Sinusoidal Steady State Analysis · Electric Circuits · GATE EE
Start PracticeMarks 1
GATE EE 2023
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
...
GATE EE 2022
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 ________....
GATE EE 2022
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 i...
GATE EE 2017 Set 2
The mean square value of the given periodic waveform f(t) is_________.
...
GATE EE 2015 Set 1
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 ne...
GATE EE 2015 Set 2
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 angu...
GATE EE 2012
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
A two phase load draws the following phase currents:
$$i_1\left(t\right)=I_m\sin\left(\omega t-\phi_1\right)$$,
$$i_2\left(t\right)=I_m\cos\le...
GATE EE 2011
The r.m.s value of the current i(t) in the circuit shown below is
...
GATE EE 2011
The voltage applied to a circuit is $$100\sqrt2\cos\left(100\mathrm{πt}\right)$$ volts and the circuit draws
a current of $$10\sqrt2\;\sin\left(100\ma...
GATE EE 2004
The value of $$Z$$ in Fig., which is most appropriate to cause parallel resonance at $$500$$ $$Hz$$ is
...
GATE EE 2001
In a series $$RLC$$ circuit at resonance, the magnitude of the voltage developed across the capacitor
GATE EE 1999
A series $$R-L-C$$ circuit when excited by a $$10$$ $$V$$ sinusoidal voltage source of variable frequency, exhibits resonance at $$100$$ $$Hz$$ and ha...
GATE EE 1999
The $$RMS$$ value of half $$-$$ wave rectified symmetrical square wave current of $$2A$$ is
GATE EE 1999
The current in the circuit shown in figure is
...
GATE EE 1998
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 reson...
GATE EE 1998
A sinusoidal source of voltage $$V$$ and frequency $$f$$ is connected to a series circuit of variables resistance, $$R$$ and a fixed reactance, $$X.$$...
GATE EE 1996
In the circuit shown in Fig. $$X$$ $$-$$ is an element which always absorbs power. During a particular operation, it sets up a current of $$1$$ $$amp...
GATE EE 1995
In the circuit of Figure, Ammeter $${A_2}$$ reads $$12$$ $$A$$ and $${A_3}$$ reads $$9$$ $$A.$$ $${A_1}$$ will read ______
...
GATE EE 1995
A series $$R-L-C$$ circuit has the following parameter values:
$$R = 10\Omega ,\,\,L = 0.01\,H,\,\,C = 100\,\,m\,\,F.$$
The $$Q$$ factor of the circ...
GATE EE 1994
At resonance, the given parallel circuit constituted by an iron - cored coil and a capacitor behaves like
...
GATE EE 1993
The following circuit (Fig.) resonates at
...
GATE EE 1993
In the following circuit (Fig.) $$i(t)$$ under steady state is
...
Marks 2
GATE EE 2024
For the circuit shown in the figure, the source frequency is 5000 rad/sec. The mutual inductance between the magnetically coupled inductors is 5 mH wi...
GATE EE 2019
A 0.1 μF capacitor charged to 100 V is discharged through a 1 kΩ resistor. The time in ms (round off to two decimal places) required for the voltage a...
GATE EE 2017 Set 2
In the circuit shown below, the value of capacitor C required for maximum power to be
transferred to the load is
...
GATE EE 2016 Set 1
In the circuit shown below, the supply voltage is 10sin(1000t) volts. The peak value of the steady
state current through the 1Ω resistor, in amperes, ...
GATE EE 2016 Set 1
The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the
admittance of the circuit becomes a pure conductance at all f...
GATE EE 2015 Set 1
The circuit shown in the figure has two sources connected in
series. The instantaneous voltage of the AC source (in volt) is
given by v(t) = 12sint. I...
GATE EE 2015 Set 2
A symmetrical square wave of 50% duty cycle
has amplitude of ±15V and time period of 0.4$$\mathrm\pi$$
ms. This square wave is applied across a series...
GATE EE 2015 Set 2
Two identical coils each having inductance L are placed together on the same core. If an
overall inductance of $$\alpha$$L is obtained by interconnect...
GATE EE 2015 Set 2
In the given network $$V_1=100\angle0^\circ V$$, $$V_2=100\angle-120^\circ V$$, $$V_3=100\angle+120^\circ V$$. The phasor
current i (in Ampere) is
...
GATE EE 2014 Set 2
The voltage across the capacitor, as sown in the figure, is expressed as
$$$V_c\left(t\right)=A_1\sin\left(\omega_1t-\theta_1\right)+A_2\sin\left(\ome...
GATE EE 2014 Set 2
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 ________...
GATE EE 2014 Set 3
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...
GATE EE 2013
Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the
chosen operating frequency. Their respective resistances are R1 and R2 . Wh...
GATE EE 2012
In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V.
The power factor of the load is...
GATE EE 2012
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...
GATE EE 2011
An RLC circuit with relevant data is given below.
The current $${\underline I}_C$$ in the figure above is ...
GATE EE 2011
An RLC circuit with relevant data is given below.
The power dissipated in the resistor R is...
GATE EE 2007
The resonant frequency for the given circuit will be
...
GATE EE 2007
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 ...
GATE EE 2007
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 va...
GATE EE 2006
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 $${\rm I...
GATE EE 2005
The $$RL$$ circuit of the figure is fed from a constant magnitude, variable frequency sinusoidal voltage source $${V_{IN.}}$$ At $$100Hz,$$ the $$R$$...
GATE EE 2004
In Fig. the admittance values of the elements in Siemens are
$${Y_R} = 0.5 + j0,$$
$${Y_L} = 0 - j\,1.5,$$
$${Y_C} = 0 + j\,0.3$$ respectively.
Th...
GATE EE 2003
In the circuit of Fig. the magnitudes of $${V_L}$$ and $${V_C}$$ are twice that of $${V_R}$$. The inductance of the coil is
...
GATE EE 2002
In the circuit shown in Fig. what value of $$C$$ will cause a unity power factor at the $$ac$$ source?
...
GATE EE 2002
A series $$R-L-C$$ circuit has $$R = 50\Omega ;$$ $$L=100$$ $$\mu H$$ and $$C = 1\,\,\mu F.$$ The lower half power frequency of the circuit is
GATE EE 2002
In the circuit shown in Fig. it is found that the input $$ac$$ voltage $$\left( {{V_i}} \right)$$ and current $$i$$ are in phase. The coupling coeffi...
GATE EE 2002
A first order, low pass filter is given with $$R = 50\,\,\Omega $$ and $$C$$ $$ = 5\mu F.$$ What is the frequency at which the gain of the voltage tr...
GATE EE 2000
If an $$ac$$ voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency...
GATE EE 2000
The impedance seen by the source in the circuit in Fig. is given by
...
GATE EE 1999
A fixed capacitor of reactance –$$j0.02$$ $$\Omega $$ is connected in parallel across a series combination of a fixed inductor of reactance $$j0.01$$ ...
GATE EE 1999
The voltage phasor of a circuit is $$10\angle {15^0}\,V$$ and the current phasor is $$2\,\,\angle - {45^0}A.$$ The active and the reactive powers in ...
GATE EE 1997
Two identical coils of negligible resistance when connected in series across a $$200V,$$ $$50$$ $$Hz$$ source draws, a current of $$10$$ $$A.$$ When t...
GATE EE 1996
A coil (which can be modeled as a series $$RL$$ circuit) has been designed for high $$-$$ $$Q$$ performance at a rated voltage and a specified frequen...
GATE EE 1994
In the given circuit, the voltage $$\overline {{V_L}} $$ has a phase angle of ____________ with respect to $$\overline {{V_S}} .$$
...
Marks 5
GATE EE 2001
Determine the resonance frequency and the $$Q$$ $$-$$ factor of the circuit shown in Fig.
Data: $$\,\,\,\,\,R = 10\,\Omega ,\,\,\,\,\,\,\,\,\,\,\,\...
GATE EE 1998
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 ...
GATE EE 1998
Determine the impedance seen by the source $${V_s} = 24\angle {0^0}$$ in the network shown in Fig.
...