GATE ECE
Network Theory
Sinusoidal Steady State Response
Previous Years Questions

Marks 1

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...
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...
In the circuit shown, the positive angular frequency $$\omega$$ (in radians per second) at which magnitude of the phase difference between the voltage...
In the circuit shown, $$V$$ is a sinusoidal voltage source. The current $$I$$ is in phase with voltage $$V$$. The ratio $${{{\rm{Amplitude of voltage...
The figure shows an $$RLC$$ circuit with a sinusoidal current source. At response, the ratio $$\left| {{{\rm I}_L}} \right|/\left| {{{\rm I}_R}} \r...
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 ...
The voltage (VC) across the capacitor (in Volts) In the network shown is ________....
At very high frequencies, the peak output voltage V0 (in Volts) is ______. ...
In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ___________. ...
For parallel RLC circuit, which one of the following statements is NOT correct?
The RC circuit shown in the figure is ...
In a series $$RLC$$ circuit $$R = 2\,k\Omega ,\,\,\,L = \,1H$$ and $$C = \,1/400\,\mu F.$$ The resonant frequency is
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...
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...
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...
The circuit of Fig. represents a ...
The parallel $$RLC$$ circuit shown in figure is in resonance. In this circuit ...
In Fig., A1, A2 and A3 are ideal ammeters. If A2 and A3 read 3 A and 4 A respectively, then A1 should read ...
In the circuit of Fig., assume that the diodes are ideal and the meter is an average indicating ammeter. The ammeter will read ...
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
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 ...
The current $$i(t)$$ through a $$10$$-$$\Omega $$ resistor in series with an inductance is given by $$i(t)$$$$ = 3 + 4\sin \left( {100t + {{45}^ \cir...
A series $$R$$-$$L$$-$$C$$ circuit has a $$Q$$ of $$100$$ and an impedance of $$\left( {100 + j0} \right)\,\Omega $$ at its resonant angular frequency...
A series LCR circuit consisting of $$R = 10\Omega $$, $$\left| {{X_L}} \right|\,\,\, = 20\Omega $$ and $$\left| {{X_C}} \right|\,\,\, = 20\Omega $$, i...
In the series circuit shown in figure, for series resonance, the value of the coupling coefficient K will be ...

Marks 2

For the circuit given in the figure, the voltage VC (in volts) across the capacitor is : ...
In the circuit shown the voltage $${V_{IN}}\,\left( t \right)$$ is described by: $$${V_{IN}}\,\left( t \right) = \left\{ {\matrix{ {0,} & {for...
The figure shows an RLC circuit excited by the sinusoidal voltage $$100cos(3t)$$ Volts, where $$t$$ is in seconds. The ratio $${{amplitude\,\,of\,\,{...
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...
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, ...
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 ...
In the given circuit, the maximum power (in Watts) that can be transferred to the load RL is ___________________. ...
The damping ratio of a series $$RLC$$ circuit can be expressed as
The steady state output of the circuit shown in the figure is given by $$$y\left( t \right) = {\rm A}\left( \omega \right)\sin \left( {\omega t + \p...
Consider the building block called 'Network N' shown in the figure. Let $$C = 100\,\mu F\,\,$$ and $$R = 10\,k\Omega $$. Two such blocks are connec...
A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supp...
A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws ...
In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is ______. ...
A periodic variable x is shown in the figure as a function of time. The root - mean - square (rms) value of x is _______ . ...
The current I in the circuit shown is ...
An AC source of RMS voltage $$20$$ $$V$$ with internal impedance $${Z_s} = \left( {1 + 2j} \right)\Omega $$ feeds a load of impedance $${Z_L} = \left...
In the AC network shown in the figure, the phasor voltage VAB (in Volts) is: ...
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 $${B_2}$$....
For the circuit in figure, the phase current $${{\rm I}_1}$$ is ...
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 ...
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 $$H\left( s \ri...
The current flowing through the resistance R in the circuit in figure has the form P cos 4t, where P is ...
An input voltage $$v(t)$$ $$ = 10\sqrt 2 \,\,\cos \,\,\left( {t + {{10}^0}} \right) + 10\sqrt 5 \,\,\cos \left( {2t + {{10}^0}} \right)\,\,V$$ is appl...
If the 3-phase balanced source in Fig. delivers 1500 W at a leading power factor of 0.844, then the value of ZL (in ohm) is approximately ...
When the angular frequency $$\omega $$ in Fig. is varied from $$0$$ to $$\infty $$ the locus of the current phasor $${{\rm I}_2}$$ is given by ...
In Fig., the steady state output voltage corresponding to the input voltage $$\left( {3 + 4\sin \,\,100\,t} \right)$$ $$V$$ is ...
In figure, A1, A2 and A3 are ideal ammeters. If A1 reads 5 A, A2, A2 reads 12 A, then A3 should read ...
For the series R-L-C circuit of figure(a), the partial phasor diagram at a certain frequency is shown in figure (b).The operating frequency of the cir...
In a series RLC high Q circuit, the current peaks at a frequency
The resonant frequency of this series circuit shown in figure is ...
The transfer function of simple RC network functioning as a controller is $$$G\,{}_c\left( s \right)\,\,\,\,{{s + {z_1}} \over {s + {p_1}}}$$$ The co...
The half - power bandwidth of the resonant circuit of figure can be increased by ...
The value of current through the 1F capacitor of figure is. ...

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 mu...
For the circuit shown in the figure, determine the phasors E2, E0, I and I1. ...
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,...
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...
Determine the frequency of resonance and the resonant impedance of the parallel circuit shown in figure. What happens when $$L = C{R^2}$$? ...
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,...
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. ...
Calculate the frequency at which zero- transmission is obtained from the Wien- bridge shown in Fig. ...

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...
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