Networks Signals and Systems | Subject Wise

Networks Signals and Systems Subject Wise

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Question 1

Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be 1 A (see (a) in the figure).
Now, if an excitation of 5 V is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1?

A	0.5 A
B	1 A
C	2 A
D	2.5 A

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Question 1 Explanation:

Question 2

The RC circuit shown below has a variable resistance R(t) given by the following expression :

for 0 ≤ t < T

where R₀ = 1 Ω, and C = 1 F. We are also given that T = 3 R₀C and the source voltage is V_s = 1 V. If the current at time
t = 0 is 1 A, then the current I(t), in amperes, at time t = T/2 is __________ (rounded off to 2 decimal places).

A	Fill in the Blank Type Question

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Question 2 Explanation:

Question 3

In the circuit shown, if v(t) = 2 sin (1000 t) volts, R = 1 kΩ and C = 1 μF, then the steady-state current i(t), in milliamperes (mA), is

A	Sin(1000 t) + cos(1000 t)
B	2 sin(1000 t) + 2 cos(1000 t)
C	3 sin(1000 t) + cos(1000 t)
D	Sin(1000 t) + 3 cos(1000 t)

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Question 3 Explanation:

Question 4

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

is ______

A	Fill in the Blank Type Question

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Question 4 Explanation:

V₁=

V₂=

Question 5

In the circuit shown, the voltage V_IN(t) is described by:

where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is _______.

A	Fill in the Blank Type Question

Discuss GATE EC 2017 Set 1 Networks Filters,AC and DC circuits

Question 5 Explanation:

Question 6

The

matrix for a two-port network is defined by:

The parameter for the given two-port network (in ohms, correct to two decimal places) is ____________.

A	Fill in the Blank Type Question

Discuss GATE EC 2018 Networks Two Port Networks

Question 6 Explanation:

Question 7

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is __________.(upto 3 decimal places)

A	Fill in the Blank Type Question

Discuss GATE EC 2018 Networks Time Domain and Frequency Analysis of Linear circuits

Question 7 Explanation:

The circuit given here has no initial conditions as no energy is stored in inductor prior to switching.

Question 8

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is __________.(upto 3 decimal places)

A	Fill in the Blank Type Question

Discuss GATE EC 2018 Networks Time Domain and Frequency Analysis of Linear circuits

Question 8 Explanation:

The circuit given here has no initial conditions as no energy is stored in inductor prior to switching.

Question 9

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is __________.(upto 3 decimal places)

A	Fill in the Blank Type Question

Discuss GATE EC 2018 Networks Time Domain and Frequency Analysis of Linear circuits

Question 9 Explanation:

The circuit given here has no initial conditions as no energy is stored in inductor prior to switching.

Question 10

Consider the network shown below with

and

The network is connected to a constant voltage source of 11 V.

The magnitude of the current (in amperes, accurate to two decimal places) through the source is ____________.

A	Fill in the Blank Type Question

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Question 10 Explanation:

Total resistance R_T is resultant of following combination,

We have values for R₁ and R₃,

and

So,

Thus, current through 11 V voltage source is,

Question 11

For the circuit given in the figure, the voltage

(in volts) across the capacitor is

A
B
C
D

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Question 11 Explanation:

Question 12

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

A	Fill in the Blank Type Question

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Question 12 Explanation:

Question 13

The output V₀ of the diode circuit shown in the figure is connected to an averaging DC voltmeter. The reading on the DC voltmeter in Volts, neglecting the voltage drop across the diode, is ______.
2.20.JPG

A	Fill in the Blank Type Question

Discuss GATE EC 2017 Set 2 Networks Filters,AC and DC circuits

Question 13 Explanation:

->Below circuit is a half wave rectifier and DC voltmeter will read the average value of V₀
->Hence average value of V₀ i.e. output of half wave rectifier is given by,

Answer Range ( 3.15 to 3.21 )

Question 14

The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0.
The current i(t) (in ampere) at t = 0.5 seconds is ________

A	Fill in the Blank Type Question

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Question 14 Explanation:

Question 15

Consider a two-port network with the transmission matrix:

If the network is reciprocal, then

A	T^-1 =T
B	T² =T
C	Determinant (T) = 0
D	Determinant (T) = 1

Discuss GATE EC 2016 Set 1 Networks Two Port Networks

Question 15 Explanation:

A two port network is reciprocal in transmission parameters
if AD – BC = 1 i.e. Determinant(T) = 1
Note : If network is reciprocal, then Determinant (T) = 1

Question 16

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

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

A
B
C
D

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Question 16 Explanation:

The property of any LTI system or network is if the excitation contains 'n' number of different frequency then the response also contains exactly n number of different frequency term and the output frequency and input frequency must be same however depending on components there is a possible change in amplitude and phase but never the frequency.

If the source has 3 frequency terms as given

then any voltage or any current of any element should have also 3 terms based on this option B. and D. are eliminated.

If we take option C.. It has 3 frequency term but it also suggest there is a phase change so 4„ but amplitude must be same as input as ak is present which may not be true always.

So option A. is correct, as it suggest frequency term of output and inputs are same with possible change in amplitude and phase, because we have (

Question 17

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

A	Fill in the Blank Type Question

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Question 17 Explanation:

At resonance

$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image034.png$
$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image035.png$
V_C=I*X_C=25V
Amplitude of 25 Volt V_C = 25 Volt
Hence, the correct answer is 25

Question 18

In the given circuit, the values of V₁ and V₂ respectively are:

A	5 V, 25 V
B	10 V, 30 V
C	15 V. 35 V
D	0 V, 20 V

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Question 18 Explanation:

Current flowing through both the parallel 4 Ω will be I.
So, $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image045.png$ by KVL
$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image046.png$ by KVL
$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image047.png$
$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image048.png$
$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image049.png$
V₁ = 5 volts
V₂ =25 volts

Question 19

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

A	Fill in the Blank Type Question

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Question 19 Explanation:

Question 20

In the circuit shown below, V_s is a constant voltage source and I_L is a constant current load.

The value of IL that maximizes the power absorbed by the constant current load is

A
B
C
D

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Question 20 Explanation:

Under maximum power transfer condition, half of V_th is droped across R_th and remaining V_th / 2 droped across load.
So we can say under MPT V_s / 2 will appear on the load
so

Question 21

The switch has been in position 1 for a long time and abruptly changes to position 2 at t= 0.

If time t is in seconds, the capacitor voltage Vc (in volts) for t>0 is given by

A	4(1 —exp^(—t/0.5))
B	10 — 6 exp^(—t/0.5)
C	4(1 — exp ^(-0.6))
D	10 — 6 exp ^(—t/0.6)

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Question 21 Explanation:

Question 22

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

At resonance, the ratio|I_L|/|I_R|, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is___

A	Fill in the Blank Type Question

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Question 22 Explanation:

At resonance (for parallel RLC circuit)
I_R = I
I_L = QI < – 90°
I_C = QI < 90°
For parallel RLC circuit

Question 23

The z-parameter matrix for the two-port network shown is

,
Where the entries are in

Suppose

Then the value of

(in

) equals to

A	Fill in the Blank Type Question

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Question 23 Explanation:

Question 24

In the given circuit, each resistor has a value equal to

What is the equivalent resistance across the terminals a and b?

A
B
C
D

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Question 24 Explanation:

Question 25

In the circuit shown in the figure, the magnitude of the current (in amperes) through R₂ is

A	Fill in the Blank Type Question

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Question 25 Explanation:

Let current through

Applying KVL,

Thus, current through

Question 26

The switch S in the circuit shown has been closed for a long time. It is opened at time t = 0 and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop.

The steady state magnitude of the capacitor voltage V_c (in volts) is ______

A	Fill in the Blank Type Question

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Question 26 Explanation:

Question 27

In the RLC circuit shown in the figure, the input voltage is given by

The output voltage V_o(t) is

A	Cos (200t) + 2sin (500t)
B	2 cos (200t) + 4sin (500t)
C	Sin (200t) + 2cos (500t)
D	2 sin (200t) + 4cos (500t)

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Question 27 Explanation:

since there are 2 frequency term output will also have 2 frequency term.

If we take 4sin500t first i.e. W = 500 then on the output section, this parallel LC combination have

so it is open circuit and V0 = Vi
3.9.1.JPG

So w.r.t. 4sin500t output must be 4sin500t without any change in amplitude and phase, this is satisfied by only option B.

Question 28

The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage V₀ (in volt) at the steady state is ________.
3.13.JPG

A	Fill in the Blank Type Question

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Question 28 Explanation:

Question 29

Assume that the circuit in the figure has reached the steady state before time t = 0 when 3Ω the resistor suddenly burns out, resulting in an open circuit. The value of current i(t) (in ampere) through 2Ω resistor at t = 0⁺ is ______.

A	Fill in the Blank Type Question

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Question 29 Explanation:

the circuit is on steady state i.e. the capacitor is open circuited so the circuit will be

at t = 0+ when is open circuited, the capacitors will have an ideal voltage source of values 4V and 6V so the circuit will be
32.1.JPG

So the current through 2Ω resistor at t = 0⁺ should be 4/(2+2) = 1A

Question 30

In the figure shown, the current i (in ampere) is ______.

A	Fill in the Blank Type Question

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Question 30 Explanation:

Nodal equation at V

By using KCL at node ‘a’.

KCL at b
-

Question 31

The z-parameter matrix

for the two-port network shown in

A
B
C
D

Discuss GATE EC 2016 Set 3 Networks Two Port Networks

Question 31 Explanation:

Since the given network is symmetric and reciprocal

And from the figure We get

Question 32

For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b is_____
Descg

A	Fill in the Blank Type Question

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Question 32 Explanation:

Question 33

The ABCD parameters of the following 2-port network are

A	$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-3_files\image115.png$
B	$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-3_files\image116.png$
C	$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-3_files\image117.png$
D	$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-3_files\image118.png$

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Question 33 Explanation:

Question 34

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

A	Fill in the Blank Type Question

Discuss GATE EC 2015 Set 3 Networks Steady State equations and Analysis

Question 34 Explanation:

Converting the circuit to phasor domain for AC analysis

If current I = 0,
Voltage at node A = input voltage
Applying KCL at node A,

Solving equation, we get

Question 35

The position control of a DC servo-motor is given in the figure. The values of the parameters are K_T = 1 N-m/A, R_a = 1W, L_a = 0.1 H, J = 5 kg-m², B = 1 N-m/(rad/sec) and K_b = 1V/(rad/sec). The steady-state position response (in radians) due to unit impulse disturbance torque T_d is _________

A	Fill in the Blank Type Question

Discuss GATE EC 2015 Set 3 Networks Steady State equations and Analysis

Question 35 Explanation:

To find the response due to T_d(s), we will use superposition making input V_a (s) = 0 and finding
Transfer function

(unit impulse response)

For steady state response,

But T_d(s) is negative, so response is also negative, i.e. -0.5

Question 36

Let the signal f(t) = 0 outside the interval T₁, T₂ where T₁ and T₂ are finite. Furthermore,

. The region of convergence (ROC) of the signal’s bilateral Laplace transform F(s) is
1. A parallel strip containing the jΩ axis
2. A parallel strip not containing the jΩ axis
3. The entire s-plane
4. A half plane containing the jΩ axis

A	A
B	B
C	C
D	D

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Question 36 Explanation:

Given, f (t) = 0 outside interval T₁, T₂.
and

So, it is a finite duration signal and for the finite duration signal ROC is always entire s-plane.

Question 37

The 2-port admittance matrix of the circuit shown is given by

A	$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image056.png$
B	$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image057.png$
C	$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image058.png$
D	$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image059.png$

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Question 37 Explanation:

Question 38

The voltage (V_c) across the capacitor (in Volts) in the network shown is ______

A	150
B	100
C	50
D	200

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Question 38 Explanation:

Question 39

In the circuit shown the average value of the voltage V_ab (in Volts) in steady state condition is ______

A	10
B	25
C	5
D	30

Discuss GATE EC 2015 Set 2 Networks Time Domain and Frequency Analysis of Linear circuits

Question 39 Explanation:

Question 40

In the circuit shown the average value of the voltage V_ab (in Volts) in steady state condition is ______

A	10
B	25
C	5
D	30

Discuss GATE EC 2015 Set 2 Networks Time Domain and Frequency Analysis of Linear circuits

Question 40 Explanation:

Question 41

An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

A	$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image137.png$
B	$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image138.png$
C	$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image139.png$
D	$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image140.png$

Discuss GATE EC 2015 Set 2 Networks Time Domain and Frequency Analysis of Linear circuits

Question 41 Explanation:

Question 42

In the circuit shown, the Norton equivalent resistance

across terminals a-b is ______.

A	2.333
B	1.333
C	1.255
D	3.333

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Question 42 Explanation:

Question 43

Let x (t) = a s (t) + s (–t) with s (t) = βe^–4t u (t), where u (t) is unit step function. If the bilateral Laplace transform of x (t) is

Then the value of β is _________

A	2
B	-2
C	1
D	-1

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Question 43 Explanation:

Given x(t) = αs(t) + s(–t)

Now, we have ROC

Taking Laplace for given ROC, we have

Coefficient of s is zero. From above equation, we conclude the result as

Question 44

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z₁ of the first section to the input impedance Z₂ of the second section is

A
B
C
D

Discuss GATE EC 2014 Set 1 Networks Two Port Networks

Question 44 Explanation:

consider the cascaded sections shown below

Z₁ = First section Output impedance
Z₂ = Second section Input impedance
For maximum power transfer, upto 1^st section is

Question 45

Consider the configuration shown in the figure which is a portion of a larger electrical network

For and currents i₁=2A, i₄=-1A, i₅=-4A which one of the following is TRUE?

A	I₆=5A
B	I₃=-4A
C	Data is sufficient to conclude that the supposed currents are impossible
D	Data is insufficient to identify the current

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Question 45 Explanation:

Question 46

A Y-network has resistances of 10 Ω each in two of its arms, while the third arm has a resistance of 11 Ω in the equivalent D − network, the lowest value in Ω among the three resistances is ______________.

A	25.09
B	27.09
C	28.09
D	29.09

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Question 46 Explanation:

i.e, lowest value among three resistances is

Question 47

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

A	(18 + j 1.5) kVA
B	(18 - j 1.5) kVA
C	(20 + j 1.5) kVA
D	(20 - j 1.5) kVA

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Question 47 Explanation:

Question 48

A periodic variable x is shown in the figure as a function of time. The root-mean-square (rms) value of x is_______.

A	0.324
B	0.368
C	0.408
D	0.442

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Question 48 Explanation:

Question 49

In the circuit shown in the figure, the value of capacitor C(in mF) needed to have critically damped response i(t) is____________.

A	5
B	10
C	15
D	20

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Question 49 Explanation:

Applying kirchoff’s voltage low in frequency domain, we have

Differentiate with respect to time,

For critically damped response,

This is the required value of C to have critically damped response i(t)

Question 50

Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance

A	in series with a current source
B	in parallel with a voltage source
C	in series with a voltage source
D	in parallel with a current source

Discuss GATE EC 2014 Set 2 Networks Network Theorems And Transformations

Question 50 Explanation:

Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance in parallel with a current source

Question 51

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 ________.

A	0.25
B	0.30
C	0.40
D	0.45

Discuss GATE EC 2014 Set 2 Networks Filters, AC and DC circuits

Question 51 Explanation:

The operating frequencyat which current leads the supply.

again magnitude of current is half the value at resonance

By substituting R, L & C values,

So, operating frequency

Question 52

In the h-parameter model of the 2-port network given in the figure shown, the value of h₂₂ (in S) is _____ .

A	1.24
B	1.28
C	1.32
D	1.36

Discuss GATE EC 2014 Set 2 Networks Two Port Networks

Question 52 Explanation:

If two,

are connected in parallel,
The y-parameter are added

Question 53

In the figure shown, the capacitor is initially uncharged. Which one of the following expressions describes the current I(t) (in mA) for t > 0?

A
B
C
D

Discuss GATE EC 2014 Set 2 Networks Steady State equations and Analysis

Question 53 Explanation:

Question 54

A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage V_S, the resistance R, the capacitance C, and the current i(t) is given below:

Which one of the following represents the current i(t)?

A
B
C
D

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Question 54 Explanation:

Question 55

In the figure shown, the value of the current I (in Amperes) is __________.

A	0.2 Amp
B	0.4 Amp
C	0.5 Amp
D	0.8 Amp

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Question 55 Explanation:

Question 56

In the circuit shown in the figure, the value of node voltage V₂ is

A
B
C
D

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Question 56 Explanation:

Question 57

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

A	2r/s
B	3 r/s
C	4r/s
D	5r/s

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Question 57 Explanation:

Norton’s equivalent impedance

Equating imaginary term to zero i.e.,

Question 58

For the Y-network shown in the figure, the value of

in the equivalent

-network is _______________.

A	5
B	10
C	15
D	20

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Question 58 Explanation:

Question 59

The circuit shown in the figure represents a

A	Voltage controlled voltage source
B	Voltage controlled current source
C	Current controlled current source
D	Current controlled voltage source

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Question 59 Explanation:

The dependent source represents a current controlled current source

Question 60

The magnitude of current (in mA) through the resistor

in the figure shown is_______.

A	2.8
B	3.4
C	5
D	4.4

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Question 60 Explanation:

Question 61

In the circuit shown in the figure, the value of

(in Volts) for

A	21.25
B	25.50
C	31.25
D	35.0

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Question 61 Explanation:

Question 62

The equivalent resistance in the infinite ladder network shown in the figure is R_e

The value of Re/R is ________

A	2.0
B	2.618
C	4.0
D	4.618

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Question 62 Explanation:

For an infinite ladder network, if all resistance are having same value of R
Then equivalent resistance is

→ For the given network, we can split in to R is in series with

Question 63

For the two-port network shown in the figure, the impedance (Z) matrix (in

) is

A
B
C
D

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Question 63 Explanation:

For the two-part network

Question 64

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 Ω should be

A	3
B	4
C	5
D	7

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Question 64 Explanation:

Question 65

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage V_WX1 100 V is applied across WX to get an open circuit voltage V_YZ1 across YZ. Next, an ac voltage V_YZ2 = 100 V is applied across YZ to get an open circuit voltage V_YZ2 across WX. Then

are respectively

A	125/100 and 80/100
B	100/100 and 80/100
C	100/100 and 100/100
D	80/100 and 80/100

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Question 65 Explanation:

An ideal transformer is an imaginary transformer which has. - no copper losses (no winding resistance) - no iron loss in a core. - no leakage flux. In other words, an ideal transformer gives output power exactly equal to the input power.

Attenuator: a device consisting of an arrangement of resistors which reduces the strength of a radio or audio signal

Given transformer

Attenuation factor will be 0.8
So,

or,

Question 66

Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂. When connected in series, their effective O factor at the same operating frequency is

A
B
C
D

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Question 66 Explanation:

Question 67

Three capacitors C₁ C₂ and C₃ whose values are 10 µF. 5 µF. and 2 µF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively,

A	2.8 and 36
B	7 and 119
C	2.8 and 32
D	7 and 80

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Question 67 Explanation:

Question 68

Consider the following figure

The current I_s in Amps in the voltage source and voltage V_s in Volts across the current source respectively, are

A	13, –20
B	8, –10
C	–8, 20
D	–13, 20

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Question 68 Explanation:

Question 69

The current in the 1 Ω resistor in Amps is(Continuation to above question)

A	2
B	3.33
C	10
D	12

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Question 69 Explanation:

Question 70

The average power delivered to an impedance

by a current

A	44.2
B	50
C	62.5
D	125

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Question 70 Explanation:

Question 71

The impedance looking into nodes 1 and 2 in the given circuit is

A	50 Ω
B	100 Ω
C	5 kΩ
D	10.1 k Ω

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Question 71 Explanation:

To find thevenin impedance across node 1 and 2. Connect a 1 V source and find the current through voltage source.
Then

By applying KCL at node B and A
i_AB + 99i_b = I_Th
i_b = i_A + I_AB
⇒ i_b – i_A + 99i_b = I_Th
⇒ 100i_b – i_A = i_Th …(1)
By applying KVL in outer loop
10 × 10³i_b = 1
i_b = 10^-4 A
And 10 × 10³i_b = -100i_A
⇒ i_A = -100i_A
From equation (i)
100i_A + 100i_b = I_Th
⇒ I_Th = 200i_b
⇒ 200 × 10⁴ = 0.02

Question 72

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

A
B
C
D	0 A

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Question 72 Explanation:

Question 73

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

A	0.8 Ω
B	1.4 Ω
C	2 Ω
D	2.8 Ω

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Question 73 Explanation:

Current through R will be

Current through 3 V source is

So power delivered to circuit B by circuit A is
P = i²R + i₁ × 3

for P to be maximum

will be aero

_{49(2+R) – 98R – 21(2+R) = 0}
98 + 42 = 49R + 21R

Question 74

If V_A – V_B = 6V, then V_C - V_D is

A	–5V
B	2V
C	3V
D	6V

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Question 74 Explanation:

= 3A …(1)
KCL at node B, we have
i = i₂ + i₁
i₂ + i₁ = 3A ..(2)
KCL at node E, we have
i₁ = i₃ + i₄ …(3)
KCL at node D we have
i₅ = i₂ + i₃ + i₄
i₅ = i₂ + i₁
i₅ = 3A
KCL at node F, we have
i₆ + 2 + i₅ = 0
i₆ = -2-i₅
So, V_C – V_D = 1 × i₆ = -5V

Question 75

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:
(i) 1 Ω connected at port B draws a current of 3 A
(ii) 2.5 Ω connected at port B draws a current of 2 A

With 10 V dc connected at port A. the current drawn by 7 Ω connected at port B is

A	3/7 A
B	5/7 A
C	1A
D	9/7 A

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Question 75 Explanation:

I_{L =}V_Th / (R_Th +R_L)

(i) R_L=1 Ω, I_L =3A,

Implies 3 = V_Th / (R_Th +1),

(ii) For R_L=2.5 Ω, I_L = 2A.

Implies 2= V_Th / (R_Th +2.5)

Divide above equations (i) and (ii),

3/2 = (R_Th + 2.5)/ (R_Th + 1),

3 R_Th + 3 = 2 R_Th + 5.

R_Th = 2 Ω.

Substitute R_Thin the above equation, V_Th = 3(2+1) = 9V.

For R_L=7 Ω, I_L= V_Th(2+R_L) = 9/(2+7) = 1A

Question 76

What is the condition for reciprocity and symmetry in Y-parameter representation?

A	Y₂₁ = Y₁₁ and Y₂₂ = Y₂₁
B	Y₂₁ = Y₁₂ and Y₁₁ = Y₂₂
C	Y₂₁ = Y₂₂ and Y₁₁ = Y₂₂
D	Y₁₁ = Y₂₂ and Y₂₁ = Y₂₂

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Question 76 Explanation:

Question 77

In hybrid parameters, h₁₁ and h₂₁ are called as

A	input impedance and forward current gain
B	reverse voltage gain and output admittance
C	input impedance and reverse voltage gain
D	output impedance and forward current gain

Discuss ESE 2019 Paper 2(Technical) Networks Two Port Networks

Question 77 Explanation:

V₁ = h₁₁ I₁ + h₁₂ V₂
I₂ = h₂₁ I₁ + h₂₂ V₂

∴ h₁₁ is input impedance

∴ h₂₁ is forward current gain
∴ Option A

Question 78

Consider the following equations:
V₁ = 6V₂ – 4I₂
I₁ = 7V₂ – 2I₂
A, B, C and D parameters are

A	6,-4 Ω, 7 mho and -2
B	6, 4 Ω, 7 mho and 2
C	-6, 4 Ω, -7 mho and 2
D	6, 4 Ω, -7 mho and -2

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Question 78 Explanation:

Question 79

A supply of 250 V, 50 Hz is applied to a series RC circuit. If the power absorbed by the resistor be 400 W at 160 V, the value of the capacitor C will be nearly

A	30.5 μF
B	41.5 μF
C	64.0 μF
D	76.8 μF

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Question 79 Explanation:

P_R = 400 watt
V_R = 160 V

Question 80

A 50 Hz sinusoidal voltage V = 311 sin ωt is applied to an RL series circuit. If the magnitude of resistance is 5 Ω and that of the inductance is 0.02 H, the r.m.s. value of the steady-state current and the relative phase angle are nearly

A	19.6 A and 51.5^o
B	27.4 A and -51.5^o
C	19.6 A and -51.5^o
D	27.4 A and 51.5^o

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Question 80 Explanation:

Question 81

In a series RC circuit, the values of R = 10 Ω and C = 25 nF A. sinusoidal voltage of 50 MHZ is applied and the maximum voltage across the capacitance is 2.5 V. The maximum voltage across the series combination will be nearly

A	172.7 V
B	184.5 V
C	196.3 V
D	208.1 V

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Question 81 Explanation:

Question 82

The peak-to-peak ripple voltage for a half-wave rectifier and filter circuit operating at 60 Hz, which has a 680 μF reservoir capacitor, an average output of 28 V and 200 load resistance, will be nearly

A	2.5 V
B	3.4 V
C	4.3 V
D	5.2 V

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Question 82 Explanation:

Given frequency, f = 60Hz
C = 680μF = 28V
V_{output average} = 28V
R_L = 200Ω
Charge stored while charging = charge discharged while discharging
∴

× C = I_DC × T_o

∴

= 3.4 V
∴ Option B

Question 83

A steady state is achieved in following Network at T = 0, find the time when Vc(t) will be maximum

A	In(9) sec
B	ln(9)^0.125 sec
C	ln(9)^0.25 sec
D	9 sec

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Question 83 Explanation:

The Correct Answer Among All the Options is B
Taking laplace transform of given circuit then finding the voltage across capacitor . then after using of concept of maxima/minima , we get the time when Vc(t) will be maximum i.e. t=ln(9)^0.125 sec
Refer the Topic Wise Question for Time Domain and Frequency Analysis of Linear circuits Networks

Question 84

Y-parameter for following network is given as

A
B
C
D

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Question 84 Explanation:

The Correct Answer Among All the Options is C
for parallel connection Y-parameters will be added , from the given figure we can observe that given circuit is symmetrical and reciprocal.
We can split the given circuit in two equivalent circuit which are connected in parallel.

Y-parameters for this circuit will be :

2^nd circuit consist of only capacitors., it is also a reciprocal and symmetrical circuit, Y-parameters for this circuit will be

On adding these two parameters , we get eqivalent Y-parameter.
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Question 85

Two resistances of values 2

and 4

made of different materials with temperature cofficients of resistance 3 ppm/⁰C and 6 ppm/⁰C respctively are connected in series. What is the temperature coefficient of resistance of the nt resistance?

A	5 ppm/⁰C
B	ppm/⁰C
C	9 ppm/⁰C
D	4.5 ppm/⁰C

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Question 85 Explanation:

The Correct Answer Among All the Options is A

are temperature coefficient of

respectively.
When

are connected in series. Then

(1+

) ,
where

equivalent temperature coefficient

Given ,

On putting these values ,

Refer the Topic Wise Question for Basic Electrical Engineering Networks

Question 86

An LC tank circuit resonates at a frequncy ‘f_r’. If the temperature coefficient of prmittivity of the dielectric material used in the Capacitance is 6 ppm/⁰C, then what is the temperature coefficient of frequency ‘f_r’.

A	-3 ppm/⁰C
B	3 ppm/⁰C
C	-6 ppm/⁰C
D	6 ppm/⁰C

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Question 86 Explanation:

The Correct Answer Among All the Options is A
Formula for resonance frequency in LC tank circuit =

Differentiate .r.t temperature(T), only Capacitance will vary because here temperature coefficient of

(permittivity ) is given.

…………………. (1)
And C=C[1+

], from this

…………………. ..(2)
From (1) and (2)

, on simplifying it we get

Now as we know for any change in temperature(

), new frequency will be

This equation shows that temperature coefficient of

will be

.
Given,

6ppm

Therefore,

= -3ppm/

.
Refer the Topic Wise Question for Steady State equations and Analysis Networks

Question 87

For a circuit given in figure, switch K is closed to position 1 at t = 0. After t = 1 TC (Time Constant), switch is moved to position 2. Find the Current I at 1TC(-) (just before on-time constant time) and ITC(+) (just after one-time constant time) respctively (assum 1/e

0.37)

A	0.0148 A and 0.055 A
B	0.0148 A and -0.055 A
C	0.0296 A and 0.11 A
D	0.0296 A and -0.11 A

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Question 87 Explanation:

The Correct Answer Among All the Options is A
For 0 < t < 1 time constant(

)
, switch is connected to “1”. Therefore circuit becomes,

=RC
=500

= 2.5

econds
So the capacitor slowly charges to 20V with following equation

At t=

= 20[1-0.37]
=12.6 V
i.e At

, the capacitor voltage is = 12.6 V
I at

=0.0148A
After 1 time constant (

) i.e. at t=

, equivalent circuit becomes

Therefore, I =

= 0.0548A

Refer the Topic Wise Question for Time Domain and Frequency Analysis of Linear circuits Networks

Question 88

For a network shown in figure, which of the following statement is true.

A	Reciprocal and symmetric
B	Rciprocal but not-symmetric
C	Symmetric but non-rciprocal
D	Neither symmetric nor reciprocal

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Question 88 Explanation:

The Correct Answer Among All the Options is D
Normally we know dependent source make a circuit non-reciprocal. As for symmetrical circuit , there should be mirror image in circuit , but in figure we can clearly see that there is no any line of symmetry. So given circuit is Non-reciprocal and not symmetric.
To check we have to calculate Z-parameter.

When

→

When

→

→

→not symmetrical

→not reciprocal
Refer the Topic Wise Question for Two Port Networks Networks

Question 89

For a network shown in figure, Calculate current i₂.

A	2/3 A
B	3/2 A
C	1/3 A
D	None of the above

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Question 89 Explanation:

The Correct Answer Among All the Options is A
In the given circuit , we can use superposition principle. While using the voltage source current source is open circuited, and while using the current source voltage source is short circuited.
And calculate

Refer the Topic Wise Question for Network Equations and Solution Methods Networks

Question 90

For a network shown in figure, a steady state is reached with switch k is open. Switch is closed at time t = 0. Calculate (di₁/dt) and (di₂/dt) at t = 0+

A	16.67 A/sec and -4.16 x 10⁴ A/sec
B	16.67 A/sec and -3.33 x 10⁴ A/sec
C	25 A/sec and -4.16 x 10⁴ A/sec
D	25 A/sec and -3.33 x 10⁴ A/sec

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Question 90 Explanation:

The Correct Answer Among All the Options is A
In steady state at t=

Inductor short circuit ,

Capacitor open circuit,

Inductor does not allow sudden change in current and capacitor does not allow sudden change in voltage.
So

and

The equivalent circuit at t=

is,

Where ,

Also,

v
For inductor,

= 16.67 A/sec
KVL for capacitor branch,
100V=

On differentiating w.r.t ‘t’
0=20

…………………………..(1)
Also,

Also., C

→

………….(2)
Put (2) in (1)
0= 20

Given, C=2

=-4.16

A/s
Refer the Topic Wise Question for Steady State equations and Analysis Networks

Question 91

Identify the correct sequence of stages in charging of a Lead-Acid battery.

A	Constant Current, Topping, Float
B	Topping, Constant Current, Float
C	Float, Topping, Constant Current
D	Float, Constant Current, Topping

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Question 91 Explanation:

The Correct Answer Among All the Options is A
The lead acid battery uses the constant current constant voltage (CC/CV) charge method. A regulated current raises the terminal voltage until the upper charge voltage limit is reached, at which point the current drops due to saturation. Lead acid batteries should be charged in three stages, which are [1] constant-current charge, [2] topping charge and [3] float charge. The constant-current charge applies the bulk of the charge and takes up roughly half of the required charge time; the topping charge continues at a lower charge current and provides saturation, and the float charge compensates for the loss caused by self-discharge.
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Question 92

For the circuit shown below, Z₁=K₁ x (s+2)/(s+5). Find Z₂, where K₁ and K₂ are constants containing circuit' element values

A	K₂ x s/(s + 5)
B	(s + 5)/(s x K₂)
C	K₂ x s/(s + 6)
D	(s 6)/(s x K₂)

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Question 92 Explanation:

The Correct Answer Among All the Options is A
Given=> Z1= K1 [(s+2)/(s+5)]
Now, We have to determine what is Z₂. Now according to general concept, Z₂ can be written as: Ls||(R₁+R₂)
This can also be written as: (R₁+R₂)Ls/Ls+R1+R2.................(a)
Now given options are having 'K' term in them. It means we have to bring Z₁ in the scenario.
So, given=> Z₁= K₁ (s+2)/(s+5)
Now in order to get R₁, R₂ and L_s in terms of K, we have to reduce Z₁ and bring it in a form so that it can be compared with the Z₁ given in the question.
Now looking at the figure we can write:
Z₁= R₁||(R₂+L_s)=> R₁(R₂+L_s)/R₁+R₂+L_s
So, we have to bring it in a particular form.
Now=> in question's Z₁ term=> 's+' term is present. It means that we have to somehow take L_s common from here. So taking Lcommon so that 's' remains inside the bracket.
So on taking 'L' term out, and simplifying we will get: Z₁= (R2/L +s)R1 / (R1+R2)/L +s
Now this can easily be compared with Z1 given in question. On comparing, we get:
R1=K1, R2/L=2
So, now putting these values in (a) we get:
Z2= (R₁+R₂)Ls/Ls+R1+R2
=> L(R1+R2)(s)/ R1+R2/L +s
Now, R1+R2/L=5(From comparing), R1=K1, and R1/L=3.
So, on putting this, we will get Z2= sK/(s+5)
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