Sinusoidal Steady State Response · Network Theory · GATE ECE

Marks 1

A series $$RLC$$ circuit has a quality factor Q of 1000 at a center frequency of $$10^6$$ rad/s. The possible values of R, L and C are

GATE ECE 2023

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

GATE ECE 2017 Set 2

In the circuit shown, the positive angular frequency $$\omega$$ (in radians per second) at which magnitude of the phase difference between the voltages $$V_1$$ and $$V_2$$ equals $$\frac{\mathrm\pi}4$$ radians, is __________.

GATE ECE 2017 Set 1

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

GATE ECE 2016 Set 3

The figure shows an $$RLC$$ circuit with a sinusoidal current source.

At response, the ratio $$\left| {{{\rm I}_L}} \right|/\left| {{{\rm I}_R}} \right|$$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is _________.

GATE ECE 2016 Set 2

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

GATE ECE 2015 Set 3

The voltage (V_C) 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 $$v\left( t \right) = \sin \,2t$$. The resulting current $$i(t)$$ 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 output voltage $${v_0}\left( t \right)$$ is equal to

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 its original value, the new Q of the circuit is

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 will read

GATE ECE 1996

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

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 of $${10^7}$$ rad/sec. The values of $$R$$ and $$L$$ are: $$R=$$ ______ ohms. $$L=$$ ________Henries.

GATE ECE 1995

The current $$i(t)$$ through a $$10$$-$$\Omega $$ resistor in series with an inductance is given by
$$i(t)$$$$ = 3 + 4\sin \left( {100t + {{45}^ \circ }} \right) + 4\sin \left( {300t + {{60}^ \circ }} \right)\,\,A$$.

The RMS value of the current and the power dissipated in the circuit are

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 total energy supplied by the voltage source, is equal to

GATE ECE 1995

A series LCR circuit consisting of $$R = 10\Omega $$, $$\left| {{X_L}} \right|\,\,\, = 20\Omega $$ and $$\left| {{X_C}} \right|\,\,\, = 20\Omega $$, is connected across an a.c. supply of $$200V$$ rms. The rms voltage across the capacitor is

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

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 graphically (where t is in seconds). The circuit element Z can be _________.

GATE ECE 2022

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

GATE ECE 2018

The figure shows an RLC circuit excited by the sinusoidal voltage $$100cos(3t)$$ Volts, where $$t$$ is in seconds. The ratio $${{amplitude\,\,of\,\,{V_2}} \over {amplitude\,\,of\,\,{V_1}}}\,\,$$ is ________ .

GATE ECE 2017 Set 1

In the circuit shown the voltage $${V_{IN}}\,\left( t \right)$$ is described by: $$${V_{IN}}\,\left( t \right) = \left\{ {\matrix{ {0,} & {for\,\,\,t < 0} \cr {15Volts,} & {for\,\,\,t \ge 0} \cr } } \right.$$$

where $$'t'$$ is in seconds. The time (in seconds) at which the current $${\rm I}$$ in the circuit will reach the value $$2$$ Ampere is ______ .

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 = 9 kΩ and that the diode is ideal.

RMS current I_rms (in mA) through the diode is _________.

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, is excited with a source of the form
$$\sum\limits_{k = 1}^3 {{a_k}\,\,\cos \,\left( {k{\omega _0}t} \right),\,\,\,} $$ where $${a_k} \ne 0,\,\,{\omega _0} \ne 0$$.

The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

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 capacitor C (in $$\mu F$$) is ________ .

GATE ECE 2015 Set 3

The damping ratio of a series $$RLC$$ circuit can be expressed as

GATE ECE 2015 Set 1

In the given circuit, the maximum power (in Watts) that can be transferred to the load R_L is ___________________.

GATE ECE 2015 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 10 kVA at 0.8 lagging power factor. The complex power delivered by the source 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 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 steady state output of the circuit shown in the figure is given by $$$y\left( t \right) = {\rm A}\left( \omega \right)\sin \left( {\omega t + \phi \left( \omega \right)} \right)$$$

If the amplitude $$\left| {{\rm A}\left( \omega \right)} \right| = 0.25$$, then the frequency $$\omega $$ is

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 Network Theory - Sinusoidal Steady State Response Question 23 English 1

Two such blocks are connected in cascade, as shown in the figure.

The transfer function $${{{V_3}\left( s \right)} \over {{V_1}\left( s \right)}}$$ of the cascaded network is

GATE ECE 2014 Set 3

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1Ω , respectively, the operating angular frequency (in rad/s) is ________.

GATE ECE 2014 Set 2

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 load of impedance $${Z_L} = \left( {7 + 4j} \right)\Omega $$ in the figure below. The reactive power consumed by the load is

GATE ECE 2009

In the AC network shown in the figure, the phasor voltage V_AB (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 $${B_2}$$. The value of $${B_1}$$/$${B_2}$$ is

GATE ECE 2007

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

GATE ECE 2005

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
$$H\left( s \right) = {{{{10}^6}} \over {{s^2} + 20s + {{10}^6}}}$$

The Quality factor (Q-factore) of this circuit 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 bipolar transistor increases if the doping concentration in the base in increased

Which one of the following is correct?

GATE ECE 2004

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 applied to a series combination of resistance $$L = 1H$$. the resulting steady - state current $$i(t)$$ in ampere is

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

If the 3-phase balanced source in Fig. delivers 1500 W at a leading power factor of 0.844, then the value of Z_L (in ohm) is approximately

GATE ECE 2002

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 2001 Network Theory - Sinusoidal Steady State Response Question 31 English 1

GATE ECE 2001 Network Theory - Sinusoidal Steady State Response Question 31 English 2

GATE ECE 2001 Network Theory - Sinusoidal Steady State Response Question 31 English 3

GATE ECE 2001

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

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 operating frequency of the circuit is:

GATE ECE 1992

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

GATE ECE 1991

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 condition for the RC network to act as a phase lead controller is

GATE ECE 1990

The resonant frequency of this series circuit shown in figure is

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

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 mutual inductances are $${M_{12}} = 3\,H$$ and $${M_{34}} = 2\,H$$.

Determine
(a) the equivalent inductance for the combination of $${L_3}$$ and $${L_4}$$,
(b) the equivalent inductance across the points A and B in the network,
(c) the resonant frequency of the network.

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,

GATE ECE 2000 Network Theory - Sinusoidal Steady State Response Question 12 English

(a)Find the frequency $${\omega _0}$$ at which the magnitude of the impedance across terminals a, b reaches maximum.

(b) Find the impedance across a, b at the frequency $${\omega _0}$$.

(c) If $${v_i}\left( t \right) = V\,\,\sin \left( {{\omega _0}t} \right),$$ find $${i_L}\left( t \right),\,\,{i_c}\left( t \right),{i_R}\left( t \right).$$

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 combination is found to draw maximum current when a sinusoidal voltage of frequency $$50$$ $$Hz$$ is applied. A second capacitor $${C_2}$$ is now in parallel with the circuit. What should be the capacitance of $${C_2}$$ for combined circuit to act purely as a resistance for a sinusoidal excitation at a frequency of $$100$$ $$Hz$$? Calculate the rms current drawn by the combined circuit at $$100$$ $$Hz$$ if the applied voltage is $$100V$$ (rms).

GATE ECE 1999

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 1998

In the circuit of Fig., all currents and voltage are sinusoids of frequency $$\omega $$ rad/sec.

GATE ECE 1997 Network Theory - Sinusoidal Steady State Response Question 15 English

(a) Find the impedance to the right of $$\left( {A,\,\,\,\,\,\,B} \right)$$ at $$\omega \,\,\, = \,\,\,\,0$$ rad/sec and $$\omega \,\,\, = \,\,\,\,\infty $$ rad/sec.

(b) If $$\omega \,\,\, = \,\,\,\,{\omega _0}$$ rad/sec and $${i_1}\left( t \right) = \,\,{\rm I}\,\,\,\sin \,\left( {{\omega _0}t} \right)\,{\rm A},$$ where $${\rm I}$$ is positive, $${{\omega _0}\,\, \ne \,\,0}$$, $${{\omega _0}\,\, \ne \,\,\infty }$$, then find $${\rm I}$$, $${{\omega _0}}$$ and $${i_2}\left( t \right)$$

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 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.

GATE ECE 1994

Marks 8

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 the following:

(a) the values of $$R$$ and $$C$$
(b) the quality factor of the circuit

GATE ECE 1987