GATE ECE

Sinusoidal Steady State Response

Network Theory

(Past Years Questions)

Marks 1

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In the circuit shown, $$V$$ is a sinusoidal voltage source. The current $$I$$ is in phase with voltage $$V$$. The ratio...
GATE ECE 2017 Set 2
In the circuit shown, the positive angular frequency $$\omega$$ (in radians per second) at which magnitude of the phase ...
GATE ECE 2017 Set 1
In the $$RLC$$ circuit shown in the figure, the input voltage is given by vi(t) = 2 cos(200t)+4 sin(500t). The out...
GATE ECE 2016 Set 3
The figure shows an $$RLC$$ circuit with a sinusoidal current source. At response, the ratio $$\left| {{{\rm I}_L}} \...
GATE ECE 2016 Set 2
At very high frequencies, the peak output voltage V0 (in Volts) is ______. ...
GATE ECE 2015 Set 3
The voltage (VC) across the capacitor (in Volts) In the network shown is ________. ...
GATE ECE 2015 Set 2
In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is _________...
GATE ECE 2015 Set 1
For parallel RLC circuit, which one of the following statements is NOT correct?
GATE ECE 2010
The RC circuit shown in the figure is ...
GATE ECE 2007
In a series $$RLC$$ circuit $$R = 2\,k\Omega ,\,\,\,L = \,1H$$ and $$C = \,1/400\,\mu F.$$ The resonant frequency is
GATE ECE 2005
The circuit shown in figure, with $$R = 1/3\Omega $$, $$L = 1/4H$$, $$C = 3F$$ has input voltage $$v\left( t \right) = \...
GATE ECE 2004
For the circuit shown in figure, the time constant $$RC = 1$$ $$ms$$. The input voltage is $${v_i}\left( t \right) = \sq...
GATE ECE 2004
A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 100. If each R, L and C is doubled from...
GATE ECE 2003
The circuit of Fig. represents a ...
GATE ECE 2000
The parallel $$RLC$$ circuit shown in figure is in resonance. In this circuit ...
GATE ECE 1998
In Fig., A1, A2 and A3 are ideal ammeters. If A2 and A3 read 3 A and 4 A respectively, then A1 should read ...
GATE ECE 1996
In the circuit of Fig., assume that the diodes are ideal and the meter is an average indicating ammeter. The ammeter wil...
GATE ECE 1996
A DC voltage source is connected across a series R-L-C circuit. Under steady-state conditions, the applied DC voltage dr...
GATE ECE 1995
Consider a DC voltage source connected to a series R-C circuit. When the steady-state reaches, the ratio of the energy s...
GATE ECE 1995
The current $$i(t)$$ through a $$10$$-$$\Omega $$ resistor in series with an inductance is given by $$i(t)$$$$ = 3 + 4\...
GATE ECE 1995
A series $$R$$-$$L$$-$$C$$ circuit has a $$Q$$ of $$100$$ and an impedance of $$\left( {100 + j0} \right)\,\Omega $$ at ...
GATE ECE 1995
A series LCR circuit consisting of $$R = 10\Omega $$, $$\left| {{X_L}} \right|\,\,\, = 20\Omega $$ and $$\left| {{X_C}} ...
GATE ECE 1994
In the series circuit shown in figure, for series resonance, the value of the coupling coefficient K will be ...
GATE ECE 1993

Marks 2

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For the circuit given in the figure, the voltage VC (in volts) across the capacitor is : ...
GATE ECE 2018
In the circuit shown the voltage $${V_{IN}}\,\left( t \right)$$ is described by: $$${V_{IN}}\,\left( t \right) = \left\...
GATE ECE 2017 Set 1
The figure shows an RLC circuit excited by the sinusoidal voltage $$100cos(3t)$$ Volts, where $$t$$ is in seconds. The ...
GATE ECE 2017 Set 1
An AC voltage source V = 10 sin(t) volts is applied to the following network. Assume that R1 = 3 kΩ, R2 = 6 kΩ and R3 = ...
GATE ECE 2016 Set 1
A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all ...
GATE ECE 2016 Set 1
In the circuit shown, the current $${\rm I}$$ flowing through the $$50\,\Omega $$ resistor will be zero if the value of ...
GATE ECE 2015 Set 3
In the given circuit, the maximum power (in Watts) that can be transferred to the load RL is ___________________. ...
GATE ECE 2015 Set 1
The damping ratio of a series $$RLC$$ circuit can be expressed as
GATE ECE 2015 Set 1
The steady state output of the circuit shown in the figure is given by $$$y\left( t \right) = {\rm A}\left( \omega \ri...
GATE ECE 2014 Set 4
Consider the building block called 'Network N' shown in the figure. Let $$C = 100\,\mu F\,\,$$ and $$R = 10\,k\Omega $$...
GATE ECE 2014 Set 3
A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such t...
GATE ECE 2014 Set 2
A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power fa...
GATE ECE 2014 Set 1
A periodic variable x is shown in the figure as a function of time. The root - mean - square (rms) value of x is _______...
GATE ECE 2014 Set 1
In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is _...
GATE ECE 2014 Set 1
The current I in the circuit shown is ...
GATE ECE 2010
An AC source of RMS voltage $$20$$ $$V$$ with internal impedance $${Z_s} = \left( {1 + 2j} \right)\Omega $$ feeds a loa...
GATE ECE 2009
In the AC network shown in the figure, the phasor voltage VAB (in Volts) is: ...
GATE ECE 2007
Two series resonant filters are as shown in the figure. Let the $$3$$-dB bandwidth of Filter $$1$$ be $${B_1}$$ and that...
GATE ECE 2007
For the circuit in figure, the phase current $${{\rm I}_1}$$ is ...
GATE ECE 2005
Consider the following statements S1 and S2. S1: The $$\beta$$ of a bipolar transistor reduces if the base width is incr...
GATE ECE 2004
The transfer function $$H\left( s \right) = {{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}}$$ of an R-L-C circui...
GATE ECE 2004
The current flowing through the resistance R in the circuit in figure has the form P cos 4t, where P is ...
GATE ECE 2003
An input voltage $$v(t)$$ $$ = 10\sqrt 2 \,\,\cos \,\,\left( {t + {{10}^0}} \right) + 10\sqrt 5 \,\,\cos \left( {2t + {{...
GATE ECE 2003
If the 3-phase balanced source in Fig. delivers 1500 W at a leading power factor of 0.844, then the value of ZL (in ohm)...
GATE ECE 2002
When the angular frequency $$\omega $$ in Fig. is varied from $$0$$ to $$\infty $$ the locus of the current phasor $${{\...
GATE ECE 2001
In Fig., the steady state output voltage corresponding to the input voltage $$\left( {3 + 4\sin \,\,100\,t} \right)$$ $...
GATE ECE 2000
In figure, A1, A2 and A3 are ideal ammeters. If A1 reads 5 A, A2, A2 reads 12 A, then A3 should read ...
GATE ECE 1993
For the series R-L-C circuit of figure(a), the partial phasor diagram at a certain frequency is shown in figure (b).The ...
GATE ECE 1992
In a series RLC high Q circuit, the current peaks at a frequency
GATE ECE 1991
The resonant frequency of this series circuit shown in figure is ...
GATE ECE 1990
The transfer function of simple RC network functioning as a controller is $$$G\,{}_c\left( s \right)\,\,\,\,{{s + {z_1}...
GATE ECE 1990
The half - power bandwidth of the resonant circuit of figure can be increased by ...
GATE ECE 1989
The value of current through the 1F capacitor of figure is. ...
GATE ECE 1987

Marks 5

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For network shown in Fig. $$R\, = \,1\,k\Omega $$ $${L_1} = 2\,H,\,{L_2} = 5\,H,\,{L_3}\, = \,1H,{L_4} = 4H\,\,\,$$ and...
GATE ECE 2002
For the circuit shown in the figure, determine the phasors E2, E0, I and I1. ...
GATE ECE 2001
For the circuit in Fig. Which is in steady state, (a)Find the frequency $${\omega _0}$$ at which the magnitude of the...
GATE ECE 2000
A coil with a quality factor $$(Q)$$ of $$10$$ is put in series with a capacitor $${C_1}$$ of $$10\,\,\mu F,$$ and the c...
GATE ECE 1999
Determine the frequency of resonance and the resonant impedance of the parallel circuit shown in figure. What happens wh...
GATE ECE 1998
In the circuit of Fig., all currents and voltage are sinusoids of frequency $$\omega $$ rad/sec. (a) Find the impedanc...
GATE ECE 1997
Write down the mesh equation of the following network in terms of i1(t) and i2(t).Derive the differential equation for i...
GATE ECE 1994
Calculate the frequency at which zero- transmission is obtained from the Wien- bridge shown in Fig. ...
GATE ECE 1994

Marks 8

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The impedance function of a parallel $$R$$, $$L$$, $$C$$ circuit has poles located at $$ - 3 \pm j4$$ rad/sec. If the ...
GATE ECE 1987

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