I B.Tech Supplimentary Examinations, Aug/Sep 2007 NETWORK ...

Code No: RR10204 Set No. 1

I B.Tech Supplimentary Examinations, Aug/Sep 2007NETWORK THEORY

( Common to Electrical & Electronic Engineering, Electronics &Communication Engineering, Computer Science & Engineering, Electronics

& Instrumentation Engineering, Bio-Medical Engineering, InformationTechnology, Electronics & Control Engineering, Computer Science &

Systems Engineering, Electronics & Telematics, Electronics & ComputerEngineering and Instrumentation & Control Engineering)

Time: 3 hours Max Marks: 80Answer any FIVE Questions

All Questions carry equal marks⋆ ⋆ ⋆ ⋆ ⋆

1. (a) State and explain KCL and KVL

(b) Distinguish between

i. independent and dependent sources

ii. Ideal and practical sources.

(c) Find Vs if r1 = 2 Ω r2 = 1 Ω r3 = 5 Ω the following figure1c

Figure 1c[2+2+2+2+8]

2. (a) Define magneto motive force (MMF), Reluctance, and flux density in a mag-netic circuit. Specify the units of each of the above quantities.

(b) Explain “dot convention” for a set of magnetically coupled coils.

(c) A cast steel electromagnetic has an air gap of length 2mm and an iron pathof length 30cms. Find the MMF needed to produce a flux density of 0.8T inthe air gap. The relative permeability of the steel core at this flux density is1000. Neglect leakage & fringing. [6+4+6]

3. (a) Define RMS value, Average Value, form factor and peak factor.

(b) Find the value of R1and X1 when a lagging current in the circuit the followingfigure3b. Gives power of 2 K.W. [6+10]

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Figure 3b

4. (a) The circuit shown in figure4a is resonant for two values of C when the fre-quency of the supply is 5000 rad/sec. Find the values of C and draw theadmittance locus.

Figure 4a

(b) Find the y-parameter of the two port network shown in figure4b.

Figure 4b[8+8]

5. (a) Derive an expression for total active and reactive Power of a 3 phase deltaconnected balanced load.

(b) A balanced star connected load has an impedance of (8+j6) ohms/ph andsupply voltage is 230ν, 3phase supply. Find

i. line current.

ii. power factor.

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iii. total active power and

iv. total reactive power

If the same impedances are connected in delta across the same supply insteadof star, determine the above quantities. [6+10]

6. (a) For the coupled network (shown in figure6a) write down the loop equations inmatrix form.

Figure 6a

(b) Using nodal Analysis, find the power supplied by 8V source the followingfigure6b.

Figure 6b

(c) Derive the expressions for the elements of m-derived∏

filter in terms of pro-totype Π filter. [4+8+4]

7. (a) State and explain the compensation theorem.

(b) Determine the value of R for Max power transfer. Hence find the max powerreceived by R for the figure shown in figure7b.

Figure 7b

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(c) Find the current through 4 ohms resistor for the figure shown in figure7c. UseMillman’s theorem. [6+6+4]

Figure 7c

8. (a) Using Laplace method find i (t). (figure8a).

Figure 8a

(b) The switch is moved from a to b at t = 0 find the current i (t). Use laplacetransform method in the following network shown in figure8b. [8+8]

Figure 8b

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1. (a) Distinguish between dependent sources and independent sources. Give someexamples.

(b) Find V1 in figure1b

Figure 1b

(c) Find Vx , r2 , and r3 in the figure1c. [4+6+6]

Figure 1c

2. (a) What is ‘Coefficient of coupling’? What is its maximum value? Why?

(b) An iron ring has a cross section of 80 milli square meters and a mean lengthof 38.2 cms. It is uniformly wound with a coil of 480 turns. For a current of2 amps the flux set up is 1.2 milli webers. Find the relative permeability ofiron at the flux density. [6+10]

3. (a) Explain how a sinusoidal quantity can be represented by a phasor.

(b) Find the form factor of the following (figure3b). [4+12]

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Figure 3b

4. (a) A three branch parallel circuit has fixed elements in 2 branches. One of theelements to the third branch is variable. The locus diagram of current is shownin figure4a. Identify all the elements if ω=5000 rad/sec.

Figure 4a

(b) Find the ABCD parameters of the network given. Also obtain h-parameter

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from this result. (figure4b).

Figure 4b[8+8]

5. (a) A 3 phase 3 wire balanced supply is connected to an unbalanced 3 wire starconnected load. Derive an expression for the neutral displacement voltagebetween supply and load neutral points.

(b) A 3phase, 3 wire 208 volts BYR system has a star connected load withZR = 66 00Ω ZY = 66 300 and ZB = 56 450. Obtain the line currents andload voltages of the circuit using the neutral displacement method. Draw thephasor diagram. [6+10]

6. (a) For the given network graph shown in figure6a, write down the basic Tiesetmatrix, taking the tree consisting of edges 2,4 and 5. Write down the KVLnetwork equations from the matrix.

Figure 6a

(b) Find the voltage across the 5Ω resistance for the coupled network shown infigure6b. [6+10]

Figure 6b

7. (a) State and explain the superposition theorem.

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(b) Using super position theorem, find the current I through ( 4 + j3)Ω impedancethe figure7b. [6+10]

Figure 7b

8. (a) Derive the expression for i(t) of a R-L series circuit when D.C voltage is appliedto it at t = 0 by closing the switch. Define the time constant of R - L circuit.

(b)

Figure 8bUsing classical method find i(t) for t ≥ 0., for the network shown in figure8b.

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1. (a) Explain the properties of R,L,C parameters

(b) A Current wave i(t) is applied to an inductance of 10H. Find v(t) (as show infigure1b)

Figure 1b[6+10]

2. (a) Explain Dot convention for magnetically coupled coils. Determine the dottedends for the magnetically coupled coils.As shown in the Figure2a

Figure 2a

(b) The magnetic circuit shown in Figure2b is designed to carry a flux of 1 mil-liweber in the air gap. Find the current in the coil of 600 turns wound onthe central limb. Assume no leakage. Dimensions are given in cms. Describepermealibity of the material is 350.

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Figure 2b[8+8]

3. (a) Distinguish between reactance, impedance, admittance and suceptance.

(b) Find RMS and average values of the following figure3b wave form.

Figure 3b

(c) Given ν1 = 100 sin (wt-300) and ν2 = 50 cos wt. Determine the resultantvoltage

i. ν3 = ν1 + ν2and. [6+6+4]

4. (a) A three branch parallel circuit has fixed elements in 2 branches. One of theelements to the third branch is variable. The locus diagram of current is shownin figure4a. Identify all the elements if ω=5000 rad/sec.

Figure 4a

(b) Find the ABCD parameters of the network given. Also obtain h-parameterfrom this result. (figure4b).

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Figure 4b[8+8]

5. (a) A 3 phase, 3-wire 400V ,ABC system supplies power to a star connected loadof Za=106 900 Zb=206 600 Zc=406 -300. Find the voltage between load andsupply,neutral point.

(b) Three impedances Za=4+j3, Zb=3-j4 and Zc=5+j0 are connected in the formof a delta. across 440v, 50HZ supply as shown in figure5b. Determine phasecurrents and line currents. Draw phasor diagram indicating voltages and cur-rents. [6+10]

Figure 5b

6. (a) What is duality? Explain the procedure for obtaining the dual of the givenplanar network shown in the Figure 6a.

Figure 6a

(b) Construct the incidence matrix for the graph shown in Figure 6b.

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Figure 6b

(c) Use nodal analysis, to determine the voltages V1 and V2 in the circuit shownthe Figure 6c. [4+4+8]

Figure 6c

7. (a) State and explain Tellegen’s theorem.

(b) Find the current in 5 Ω resistor using superposition theorem for the followingnetwork shown in figure7b. [4+12]

Figure 7b

8. (a) Derive the expression for i(t) and voltage across capacitance Vc(t) for series R– C circuit with D.C. voltage applied to it at t = 0. Explain about the timeconstant of RC circuit.

(b) Switch S is moved from position 1 to 2 at t = 0 find the voltages VR(t) andVc(t) for t≥0 the following figure8b. [8+8]

Figure 8b

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1. (a) Write a note on independent and dependent sources

(b) What is the value of R such that the powers supplied by both the sources areequal as shown in figure1b [4+12]

Figure 1b

2. (a) Explain the terms ‘leakage flux’, ‘mutual flux’, ‘coefficient of coupling’.

(b) Find the input impedance Z of the network of Figure2b. [6+10]

Figure 2b

3. (a) Explain how a sinusoidal quantity can be represented by a phasor.

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(b) Find the form factor of the following (figure3b). [4+12]

Figure 3b

4. (a) Obtain the y-parameters of the following figure4a bridged T- network.

Figure 4a

(b) Obtain the expression for Y-parameter in terms of transmission parameters.

(c) For a series resonance circuit obtain the expression for band width in terms

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of resonance frequency and Q-factor. [6+6+4]

5. (a) A 3 phase 3 wire balanced supply is connected to an unbalanced 3 wire starconnected load. Derive an expression for the neutral displacement voltagebetween supply and load neutral points.

(b) A 3phase, 3 wire 208 volts BYR system has a star connected load withZR = 66 00Ω ZY = 66 300 and ZB = 56 450. Obtain the line currents andload voltages of the circuit using the neutral displacement method. Draw thephasor diagram. [6+10]

6. (a) What is duality? Explain the procedure for obtaining the dual of the givenplanar network shown in the Figure 6a.

Figure 6a

(b) Construct the incidence matrix for the graph shown in Figure 6b.

Figure 6b

(c) Use nodal analysis, to determine the voltages V1 and V2 in the circuit shownthe Figure 6c. [4+4+8]

Figure 6c

7. (a) State and explain the superposition theorem.

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(b) Using super position theorem find the current in 2 ohms resistor from thefollowing network shown in figure7b. [6+10]

Figure 7b

8. (a) Compare the classical and laplace transform method of solution of the network.

(b) Draw the network in laplace domain and find i1(t) and i2(t)in the followingnetwork shown in figure8b [4+12]

Figure 8b

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