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INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous)

Dundigal, Hyderabad - 500 043

ELECTRICAL AND ELECTRONICS ENGINEERING

Course Name : NETWORK THEORY

Course Code : A40213

Class : II-B.TECH II SEM

Branch : Electrical and Electronics Engineering

Year : 2015-2016

Course

Coordinator : Ms. Lekha Chandran, Associate Professor

Course Faculty : Ms. Lekha Chandran, Associate Professor

OBJECTIVE: This course introduces the basic concepts of network theory which is the foundation for all subjects of the

electrical engineering discipline. The emphasis of this course if laid on the basic analysis of circuit which

includes three phase circuits, transient analysis of DC and AC circuits , Network functions, two port

network parameters, Fourier analysis of ac circuits, Design and analysis of filters

1. GROUP - I (SHORT ANSWER QUESTIONS)

S.

No QUESTION Blooms

Taxonomy Level Course

Outcome

UNIT-I

THREE PHASE CIRCUITS

1 What are the advantages of a poly phase system over a single phase system Understand 1

Derive the relationship between line and phase quantities in a 3-phaseStar

Star connected system

2 connected system Understand 1

balanced,

i) Star connected system

3 Derive the relationship between line and phase quantities in a 3-phase Understand 1

Delta connected system for balanced delta system

Three identical impedances of (3+j4) ohm are connected in delta. Find an Evaluate

4 equivalent star network such that the line current is the same when connected to 2

the the same supply

5 Derive the expressions for wattmeter readings in two wattmeter method with Understand 1

balanced star connected load connected load

6 On a symmetrical 3-phase system, phase sequence RYB, a capacitive reactance Evaluate 2

of 8 is across YB and a coil (R+jX) cross RY. Find R and X such that Iy =0

7 Derive the formula for power factor in two wattmeter method Understand 1

Three identical resistances are connected in a star fashion against a balanced Evaluate

8 three phase voltage supply. If one of the resistances is removed, how much 2

power is to be reduced?

9 Explain the effect of power factor on wattmeter readings in two wattmeter Remember 1

method.

10 Explain how reactive power can be measured in three phase circuits remember 1

11 Three identical impedances of (10+j4) ohm are connected in star. Find

equivalent delta circuit Evaluate 1

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12 Explain how three phase emfs can be generated Understand 1

13 What are the possible numbers of phase sequence. Explain Understand 1

14

A symmetrical 3 phase , three wire 440V supply is connected to a Y connected

load and the impedance of each branch are 2 + j3 ohms. Obtain the line currents

and phase currents across the load Understand 1

S.

No QUESTION Blooms

Taxonomy Leve Course

Outcome

UNIT-II

DC AND A.C TRANSIENT ANALYSIS

1 Explain why the current in a pure inductance cannot change in zero time. Remember 1

Explain why the voltage across a capacitor cannot change instantaneously. Remember 1

3 What is the significance of time constant of R-L circuit? What are the different

Remember 1

ways of defining time constant?

Derive the expression for i(t) of a R-L series circuit when DC voltage is applied Analyze

4 to it at t=0 by closing the switch. Draw the response curve i(t) vs t. define time 2

constant of R-L series circuit.

Derive the expression for I (t) and voltage across a capacitor Vc(t) for series R-C

5 circuit with D.C voltage applied to it at t=0.Explain about the time constant of Evaluate 2

R-C circuit

6 Compare the classical and Laplace transform methods of solution of the network Understand

1

7 Derive an expression for the current response in R-L series circuit with a

Remember 1

sinusoidal source

8 Distinguish between steady state and transient response Remember 1

A Sinusoidal Voltage of 12 sin 8 t Volts is applied at t = 0 to a RC series of R=

9 4Ω and c = 1 H. By Laplace transform method determine the circuit current I (t) Evaluate 2

for. Assume zero initial condition

10

A Sinusoidal Voltage of 12 sin 8 t Volts is applied at t = 0 to a RL series of R=

4Ω and L = 1 H. By Laplace transform method determine the circuit current I (t)

for. Assume zero initial condition Evaluate 2

11 What are initial conditions? Explain the procedure to evaluate

Remember 1

initial conditions

12 Transient response occrs in which type of circuits? Explain Understand 1

S. No QUESTION Blooms Course

Taxonomy Level Outcome

UNIT-III

NETWORK FUNCTIONS

1 What is a pole-zero plots? What is its significance? Explain time domain

Understand 1

behavior from pole zero plot.

2 Define and explain the following : port, driving point functions

Understand 1

And Transfer functions.

3 What is a transfer function? Explain the necessary conditions for transfer

Remember 1

functions

4 What is a driving point function? Explain the necessary conditions for driving Remember

1

point functions

5 According to Routh Criteria when a network is said to be stable? Apply 5

6 The Laplace transform of a voltage v(t) is V(s)=4(s+1)/(s+2)(s+3). Draw poles

Apply 5

and zeros of this function and determine v(t) using pole-zero plot

7 The transform voltage V(s) of a network is given by V(s) =4s/(s+2)(s2+2s+2)

5

plot its pole-zero diagram and hence obtain v(t) Apply

8 Find the stability of the network

Evaluate 5

Q(S) =40S/S3 +2S2+8S+1

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Find Y parameters for the above network shown in Figure

9 Evaluate 2

For the given network function draw pole zero diagram and hence obtain the

10 time domain response i(t) if Apply 5

I(s) = 5S / (S+1)(s2+4S+8)

S. No QUESTION Blooms Course

Taxonomy Level Outcome

UNIT-IV

NETWORK PARAMETERS

1 Define active and passive ports Understand 1

2 Why Z-parameters are called as open circuit impedance (Z) parameter Understand 1

3 Define open circuit forward transfer impedance Understand 1

4 Give the condition for reciprocity for Z parameters Understand 1

5 Why Y parameters are called as short circuit admittance

Understand 1

Parameters

6 What are the applications of cascaded ABCD parameters Understand 1

7 Express y-parameters in terms of h-parameters Understand 1

8 Express Z-parameters in terms of h-parameters Understand 1

9

1) A two port n/w has the following Z - parameters Z11 = 40 ohm, Z22 = 30, Z12 =

Z21 = 20. Compute the transmission parameters for the n/w. Hence write the n/w

equations with the use of the parameters Analyse 1

10 Express Z parameters in terms of ABCD parameters Understand 1

11 Express h-parameters in terms of ABCD parameters Understand 1

12

) Find the transmission parameters of the network shown in figure below.

Analyse 1

S. No

QUESTION

Blooms Course

Taxonomy Level

Outcome

UNIT-V

FILTERS AND FOURIER ANALYSIS OF A.C CIRCUITS

1 Define a filter and What are the classification of filters Understand 1

2 Explain the formula for characteristic impedance of symmetrical T-Section Understand 1

3

Explain the design procedure for a constant K low pass filter and its Understand

1

characteristics

Find the component values of a constant K. LPF having characteristic

4 impedance Z = 500Ω and cut off frequency of ‘fc’= 500 Hz. Find the frequency Evaluate 5

0

at which this filter produces an alternation constant of 38.2 dB

5 Write short note on m-derived filters Remember 1

6

Design a constant K band elimination filter with cut off frequency 1750 Hz to Evaluate

1

4250 Hz and a characteristic impedance of 250Ω

7 Write short notes on Fourier transform theorems. Understand 1

8 Write short notes on Exponential form of Fourier series Understand 1

9 Write short notes on Line and phase angle spectra Understand 1

10 Write short notes on Fourier integrals Understand 1

11

.Design a Band elimination filter having a design impedance of 500 ohms and

cut-off frequencies f1=1 KHz, f2=5 KHz? evaluate 1

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12 Explain about Band Pass Filter Understand 1

13 Explain the characteristics of an ideal filter Understand 1

2. Group - II (Long Answer Questions)

S. No

QUESTION

Blooms Taxonomy Course

Level

Outcome

UNIT-I

THREE PHASE CIRCUITS

A three phase balanced delta connected load of (10+j8) ohm is connected across

1

a 400V, 3-Ø balanced supply. Determine the phase currents and line currents. Evaluate

2

Assume the phase of sequence to be RYB. Also calculate the power drawn by

load.

Three impedance each 5 +j12 ohm is connected in star are connected to a 220 V 2

2

three phase, 50 HZ supply. Calculate the line currents and the power drawn Evaluate

by the circuit

A three phase balanced delta connected load of (4+j8) ohm is connected across

3

a400V, 3-Ø balanced supply. Determine the phase currents and line currents. Evaluate

2

Assume the phase of sequence to be RYB. Also calculate the power drawn by

load.

A balanced 3-phase star connected load of 200 kW takes a leading current of 2

4

150 amps with a line voltage of 1200 V at 50 Hz. What are the circuit constants Evaluate

of the load per phase?

The two watt meter readings in a 3 - phase power measurement are 800 W and 2

5

400 W. The latter reading is being obtained after the reversal of current coil. Evaluate

Calculate the total power and power factor of the load

A 3-phase 500 V motor operates at a power factor of 0.4 and takes an input 2

6

power of 30 kW. Two watt meters are employed to measure the input power. Evaluate

Find readings on each instrument.

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A balanced three phase is connected to balanced 3 - phase power system. The

line voltage is 480 volts and the line current is 10 A. the angle of the phase Evaluate

2

impedance of the load 60. Find the complex power and real power absorbed by

7

the load.

Two wattmeters are used to measure power in a 3-phase three wire load.

8 Determine the total power, power factor and reactive power, if the two 2

wattmeter’s read i) 1000W each, both positive ii) 1000W each, but of opposite Evaluate

sign.

Three star connected impedances 5030, 4060, 4060 ohms are connected to a

9 400V, 3-Phase supply. Determine the line currents and the two watt meter

Evaluate 2

readings when power is measured by 2 watt meter method and abc is the phase

sequence.

A star connected load of Z = 6Ω, Z = j5Ω, Z = j7Ω is supplied by a 400V, 3- 2

10 R Y B Evaluate

Ø symmetrical supply. Determine the line currents. The phase sequence is

RYB.

S. No

QUESTION Blooms Taxonomy Course

Level Outcome

UNIT-II

For the circuit shown in Figure determine the particular solution for i(t) through

the circuit. Assume zero initial conditions

1

Evaluate 2

Derive an expression for the response in the system in Figure.2

2

2 By time domain and Laplace transform techniques. Cross Evaluate

Check the answer. V (t) = 5(Sin1000t+π/6).

For the circuit given in Figure steady state conditions are reached for the switch

K in position ‘1’. At t = 0, the switch is changed to position 2. Use the time

domain method to determine the current through the inductor for all t≥0.

3 Evaluate 2

A series RL circuit with R = 50 ohms and L = 0.2 H has a sinusoidal voltage

Evaluate 2

4 source V = 150 (500Sint φ+ volts applied at a time when φ=0. Find the

expression for the total current. Use Laplace transforms method.

A series R C circuit with R = 100 Ω and C = 25 μF has a Evaluate 2

5 Sinusoidal excitation V (t) = 250 Sin 500t. Find the total

current assuming that the capacitor is initially uncharged

6 For the circuit shown in Figure determine the particular solution for i(t) through

Evaluate 2

the circuit. Assume zero initial conditions

COURTESY IARE

A series RC circuit with R = 50 ohms and C = 2 micro farad has a sinusoidal

2

7 voltage source V = 150 (500Sint φ+π/3) volts applied at a time when φ=0. Find Evaluate

the expression for the total current. Use Laplace transforms method

A dc voltage of 20V is applied in a RL circuit where R = 5 2

8 And L = 10H. Find i. The time constant ii. The Evaluate

maximum value of stored energy

A dc voltage of 100V is applied in the circuit shown in figure a and the switch is

kept open. The switch K is closed at t = 0. Find the complete expression for the

current

9

Evaluate 2

A Sinusoidal Voltage of 12 sin 8 t Volts is applied at t = 0 to a RC series of R=

2

10 4Ω and L = 1 H. By Laplace transform method determine the circuit current i (t) Evaluate

for. Assume zero initial condition.

S. No QUESTION Blooms Taxonomy Course

Level Outcome

UNIT-III

NETWORK FUNCTIONS

1 Find the transfer function V2(S)/V1(S) for the circuit in the figure

Evaluate 5

For the following network shown in figure determine Z parameters

2 Evaluate 5

Draw the transformed network for the given circuit 3

Evaluate 5

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4 For the network shown in the figure below determine the transfer functions G21

(S) And Z21(S). Also find Z11(S)

Analyze

5

5 Find Z parameters for the network shown in Figure

Evaluate

5

6

Find the transfer function V2(S)/V1(S)for the circuit in Figure

Evaluate

5

7 Draw the transformed circuit for given circuit and obtain i(t)

Evaluate

5

For the two port network shown in the Figure find G12[V2(S)/V1(S)]

8

Evaluate 5

9 For the circuit shown in the Figure.3, find i(t). Assume zero initial conditions.

Use 5

Laplace transforms approach. The switch is closed at t = 0.

Evaluate

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10 Find Y for the circuit in Figure

12

Evaluate 5

S. No QUESTION Blooms Taxonomy Course

Level Outcome

UNIT-IV

NETWORK PARAMETERS

Obtain Z-parameters of the two port network

1 Evaluate 2

Find the Z parameters of the circuit shown

2 Evaluate 2

Determine the ABCD parameters of two networks connected in cascade as

shown in figure

3 Evaluate 2

4 Find the h-parameters for the circuit in figure Evaluate 2

COURTESY IARE

Find the Y-parameters of the network shown

5 Evaluate 2

Determine the ABCD parameters of two networks connected in cascade as

shown

6 Evaluate 2

7 The Z parameters of a two port network are Z11=6Ω, Z22=4Ω, Z12=Z21= 3Ω Evaluate 2

Compute Y and ABCD Parameters and write the describing equations

8 Discuss in detail about series and parallel connection of two port networks Analyze

2

For the two port network given below (Shown in Figure.3) determine ABCD &

hybrid parameters

9 Evaluate 2

For the two port network given below (shown in Figure.4) determine Y and

ABCD parameters

10 Evaluate 2

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S. No QUESTION

Blooms Taxonomy Course

Level

Outcome

UNIT-V

FILTERS AND FOURIER ANALYSIS OF A.C CIRCUITS

1

Design a low pass filter (both T and π sections) having a cutoff frequency of 2 Analyze

5

KHz to operate with a terminated load resistance of 500Ω

2

Design a symmetrical T-attenuation to give 20 dB attenuation and to have Analyze

5

characteristic impedance of 300Ω

3

Design a symmetrical T attenuator to give 2 dB attenuation to have a Analyze

5

characteristic impedance of 150Ω

4

Draw the circuit diagram of a Band pass filter. Explain the design procedure of Analyze

5

the above filter in detail

5

Draw the circuit diagram of a High pass filter. Explain the design procedure of Analyze

5

the above filter in detail

6

Draw the circuit diagram of a Low pass filter. Explain the design procedure of Analyze

5

the above filter in detail

7

Design a proto type section of band pass filter having cut-off frequencies of Analyze

5

12KHz and,16 KHz and a design impedance of 600 ohm

Find the trigonometric Fourier series for the wave shown in fig. and plot the

spectrum

8 Analyze 2

Find the exponential Fourier series for the waveform

shown in figure

9

Analyze

2

Find the exponential Fourier series for the waveform shown in fig and plot the

spectrum

10

Analyze

2

Group – III ANALYTICAL

S. No QUESTION

Blooms Taxonomy Course

Level

Outcome

UNIT-I

THREE PHASE CIRCUITS

1 A r.m.s voltage in a three phase star circuit is given by 231V (ph. –N). Write the Evaluate

instantaneous voltage expression. If the current in each phase lag the 2

corresponding phase voltages by 30ᵒ what are the expressions of instantaneous

currents?

2 A Three phase 4 wire 100 V (L-L) system supplied a balanced Y connected load Evaluate 2

having impedances of 10 - 30ᵒΩ in each phase. Find line currents and draw the

phasor diagram. How much current is flowing through the neutral

3 A ∆ connected load half a parallel combination of resistance (5 Ω) in each Evaluate 2

phase. If a balanced 3 phase 400 V supply is applied between lines, find the

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phase currents and line currents and draw the phasor diagram.

4 A 3 phase, star connected system with 400 V (L-L) is disconnected to three Evaluate 2

loads: 25 0ᵒ , 11 - 20ᵒ ohm (also connected in star). Find the line current, power

and the current in the neutral of the system.

5 A three phase Y connected load has an inductor of 500 mH and capacitance of Evaluate 2

100 µF in each phase. The load is connected across a 100V, 50Hz three phase

balanced system Find the line currents for the load.

6 The power in a three phase circuits is measured by two wattmeters. If the total Evaluate 2

power is d50kW, power factor being 0.8 leading, what will be the reading of

each wattmeter? For what plf. Will one of the wattmeter’s read zero?

7 A three phase 400 V, 50Hz, 25 HP motorist delta connected and is operating at Evaluate 2

0.85 lag and efficiency of 80% What is the line current?

8 A three phase induction motor takes 100 kVA at 0.6 p.f. (lag) from a 440 V Evaluate

three phase 50 Hz source (balanced). There is another load on the same line and 2

the load is connected in form of a ∆ having 8 Ω resistance and – j 24 Ω

reactance in series in each phase. Find the total VA power, average power,

reactive power. Line current and the p.f. of the combination.

9 A balanced Y connected 3 phase load has an impedance of Zph(=5-j 4) ohms in Evaluate 2

each phase. Find the line currents if a balanced 3 ph source of 100 V are applied

across it. Draw the phasor diagdram?

UNIT-II

TRASIENT ANALYSIS

What is mean by steady state condition. A dc voltage of 100V is applied in the

circuit shown in figure a and the switch is kept open. The switch K is closed at t

= 0. Find the complete expression for the current

1

Analyze

2

A dc voltage of 20V is applied in a RL circuit where R = 5 and L = 10H. Find 2

2 i. The time constant Analyze

ii. The maximum value of stored energy.

Find i (t) in the circuit for the following figure Use Laplace method

3

Analyze 2

4 Find I c (t) at t = 0 + while the switching is done from x to y at t = 0. As shown

Analyze ii

in figure.

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5 Define 1) Delay time 2) Peak over shoot 3) Settling time Analyze 2

A DC voltage of 20V is applied in a R-L circuit where R=5_ and L=10H. Find

6 the

Analyze 2

i) Time constant

ii) The maximum value of stored energy

A series R-L circuit with R=100_, L=1H has a sinusoidal voltage source 200sin

(500t+¢) applied at time when¢=0. Find 2

7 i) The expression for current Analyze

ii) At what value of ¢ must the switch be closed so that the current directly enter

steady state.

8 A series RC circuit, with R=50_, C=10μF has a sinusoidal voltage 230_2sin

Analyze 2

(2_x50t). Find the transient response

A series R-L circuit with R=50_ and L=0.2H, has a sinusoidal voltage source 2

9 V=150sin (500t+¢)V applied at time when¢=0. Find Analyze

the complete current

A series RLC circuit with R=5_, L=0.1H, C=500μF has a sinusoidal voltage 2

10 v=100sin(250t+¢) volts applied at time when¢=0. Analyze

Find the resulting current

UNIT-III

NETWORK FUNCTIONS

Find the transfer function V2(S)/V1(S) for the circuit in the figure

1 Evaluate 2

For the following network shown in figure determine Y parameters

2 Evaluate 2

3 For the circuit given below determine current supplied by the source, total

Evaluate 2

active & reactive powers also draw the phasor diagram.

COURTESY IARE

For the network shown in the figure below determine the Yparameters

Evaluate 2

4

Find Z parameters for the network shown in Figure

5

Evaluate 2

Find the transfer function V2(S)/V1(S)for the circuit in Figure

6

Evaluate 2

Draw the transformed circuit for given circuit and obtain i(t) at time t=0

7 Evaluate 2

For the two port network shown in the Figure find impedance parameters

8 Evaluate 2

9 For the circuit shown in the Figure.3, find i(t). Assume zero initial conditions. 2

COURTESY IARE

Use Laplace transform approach. The switch is closed at t = 0. Evaluate

Find Z parameters for the circuit in Figure

Evaluate

10 5

UNIT-IV

NETWORK PARAMETERS

1 In a T network Z1 = 2_ 0o, Z2 = 5 _− 90o, Z3 = 3_ 90o, find the Z-

Analyze 2

parameters

2 Z-parameters for a two port network are given as Z11=25, Z12=Z21=20,

Analyze 2

Z22=50. Find the equivalent T-network.

3

Analyze 2

Find the Z-parameters in the above circuit

Find the Z-parameters in the circuit

4

Analyze 2

5 Two two-port networks a and b with transmission parameters Ta and Tb are

Analyze 2

connected in cascade. Obtain Z parameters of the combination.

6 Find the Z-parameters of the two-port circuit of Fig. Analyze 2

COURTESY IARE

7 Derive the formulas for image impedance of two port networks. Analyze 1i

8 Obtain Y parameters in terms of transmission parameters. Analyze 1

9 What is the condition of reciprocity and symmetry for H parameters? Analyze 1

10 What is the condition of reciprocity and symmetry for ABCD parameters? Analyze 1

UNIT-V

FILTERS AND FOURIER ANALYSIS OF A.C CIRCUITS

1 Design a low pass T and _ section filters having a design impedance R0=600_

Analyze 5

and cut-off frequency =2000Hz

2 Design a proto type section of band pass filter having cut-off frequencies of 1

Analyze 5

KHz and, 5 KHz and a design impedance of 600Ω_?

3 Design a proto type section of band pass filter having cut-off frequencies of

Analyze 5

12KHz and,16 KHz and a design impedance of 600 ohm?

A constant K low pass filter is designed to cut-off at a frequency of 1000Hz 5

4 and the resistance of the load circuit is 50ohm. Calculate the values of the Analyze

corresponding components required.

5 Design a constant k-high pass filter to have a cut-off frequency of 2 KHz and

Analyze 5

a design impedance of 100ohm

6 Design a constant k filter to eliminate band of frequencies lying between

Analyze 5

2000Hz and 5000Hz with a design impedance of 600ohm

7 Design a band pass filter with cut off frequencies of 2000Hz and 5000Hz and

Analyze 5

a design impedance of 500ohm

8 Design a constant k high pass filter to cut off at 10KHz and design impedance

Analyze 5

of 600ohm

Find the trigonometric Fourier series for the triangular wave shown in fig. and

plot the spectrum

9 Analyze 2

10 What are the properties of Fourier series Analyze 2

11 Design a low pass T and _ section filters having a design impedance R0=600_

Analyze 2

and cut-off frequency =2000Hz