English
GATE EE 2015 Set 1
7
A symmetrical square wave of 50% duty cycle has amplitude of ±15V and time period of 0.4$$\mathrm\pi$$ ms. This square wave is applied across a series RLC circuit with R = 5Ω, L = 10 mH, and C = 4μF. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is __________. GATE EE 2015 Set 2 Electric Circuits - Sinusoidal Steady State Analysis Question 49 English
GATE EE 2015 Set 2
8
Two identical coils each having inductance L are placed together on the same core. If an overall inductance of $$\alpha$$L is obtained by interconnecting these two coils, the minimum value of $$\alpha$$ is ________.
GATE EE 2015 Set 2
9
In the given network $$V_1=100\angle0^\circ V$$, $$V_2=100\angle-120^\circ V$$, $$V_3=100\angle+120^\circ V$$. The phasor current i (in Ampere) is GATE EE 2015 Set 2 Electric Circuits - Sinusoidal Steady State Analysis Question 51 English
GATE EE 2015 Set 2
10
The total power dissipated in the circuit, show in the figure, is 1kW. GATE EE 2014 Set 2 Electric Circuits - Sinusoidal Steady State Analysis Question 46 English The ideal voltmeter, across the load, reads 200 V. The value of XL is _________.
GATE EE 2014 Set 2
11
The voltage across the capacitor, as sown in the figure, is expressed as $$$V_c\left(t\right)=A_1\sin\left(\omega_1t-\theta_1\right)+A_2\sin\left(\omega_2t-\theta_2\right)$$$ GATE EE 2014 Set 2 Electric Circuits - Sinusoidal Steady State Analysis Question 45 English The value of A1 and A2 respectively, are
GATE EE 2014 Set 2
12
A series RLC circuit is observed at two frequencies. At $$\omega_1$$ = 1k rad / s, we note that source voltage $$V_1=100\angle0^\circ V$$ results in a current $$I_1=0.03\angle31^\circ\;A$$. At $$\omega_2$$ = 2 k rad/s, the source voltage $$V_2=100\angle0^\circ\;V$$ results in a current $$I_2=2\angle0^\circ\;A$$. The closest values for R,L,C out of the following options are
GATE EE 2014 Set 3
13
Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2 . When connected in series, their effective Q factor at the same operating frequency is
GATE EE 2013
14
In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V. GATE EE 2012 Electric Circuits - Sinusoidal Steady State Analysis Question 43 English The power factor of the load is
GATE EE 2012
15
In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V. GATE EE 2012 Electric Circuits - Sinusoidal Steady State Analysis Question 42 English If RL=5 Ω , the approximate power consumption in the load is
GATE EE 2012
16
An RLC circuit with relevant data is given below. GATE EE 2011 Electric Circuits - Sinusoidal Steady State Analysis Question 40 English The current $${\underline I}_C$$ in the figure above is
GATE EE 2011
17
An RLC circuit with relevant data is given below. GATE EE 2011 Electric Circuits - Sinusoidal Steady State Analysis Question 41 English The power dissipated in the resistor R is
GATE EE 2011
18
The $$R-L-C$$ series circuit shown is supplied from a variable frequency voltage source. The admittance $$-$$ locus of the $$R-L$$ $$-C$$ network at terminals $$AB$$ for increasing frequency $$\omega $$ is GATE EE 2007 Electric Circuits - Sinusoidal Steady State Analysis Question 11 English
GATE EE 2007
19
In the figure given below, all phasors are with reference to the potential at point $$''O''.$$ The locus of voltage phasor $${V_{YX}}$$ as $$R$$ is varied from zero to infinity is shown by GATE EE 2007 Electric Circuits - Sinusoidal Steady State Analysis Question 10 English
GATE EE 2007
20
The resonant frequency for the given circuit will be GATE EE 2007 Electric Circuits - Sinusoidal Steady State Analysis Question 9 English
GATE EE 2007
21
The circuit shown in the figure is energized by a sinusoidal voltage source $${V_1}$$ at a frequency which causes resonance with a current of $${\rm I}$$. GATE EE 2006 Electric Circuits - Sinusoidal Steady State Analysis Question 12 English

The phasor diagram which is applicable to this circuit is

GATE EE 2006
22
The $$RL$$ circuit of the figure is fed from a constant magnitude, variable frequency sinusoidal voltage source $${V_{IN.}}$$ At $$100Hz,$$ the $$R$$ and $$L$$ elements each have a voltage drop $${u_{RMS}}.$$ If the frequency of the source is changed to $$50Hz,$$ then new voltage drop across $$R$$ is GATE EE 2005 Electric Circuits - Sinusoidal Steady State Analysis Question 14 English
GATE EE 2005
23
In Fig. the admittance values of the elements in Siemens are
$${Y_R} = 0.5 + j0,$$
$${Y_L} = 0 - j\,1.5,$$
$${Y_C} = 0 + j\,0.3$$ respectively.
The value of $${\rm I}$$ as a phasor when the voltage $$E$$ across the elements is $$10\angle {0^0}\,V$$ is GATE EE 2004 Electric Circuits - Sinusoidal Steady State Analysis Question 15 English
GATE EE 2004
24
In the circuit of Fig. the magnitudes of $${V_L}$$ and $${V_C}$$ are twice that of $${V_R}$$. The inductance of the coil is GATE EE 2003 Electric Circuits - Sinusoidal Steady State Analysis Question 16 English
GATE EE 2003
25
In the circuit shown in Fig. it is found that the input $$ac$$ voltage $$\left( {{V_i}} \right)$$ and current $$i$$ are in phase. The coupling coefficient is $$K = {M \over {\sqrt {{L_1}{L_2}} }},$$ where $$M$$ is the mutual inductance between the two coils. The value of $$K$$ and the dot polarity of the coil $$P-Q$$ are GATE EE 2002 Electric Circuits - Sinusoidal Steady State Analysis Question 17 English
GATE EE 2002
26
A first order, low pass filter is given with $$R = 50\,\,\Omega $$ and $$C$$ $$ = 5\mu F.$$ What is the frequency at which the gain of the voltage transfer function of the filter is $$0.25?$$
GATE EE 2002
27
A series $$R-L-C$$ circuit has $$R = 50\Omega ;$$ $$L=100$$ $$\mu H$$ and $$C = 1\,\,\mu F.$$ The lower half power frequency of the circuit is
GATE EE 2002
28
In the circuit shown in Fig. what value of $$C$$ will cause a unity power factor at the $$ac$$ source? GATE EE 2002 Electric Circuits - Sinusoidal Steady State Analysis Question 20 English
GATE EE 2002
29
The impedance seen by the source in the circuit in Fig. is given by GATE EE 2000 Electric Circuits - Sinusoidal Steady State Analysis Question 22 English
GATE EE 2000
30
If an $$ac$$ voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency component in terms of
GATE EE 2000
31
A fixed capacitor of reactance –$$j0.02$$ $$\Omega $$ is connected in parallel across a series combination of a fixed inductor of reactance $$j0.01$$ $$\Omega $$ and a variable resistance $$R.$$ As $$R$$ is varied from zero to infinity, the locus diagram of the admittance of this $$L-C-R$$ circuit will be
GATE EE 1999
32
The voltage phasor of a circuit is $$10\angle {15^0}\,V$$ and the current phasor is $$2\,\,\angle - {45^0}A.$$ The active and the reactive powers in the circuit are
GATE EE 1999
33
Two identical coils of negligible resistance when connected in series across a $$200V,$$ $$50$$ $$Hz$$ source draws, a current of $$10$$ $$A.$$ When the terminals of one of the coils are reversed, then current drawn is $$8$$ $$A.$$ The coefficient of coupling between the two coils is
GATE EE 1997
34
A coil (which can be modeled as a series $$RL$$ circuit) has been designed for high $$-$$ $$Q$$ performance at a rated voltage and a specified frequency. If the frequency of operation is doubled, and the coil is operated at the same rated voltage, then the $$Q$$$$-$$factor and the active power $$P$$ consumed by the coil will be affected as follows
GATE EE 1996
35
In the given circuit, the voltage $$\overline {{V_L}} $$ has a phase angle of ____________ with respect to $$\overline {{V_S}} .$$ GATE EE 1994 Electric Circuits - Sinusoidal Steady State Analysis Question 13 English
GATE EE 1994

Marks 5

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