Sinusoidal Steady State Analysis - Network Analysis

Q#1 Sinusoidal Steady State Analysis GATE EC 2025 (Set 1) MCQ +1 mark -0.33 marks

Let , and be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens (S).

Which one of the following is TRUE?

Q#2 Sinusoidal Steady State Analysis GATE EC 2025 (Set 1) MCQ +2 marks -0.66 marks

In the circuit below, is an ideal AC voltmeter and is an ideal AC ammeter. The source voltage (in Volts) is .

What should be the value of the variable capacitor such that the RMS readings on and are 25 V and 5 A, respectively?

Insufficient information to find C

Q#3 Sinusoidal Steady State Analysis GATE EC 2023 (Set 1) MCQ +1 mark -0.33 marks

A series RLC circuit has a quality factor of 1000 at a center frequency of . The possible values of and are

and

Q#4 Sinusoidal Steady State Analysis GATE EC 2022 (Set 1) MCQ +2 marks -0.66 marks

For the circuit shown, the locus of the impedance is plotted as increases from zero to infinity. The values of and are:

Q#5 Sinusoidal Steady State Analysis GATE EC 2022 (Set 1) MCQ +2 marks -0.66 marks

Consider the circuit shown in the figure with input in volts. The sinusoidal steady state current flowing through the circuit is shown graphically (where is in seconds). The circuit element can be _______.

a capacitor of

an inductor of

a capacitor of

an inductor of

Q#6 Sinusoidal Steady State Analysis GATE EC 2020 (Set 1) NAT +1 mark -0 marks

The current in the RL-circuit shown below is .

The value of the inductor (rounded off to two decimal places) is _____H.

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Q#7 Sinusoidal Steady State Analysis GATE EC 2020 (Set 1) MCQ +2 marks -0.66 marks

The current I in the given network is

Q#8 Sinusoidal Steady State Analysis GATE EC 2019 (Set 1) MCQ +2 marks -0.66 marks

In the circuit shown, ifVolts, R=1kΩ and C=1µF, then the steady state current i(t), in milliamperes (mA) is

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Q#9 Sinusoidal Steady State Analysis GATE EC 2018 (Set 1) MCQ +2 marks -0.66 marks

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

Q#10 Sinusoidal Steady State Analysis GATE EC 2017 (Set 1) NAT +1 mark -0 marks

In the circuit shown, the positive angular frequency (in radians per second) at which the magnitude of the phase difference between the voltages and equals radians, is

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Angle of must befor which real & imaginary part must be equal or

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Q#11 Sinusoidal Steady State Analysis GATE EC 2017 (Set 1) NAT +2 marks -0 marks

The figure shows an RLC circuit excited by the sinusoidal voltage 100 cos (3t) Volts, where t is in seconds. The ratio is _________________.

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Q#12 Sinusoidal Steady State Analysis GATE EC 2017 (Set 2) NAT +1 mark -0 marks

In the circuit shown, V is a sinusoidal voltage source. The current I is in phase with voltage V. The ratio is ______________.

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Q#13 Sinusoidal Steady State Analysis GATE EC 2016 (Set 2) NAT +1 mark -0 marks

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

At resonance, the ratio , i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________.

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Q#14 Sinusoidal Steady State Analysis GATE EC 2016 (Set 1) MCQ +1 mark -0.33 marks

In the RLC circuit shown, the input voltage is given by . The output voltage V₀(t) is

Q#15 Sinusoidal Steady State Analysis GATE EC 2015 (Set 1) NAT +1 mark -0 marks

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

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Q#16 Sinusoidal Steady State Analysis GATE EC 2015 (Set 1) NAT +2 marks -0 marks

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

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Q#17 Sinusoidal Steady State Analysis GATE EC 2015 (Set 2) NAT +1 mark -0 marks

The voltage ( ) across the capacitor (in Volts) in the network shown is ____.

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Q#18 Sinusoidal Steady State Analysis GATE EC 2015 (Set 2) NAT +1 mark -0 marks

In the circuit shown, the average value of the voltage (in Volts) in steady state condition is____.

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Q#19 Sinusoidal Steady State Analysis GATE EC 2015 (Set 3) NAT +1 mark -0 marks

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

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Q#20 Sinusoidal Steady State Analysis GATE EC 2015 (Set 3) NAT +2 marks -0 marks

In the circuit shown, the current I flowing through the 50 Ω resistor will be zero if the value of capacitor C (in μF) is ______.

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Q#21 Sinusoidal Steady State Analysis GATE EC 2014 (Set 1) MCQ +1 mark -0.33 marks

The maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedanceof the first section to the input impedance of the second section is

Q#22 Sinusoidal Steady State Analysis GATE EC 2014 (Set 1) MCQ +2 marks -0.66 marks

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 10kVA at 0.8 lagging power factor. The complex power delivered by the source is

kVA

Q#23 Sinusoidal Steady State Analysis GATE EC 2014 (Set 2) NAT +2 marks -0 marks

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 1 Ω, respectively, the operating angular frequency (in rad/s) is ________.

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Q#24 Sinusoidal Steady State Analysis GATE EC 2014 (Set 3) MCQ +2 marks -0.66 marks

In the circuit shown in the figure, the value of node voltage is

22 + j 2 V

2 + j 22 V

22 – j 2 V

2 – j 22 V

Q#25 Sinusoidal Steady State Analysis GATE EC 2014 (Set 3) NAT +2 marks -0 marks

In the circuit shown in the figure, the angular frequency ω (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b′ is purely resistive, is _________.

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Q#26 Sinusoidal Steady State Analysis GATE EC 2014 (Set 4) MCQ +2 marks -0.66 marks

The steady state output of the circuit shown in the figure is given by . If the amplitude, then the frequency ω is

Q#27 Sinusoidal Steady State Analysis GATE EC 2013 (Set 1) MCQ +1 mark -0.33 marks

A source has an internal impedance of. If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in should be

3

4

5

7

Q#28 Sinusoidal Steady State Analysis GATE EC 2013 (Set 1) MCQ +2 marks -0.66 marks

In the circuit shown below, if the source voltage then the Thevenin’s equivalent voltage in Volts as seen by the load resistance is

Q#29 Sinusoidal Steady State Analysis GATE EC 2012 (Set 1) MCQ +1 mark -0.33 marks

The average power delivered to an impedance by a current is

44.2 W

50 W

62.5 W

125 W

Q#30 Sinusoidal Steady State Analysis GATE EC 2012 (Set 1) MCQ +1 mark -0.33 marks

In the circuit shown below, the current through the inductor is

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Q#31 Sinusoidal Steady State Analysis GATE EC 2011 (Set 1) MCQ +1 mark -0.33 marks

The circuit shown below is driven by a sinusoidal input. The steady state output is

Q#32 Sinusoidal Steady State Analysis GATE EC 2011 (Set 1) MCQ +2 marks -0.66 marks

In the circuit shown below, the current I is equal to

Q#33 Sinusoidal Steady State Analysis GATE EC 2010 (Set 1) MCQ +1 mark -0.33 marks

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

The bandwidth of the circuit decreases if R is increased

The bandwidth of the circuit remains same if L is increased

At resonance, input impedance is a real quantity

At resonance, the magnitude of input impedance attains its minimum value

Q#34 Sinusoidal Steady State Analysis GATE EC 2010 (Set 1) MCQ +2 marks -0.66 marks

The current I in the circuit shown is

–j1A

J1A

0A

20A

Q#35 Sinusoidal Steady State Analysis GATE EC 2009 (Set 1) MCQ +2 marks -0.66 marks

An AC source of RMS voltage 20 V with internal impedance feeds a load of impedance in the figure below. The reactive power consumed by the load is

8 VAR

16 VAR

28 VAR

32 VAR

Q#36 Sinusoidal Steady State Analysis GATE EC 2007 (Set 1) MCQ +1 mark -0.33 marks

An independent voltage source in series with an impedance delivers a maximum average power to a load impedance when

Q#37 Sinusoidal Steady State Analysis GATE EC 2007 (Set 1) MCQ +1 mark -0.33 marks

The RC circuit shown in the figure is

A low-pass filter

A high-pass filter

A band-pass filter

A band-reject filter

Q#38 Sinusoidal Steady State Analysis GATE EC 2007 (Set 1) MCQ +2 marks -0.66 marks

Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth of Filter 1 be and that of Filter 2 be The value of is

Q28_1

Q28_2

4

1

Q#39 Sinusoidal Steady State Analysis GATE EC 2007 (Set 1) MCQ +2 marks -0.66 marks

in the AC network shown in the figure, the phasor voltage (in Volts) is

0

Q#40 Sinusoidal Steady State Analysis GATE EC 2006 (Set 1) MCQ +2 marks -0.66 marks

A negative resistance is connected to a passive network N having driving point impedance as shown below. For to be positive real,

,

Q#41 Sinusoidal Steady State Analysis GATE EC 2005 (Set 1) MCQ +1 mark -0.33 marks

In a series RLC circuit, L = 1H and . The resonant frequency is

Q#42 Sinusoidal Steady State Analysis GATE EC 2005 (Set 1) MCQ +2 marks -0.66 marks

For the circuit in figure the instantaneous current is

Amps

Q#43 Sinusoidal Steady State Analysis GATE EC 2004 (Set 1) MCQ +1 mark -0.33 marks

The circuit shown in figure, with, , C = 3F has input voltage . The resulting current i(t) is

5sin (2t + 53.1º)

5sin (2t - 53.1º)

25sin (2t + 53.1º)

25sin (2t - 53.1º)

Q#44 Sinusoidal Steady State Analysis GATE EC 2004 (Set 1) MCQ +1 mark -0.33 marks

For the circuit shown in Figure, the time constant RC=1ms. The input voltage is. The output voltage is equal to

Q#45 Sinusoidal Steady State Analysis GATE EC 2004 (Set 1) MCQ +2 marks -0.66 marks

The transfer function of an R-L-C circuit is given by. The Quality factor (Q-factor) of this circuit is

25

50

100

5000

Q#46 Sinusoidal Steady State Analysis GATE EC 2004 (Set 1) MCQ +2 marks -0.66 marks

Consider the following statements and

: At the resonant frequency the impedance of a series R-L-C circuit is zero.

: In a parallel G-L-C circuit, increasing the conductance G results in increase in its Q factor.

Which one of the following is correct?

is FALSE and is TRUE

both and are TRUE

is TRUE and is FALSE

both and are FALSE

Q#47 Sinusoidal Steady State Analysis GATE EC 2003 (Set 1) MCQ +1 mark -0.33 marks

A source of angular frequency 1rad/sec has a source impedance consisting of 1Ω resistance in series with 1 H inductance. The load that will obtain the maximum power transfer is

1 Ω resistance

1 Ω resistance in parallel with 1 H inductance

1 Ω resistance in series with 1 F capacitor

1 Ω resistance in parallel with 1 F capacitor

Q#48 Sinusoidal Steady State Analysis GATE EC 2003 (Set 1) MCQ +1 mark -0.33 marks

A series RLC circuit has a response 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

25

50

100

200

Q#49 Sinusoidal Steady State Analysis GATE EC 2003 (Set 1) MCQ +2 marks -0.66 marks

The driving point impedance Z(s) of a network has the pole-zero locations as shown in figure. If Z(0) = 3, then Z(s) is

Q#50 Sinusoidal Steady State Analysis GATE EC 2001 (Set 1) MCQ +2 marks -0.66 marks

In figure shown below, the value of the load resistor R which maximizes the power delivered to it is

14.14Ω

10Ω

200Ω

28.28Ω

Q#51 Sinusoidal Steady State Analysis GATE EC 2001 (Set 1) MCQ +2 marks -0.66 marks

When the angular frequency in figure is varied from 0 to , the locus of the current phasor is given by

Q#52 Sinusoidal Steady State Analysis GATE EC 2001 (Set 1) MSQ +2 marks -0 marks

For the circuit shown in Figure, determine the phasors and

Q#53 Sinusoidal Steady State Analysis GATE EC 2000 (Set 1) MCQ +1 mark -0.33 marks

The circuit of Figure represents a

Low pass filter

High pass filter

Band pass filter

Band reject filter

Q#54 Sinusoidal Steady State Analysis GATE EC 2000 (Set 1) MCQ +2 marks -0.66 marks

In Figure, the steady state output voltage corresponding to the input voltage is

Q#55 Sinusoidal Steady State Analysis GATE EC 2000 (Set 1) MSQ +2 marks -0 marks

For the circuit in Figure, which is in steady state

at which the magnitude of the impedance across terminals a and b reaches a maximum.

Given .

Impedance across a, b at the frequency

Q#56 Sinusoidal Steady State Analysis GATE EC 1999 (Set 1) MCQ +2 marks -0.66 marks

The Thevenin’s equivalent voltage appearing between the terminals A and B of the network shown in Figure is given by

Q#57 Sinusoidal Steady State Analysis GATE EC 1999 (Set 1) NAT +2 marks -0 marks

For the network shown in Figure, evaluate the magnitude of the current I flowing through the resistor using superposition theorem.

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Q#58 Sinusoidal Steady State Analysis GATE EC 1999 (Set 1) MSQ +2 marks -0 marks

A coil with a quality factor (Q) of 10 is put in series with capacitor of , and the combination is found to draw maximum current when a sinusoidal voltage of frequency 50 Hz is applied. A second capacitor is now in parallel with the circuit. What should be the capacitance of for combined circuit to act purely as a resistance for a sinusoidal excitation at a frequency of 100Hz? Calculate the RMS current drawn by the combined circuit at 100 Hz if the applied voltage is 100 V(RMS).

Q#59 Sinusoidal Steady State Analysis GATE EC 1998 (Set 1) MCQ +1 mark -0.33 marks

The parallel RLC circuit shown in Figure is in resonance. In this circuit

Q#60 Sinusoidal Steady State Analysis GATE EC 1998 (Set 1) MSQ +2 marks -0 marks

Determine the frequency of resonance and the resonant impedance of the parallel circuit shown in figure. What happens when ?

At
Impedance becomes frequency dependent and circuit resonates at infinite number of frequencies

Resonance frequency

Resonant impedance

At
Impedance becomes frequency independent and circuit resonates at infinite number of frequencies

Q#61 Sinusoidal Steady State Analysis GATE EC 1998 (Set 1) NAT +2 marks -0 marks

A voltage source of internal impedance supplies power to a load of impedance in which only is variable. Determine the value of for maximum power transfer from the source to the load. Also, find the numerical value of if the source impedance is (purely resistive) and is .

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Q#62 Sinusoidal Steady State Analysis GATE EC 1997 (Set 1) MCQ +1 mark -0.33 marks

In the circuit of the figure is the equivalent impedance seen across terminals a, b is

None of the above

Q#63 Sinusoidal Steady State Analysis GATE EC 1997 (Set 1) MSQ +2 marks -0 marks

In the circuit of the figure is all currents and voltages are sinusoids of frequency rad/sec. If (resonance frequency) and, where I is positive, then find I, and

impedance to the right of (A, B)
at ,
at ,

,

impedance to the right of (A, B)
at ,
at ,

Q#64 Sinusoidal Steady State Analysis GATE EC 1997 (Set 1) MSQ +2 marks -0 marks

For the circuit shown in the figure is choose state variables, to be ,,

If , , , , then what would the total energy dissipated in the resistors in the interval be?

State equations

Q#65 Sinusoidal Steady State Analysis GATE EC 1996 (Set 1) MCQ +1 mark -0.33 marks

In the given figure, , and are ideal ammeters. If and read 3 A and 4 A respectively, then should be read

1 A

5 A

7 A

None of these

Q#66 Sinusoidal Steady State Analysis GATE EC 1995 (Set 1) MCQ +1 mark -0.33 marks

The current, i(t), through a resistor in series with an inductance, is given by

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

A, 410 W, respectively

A, 350 W, respectively

5 A, 250 W, respectively

11 A, 1210 W, respectively

Q#67 Sinusoidal Steady State Analysis GATE EC 1995 (Set 1) MSQ +1 mark -0 marks

A series R-L-C circuit has a Q of 100 and an impedance of at its resonant angular frequency of radiation/sec. The values of R and L are:

R = ___________ ohms, L = _________ H.

R=100 ohms

R=150 ohms

L=1mH

L=1.5mH

Q#68 Sinusoidal Steady State Analysis GATE EC 1994 (Set 1) MCQ +1 mark -0.33 marks

A series RLC circuit consisting of , and , is connected across an a.c. supply of 200 V rms. The rms voltage across the capacitor is

Q#69 Sinusoidal Steady State Analysis GATE EC 1994 (Set 1) NAT +1 mark -0 marks

A generator of internal impedance, , deliver maximum power to a load impedance,, only if . (True=1, False=0 )

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Q#70 Sinusoidal Steady State Analysis GATE EC 1994 (Set 1) NAT +1 mark -0 marks

represents the input impedance of a network. ( True =1 , False=0)

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Q#71 Sinusoidal Steady State Analysis GATE EC 1994 (Set 1) MCQ +1 mark -0.33 marks

The response of an LCR circuit to a step input is If the transfer function has

(A) Over damped

(B) Critically damped

(C) Oscillatory

(1) Poles on the negative real axis

(2) Poles on the imaginary axis

(3) Multiple poles on the positive real axis

(4) Poles on the positive real axis

(5) Multiple poles on the negative real axis

(A) => (1)
(B) => (2)
(C) => (3)

(A) => (1)
(B) => (5)
(C) => (2)

(A) => (1)
(B) => (5)
(C) => (4)

(A) => (4)
(B) => (5)
(C) => (2)

Q#72 Sinusoidal Steady State Analysis GATE EC 1993 (Set 1) MCQ +1 mark -0.33 marks

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

0.25

0.5

0.999

1.0

Q#73 Sinusoidal Steady State Analysis GATE EC 1993 (Set 1) MCQ +1 mark -0.33 marks

In figure, , and are ideal ammeters? If reads 5A, reads 12A, then should be read.

7 A

12 A

13 A

17 A

Q#74 Sinusoidal Steady State Analysis GATE EC 1992 (Set 1) MCQ +2 marks -0.66 marks

For the series R-L-C circuit of figure, the partial phasor diagram at a certain frequency is shown in figure, The operating frequency of the circuit is:

Equal to the resonance frequency

Less than the resonance frequency

Greater than resonance frequency

Not zero

Q#75 Sinusoidal Steady State Analysis GATE EC 1991 (Set 1) MCQ +1 mark -0.33 marks

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

Equal to the resonant frequency

Greater than the resonant frequency

Less than the resonant frequency

None of the above

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GATE EC

Network Analysis
Sinusoidal Steady State Analysis

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