Sinusoidal Steady State Analysis · Electric Circuits · GATE EE
Marks 1
1
A single-phase voltage source $v_s=325 \sin (2 \pi 50 t) \vee$ delivers a current, $i=12 \sin (2 \pi 50 t) +9 \sin (2 \pi 50 t)$ A to a load.
The load power factor, correct up to two decimal places, is
GATE EE 2026
2
The input voltage $v(t)$ and current $i(t)$ of a converter are given by, $v(t)=300 \sin (\omega t) \mathrm{V}$
$$ i(t)=10 \sin \left(\omega t-\frac{\pi}{6}\right)+2 \sin \left(3 \omega t+\frac{\pi}{6}\right)+\sin \left(5 \omega t+\frac{\pi}{2}\right) A $$
where, $\omega=2 \pi \times 50 \mathrm{rad} / \mathrm{s}$. The input power factor of the converter is closest to
GATE EE 2025
3
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
4
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
5
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
6
A signal generator having a source resistance of $50 \Omega$ is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to 8 V peak-to-peak. The value of this capacitor is $\_\_\_\_$ $\mu \mathrm{F}$. (Round off to 2 decimal places)
GATE EE 2021
7
The mean square value of the given periodic waveform f(t) is_________.
GATE EE 2017 Set 2
8
An inductor is connected in parallel with a capacitor as shown in the figure.
As the frequency of current i is increased, the impedance (Z) of the network varies as
As the frequency of current i is increased, the impedance (Z) of the network varies asGATE EE 2015 Set 1
9
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
10
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
11
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
12
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
13
The r.m.s value of the current i(t) in the circuit shown below is
GATE EE 2011
14
The value of $$Z$$ in Fig., which is most appropriate to cause parallel resonance at $$500$$ $$Hz$$ is
GATE EE 2004
15
In a series $$RLC$$ circuit at resonance, the magnitude of the voltage developed across the capacitor
GATE EE 2001
16
The current in the circuit shown in figure is
GATE EE 1999
17
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
18
The $$RMS$$ value of half $$-$$ wave rectified symmetrical square wave current of $$2A$$ is
GATE EE 1999
19
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
20
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
21
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
22
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
$$R = 10\Omega ,\,\,L = 0.01\,H,\,\,C = 100\,\,m\,\,F.$$
The $$Q$$ factor of the circuit at resonance is
GATE EE 1995
23
In the circuit of Figure, Ammeter $${A_2}$$ reads $$12$$ $$A$$ and $${A_3}$$ reads $$9$$ $$A.$$ $${A_1}$$ will read ______
GATE EE 1995
24
At resonance, the given parallel circuit constituted by an iron - cored coil and a capacitor behaves like
GATE EE 1994
25
The following circuit (Fig.) resonates at
GATE EE 1993
26
In the following circuit (Fig.) $$i(t)$$ under steady state is
GATE EE 1993
Marks 2
1
An electrical component has voltage drop $v=V_m \sin (\omega t)$, when the current through it is $i=I_m \sin (\omega t-\theta)$. What is the average power dissipated over a half cycle corresponding to $\omega$ ?
GATE EE 2026
2
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
3
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
4
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
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
6
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
7
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
8
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
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
10
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
11
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
12
The voltage across the capacitor, as sown in the figure, is expressed as
$$$V_c\left(t\right)=A_1\sin\left(\omega_1t-\theta_1\right)+A_2\sin\left(\omega_2t-\theta_2\right)$$$
The value of A1 and A2 respectively, are
The value of A1 and A2 respectively, areGATE EE 2014 Set 2
13
The total power dissipated in the circuit, show in the figure, is 1kW.
The ideal voltmeter, across the load, reads 200 V. The value of XL is _________.
The ideal voltmeter, across the load, reads 200 V. The value of XL is _________.
GATE EE 2014 Set 2
14
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
15
In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V.
If RL=5 Ω , the approximate power consumption in the load is
If RL=5 Ω , the approximate power consumption in the load isGATE EE 2012
16
In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V.
The power factor of the load is
The power factor of the load isGATE EE 2012
17
An RLC circuit with relevant data is given below.
The power dissipated in the resistor R is
The power dissipated in the resistor R isGATE EE 2011
18
An RLC circuit with relevant data is given below.
The current $${\underline I}_C$$ in the figure above is
The current $${\underline I}_C$$ in the figure above is GATE EE 2011
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
20
The resonant frequency for the given circuit will be
GATE EE 2007
21
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
22
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 $${\rm I}$$.
The phasor diagram which is applicable to this circuit is
GATE EE 2006
23
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
24
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
$${Y_R} = 0.5 + j0,$$
$${Y_L} = 0 - j\,1.5,$$
$${Y_C} = 0 + j\,0.3$$ 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
25
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
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
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
28
In the circuit shown in Fig. what value of $$C$$ will cause a unity power factor at the $$ac$$ source?
GATE EE 2002
29
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
30
The impedance seen by the source in the circuit in Fig. is given by
GATE EE 2000
31
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
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
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
34
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
35
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
36
In the given circuit, the voltage $$\overline {{V_L}} $$ has a phase angle of ____________ with respect to $$\overline {{V_S}} .$$
GATE EE 1994
Marks 5
1
Determine the resonance frequency and the $$Q$$ $$-$$ factor of the circuit shown in Fig.
Data: $$\,\,\,\,\,R = 10\,\Omega ,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C = 3\,\mu F,$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{L_1} = 40\,mH,\,\,\,\,\,\,\,\,{L_2} = 10\,mH$$
and $$\,\,\,\,\,\,\,\,M = 10\,mH.$$
Data: $$\,\,\,\,\,R = 10\,\Omega ,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C = 3\,\mu F,$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{L_1} = 40\,mH,\,\,\,\,\,\,\,\,{L_2} = 10\,mH$$
and $$\,\,\,\,\,\,\,\,M = 10\,mH.$$
GATE EE 2001
2
A circuit consisting of a single resistor $$R$$ and an inductor $$L$$ in series is driven by a $$25$$ $$V$$ $$rms,$$ $$50$$ $$Hz$$ sinusoidal voltage source. A capacitor is to be placed in parallel with the source to improve the power factor. Given that the average power dissipated in the $$R$$ is $$100$$ $$W$$ and that the reactive power delivered to the $$L$$ is $$75$$ $$VAR,$$ what value of $$C$$ will yield a $$0.9$$ $$p.f.$$ lagging as seen by the source?
GATE EE 1998
3
Determine the impedance seen by the source $${V_s} = 24\angle {0^0}$$ in the network shown in Fig.
GATE EE 1998