# Sinusoidal Steady State Response · Network Theory · GATE ECE

Start Practice## Marks 1

GATE ECE 2022

For the circuit shown, the locus of the impedance Z(j$$\omega$$) is plotted as $$\omega$$ increases from zero to infinity. The values of R1 and R2 are...

GATE ECE 2022

Consider the circuit shown in the figure with input V(t) in volts. The sinusoidal steady state current I(t) flowing through the circuit is shown graph...

GATE ECE 2017 Set 1

In the circuit shown, the positive angular frequency $$\omega$$ (in radians per second) at which
magnitude of the phase difference between the voltage...

GATE ECE 2017 Set 2

In the circuit shown, $$V$$ is a sinusoidal voltage source. The current $$I$$ is in phase with voltage $$V$$. The ratio $${{{\rm{Amplitude of voltage...

GATE ECE 2016 Set 2

The figure shows an $$RLC$$ circuit with a sinusoidal current source.
At response, the ratio $$\left| {{{\rm I}_L}} \right|/\left| {{{\rm I}_R}} \r...

GATE ECE 2016 Set 3

In the $$RLC$$ circuit shown in the figure, the input voltage is given by vi(t) = 2 cos(200t)+4 sin(500t). The output voltage v0(t) is
...

GATE ECE 2015 Set 2

The voltage (VC) across the capacitor (in Volts) In the network shown is ________....

GATE ECE 2015 Set 3

At very high frequencies, the peak output voltage V0 (in Volts) is ______.
...

GATE ECE 2015 Set 1

In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across
the capacitor is ___________.
...

GATE ECE 2010

For parallel RLC circuit, which one of the following statements is NOT correct?

GATE ECE 2007

The RC circuit shown in the figure is
...

GATE ECE 2005

In a series $$RLC$$ circuit $$R = 2\,k\Omega ,\,\,\,L = \,1H$$ and $$C = \,1/400\,\mu F.$$ The resonant frequency is

GATE ECE 2004

For the circuit shown in figure, the time constant $$RC = 1$$ $$ms$$. The input voltage is $${v_i}\left( t \right) = \sqrt 2 \,\sin \,{10^3}t$$. The o...

GATE ECE 2004

The circuit shown in figure, with $$R = 1/3\Omega $$, $$L = 1/4H$$, $$C = 3F$$ has input voltage $$v\left( t \right) = \sin \,2t$$. The resulting curr...

GATE ECE 2003

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 its original value, the new Q...

GATE ECE 2000

The circuit of Fig. represents a
...

GATE ECE 1998

The parallel $$RLC$$ circuit shown in figure is in resonance. In this circuit
...

GATE ECE 1996

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 will read
...

GATE ECE 1995

A DC voltage source is connected across a series R-L-C circuit. Under steady-state conditions, the applied DC voltage drops entirely across the

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 stored in the capacitor to the ...

GATE ECE 1995

The current $$i(t)$$ through a $$10$$-$$\Omega $$ resistor in series with an inductance is given by
$$i(t)$$$$ = 3 + 4\sin \left( {100t + {{45}^ \cir...

GATE ECE 1995

A series $$R$$-$$L$$-$$C$$ circuit has a $$Q$$ of $$100$$ and an impedance of $$\left( {100 + j0} \right)\,\Omega $$ at its resonant angular frequency...

GATE ECE 1994

A series LCR circuit consisting of $$R = 10\Omega $$, $$\left| {{X_L}} \right|\,\,\, = 20\Omega $$ and $$\left| {{X_C}} \right|\,\,\, = 20\Omega $$, i...

GATE ECE 1993

In the series circuit shown in figure, for series resonance, the value of the
coupling coefficient K will be
...

## Marks 2

GATE ECE 2018

For the circuit given in the figure, the voltage
VC
(in volts) across the capacitor is :
...

GATE ECE 2017 Set 1

In the circuit shown the voltage $${V_{IN}}\,\left( t \right)$$ is described by:
$$${V_{IN}}\,\left( t \right) = \left\{ {\matrix{
{0,} & {for...

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 ratio $${{amplitude\,\,of\,\,{...

GATE ECE 2016 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 = 9 kΩ
and that the diode is ide...

GATE ECE 2016 Set 1

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, ...

GATE ECE 2015 Set 3

In the circuit shown, the current $${\rm I}$$ flowing through the $$50\,\Omega $$ resistor will be zero if the value of capacitor C (in $$\mu F$$) is ...

GATE ECE 2015 Set 1

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 2014 Set 4

The steady state output of the circuit shown in the figure is given by
$$$y\left( t \right) = {\rm A}\left( \omega \right)\sin \left( {\omega t + \p...

GATE ECE 2014 Set 3

Consider the building block called 'Network N' shown in the figure.
Let $$C = 100\,\mu F\,\,$$ and $$R = 10\,k\Omega $$.
Two such blocks are connec...

GATE ECE 2014 Set 2

A series LCR circuit is operated at a frequency different from its resonant frequency. The
operating frequency is such that the current leads the supp...

GATE ECE 2014 Set 1

A 230 V rms source supplies power to two loads connected in parallel. The first load draws
10 kW at 0.8 leading power factor and the second one draws ...

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

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 2010

The current I in the circuit shown is
...

GATE ECE 2009

An AC source of RMS voltage $$20$$ $$V$$ with internal impedance $${Z_s} = \left( {1 + 2j} \right)\Omega $$ feeds a load of impedance $${Z_L} = \left...

GATE ECE 2007

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 of Filter $$2$$ be $${B_2}$$....

GATE ECE 2005

For the circuit in figure, the phase current $${{\rm I}_1}$$ is
...

GATE ECE 2004

Consider the following statements S1 and S2.
S1: The $$\beta$$ of a bipolar transistor reduces if the base width is increased.
S2: The $$\beta$$ of a ...

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 circuit is given by
$$H\left( s \ri...

GATE ECE 2003

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 $$v(t)$$ $$ = 10\sqrt 2 \,\,\cos \,\,\left( {t + {{10}^0}} \right) + 10\sqrt 5 \,\,\cos \left( {2t + {{10}^0}} \right)\,\,V$$ is appl...

GATE ECE 2002

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) is approximately
...

GATE ECE 2001

When the angular frequency $$\omega $$ in Fig. is varied from $$0$$ to $$\infty $$ the locus of the current phasor $${{\rm I}_2}$$ is given by
...

GATE ECE 2000

In Fig., the steady state output voltage corresponding to the input voltage $$\left( {3 + 4\sin \,\,100\,t} \right)$$ $$V$$ is
...

GATE ECE 1993

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 1992

For the series R-L-C circuit of figure(a), the partial phasor diagram at a certain
frequency is shown in figure (b).The operating frequency of the cir...

GATE ECE 1991

In a series RLC high Q circuit, the current peaks at a frequency

GATE ECE 1990

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
$$$G\,{}_c\left( s \right)\,\,\,\,{{s + {z_1}} \over {s + {p_1}}}$$$
The co...

GATE ECE 1989

The half - power bandwidth of the resonant circuit of figure can be increased by
...

GATE ECE 1987

The value of current through the 1F capacitor of figure is.
...

## Marks 5

GATE ECE 2002

For network shown in Fig. $$R\, = \,1\,k\Omega $$
$${L_1} = 2\,H,\,{L_2} = 5\,H,\,{L_3}\, = \,1H,{L_4} = 4H\,\,\,$$ and $$C - 0.2\,\,\mu F.$$. The mu...

GATE ECE 2001

For the circuit shown in the figure, determine the phasors E2, E0, I and I1.
...

GATE ECE 2000

For the circuit in Fig. Which is in steady state,
(a)Find the frequency $${\omega _0}$$ at which the magnitude of the impedance across terminals a,...

GATE ECE 1999

A coil with a quality factor $$(Q)$$ of $$10$$ is put in series with a capacitor $${C_1}$$ of $$10\,\,\mu F,$$ and the combination is found to draw ma...

GATE ECE 1998

Determine the frequency of resonance and the resonant impedance of the parallel circuit shown in figure. What happens when $$L = C{R^2}$$?
...

GATE ECE 1997

In the circuit of Fig., all currents and voltage are sinusoids of frequency $$\omega $$ rad/sec.
(a) Find the impedance to the right of $$\left( {A,...

GATE ECE 1994

Write down the mesh equation of the following network in terms of i1(t) and i2(t).Derive the differential equation for i1(t) from these and solve it.
...

GATE ECE 1994

Calculate the frequency at which zero- transmission is obtained from the Wien- bridge shown in Fig.
...

## Marks 8

GATE ECE 1987

The impedance function of a parallel $$R$$, $$L$$, $$C$$ circuit has poles located at $$ - 3 \pm j4$$ rad/sec. If the value of $$L = 1H$$, determine...