Network Theory

Code No: RR10204 Set No.1

I B.Tech. Regular Examinations, June -2005NETWORK 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) Write a note on source transformation.

(b) Using KCL and KVL, find the currents in all the sources of the circuit of thefollowing figure1

Figure 1:

2. (a) Calculate the current to be passed through the coil so that a flux of 1 mwb isproduced in the air gap.As shown in the Figure2The core is of square cross section over its entire length and has a permeabilityof 800.

(b) Define the following terms.

i. Coefficient of coupling in coupled coils

ii. Magnetic flux density.

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Figure 2:

iii. Reluctance of magnetic path

iv. Permeability.

3. (a) A series R – C circuit is excited by sinusoidal voltage I=Im sin wt. Find theexpression for impedance using phasor diagram.

(b) Determine the supply voltage and the power factor in the following figure3network if the total power delivered is 200 w.

Figure 3:

4. (a) For a series RL circuit obtain the locus of current as inductance is changedform 0 to ∞ when the applied voltage is constant

(b) Show that for a series resonant circuit f1 f2 = f2r where f1 and f2 are half powerfrequencies and fr is the resonance frequency.

(c) Obtain the z-parameters of the following figure4 Two port network.

5. (a) Determine the line currents and total power supplied to a delta connected loadof Zab = 10 6 600 Zbc = 20 6 900 Zca = 25 6 300. Assume a 3phase, 400v, ABCsystem.

(b) Explain two wattmeter method of measurement of power in a 3 phase system.Derive the readings of the wattmeter for a balanced 3 phase load.What is thepower factor of the balanced load when

i. both the meters read zero.

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Figure 4:

ii. both meters read equal but one is negative.

iii. one reads twice the other.

6. (a) Explain clearly what you understand by a cutest, and a Tieset. Write down thebasicTieset schedule for the network shown in figure5 by taking 10Ω resistorbranches as Tree branches.

Figure 5:

(b) For the network shown the figure6, determine the ratio of I2 / I1.

Figure 6:

(c) Draw the frequency response characteristics of Low pass, High pass and Bandpass filters.

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

(b) Using super position theorem find the current in 2 ohms resistor. Verify yourresult by any other method the following f i gure 7.

8. (a) Derive the expression for i(t) for R – L series circuit when excited by a sinu-soidal source.

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Figure 7:

(b) For R – L – C series circuit with R = 10Ω, L = 0.2 H, C = 50 micro farads,determine the current i(t) when the switch is closed at t = 0. Applied voltageis V(t) = 100 Cos (1000 t + 60)0

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1. (a) What are passive and active circuit elements? Explain the voltage-currentrelationships of passive elements with examples.

(b) Reduce the network of Figure8. into an equivalent network across terminalsA and B with

i. one equivalent voltage source

ii. one equivalent current source.

Figure 8:

2. (a) A cast steal iron core has a square cross section of side 3cm. Assuming thepermeability of steel to be 800, find the m.m.f required to produce a fluxφ = 0.2 mwb in the right limb as shown in the figure9.

(b) Define self and mutual inductances. Establish the polarity of two mutuallycoupled coils on a single magnetic core.

(c) Find the equivalent inductance of the following circuit Figure10.

3. (a) Explain about active, Reactive and apparent powers.Give expression for theabove. Draw the power triangle.

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Figure 9:

Figure 10:

(b) Given i = 50 sin (wt + 60)ν = 200 sin (wt + 30) Find the elements of the network with their valuesactive, reactive and apparent power.

4. (a) Obtain the expression for frequency at which the voltage across the inductancebecomes a maximum in a series RLC circuit. Explain what is meant by voltagemagnification factor.

(b) Obtain the transmission parameters for the following figure11 circuit. Verifyyour result for reciprocity condition.

Figure 11:

5. (a) Show that two watt meters are sufficient to measure power in a 3 phase circuit.Derive the expressions for wattmeter readings for a balanced 3phase load.

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(b) A 3 phase, 400v, 4wire system has a star connected load with ZA=(10+j0)ohms,ZB =(15+j10) ohms, ZC=(0+j5) ohms. Find the line currents and currentthrough neutral conductor. Draw the phasor diagram.

6. (a) What is duality? Explain the procedure for obtaining the dual of the givenplanar network shown below the f i gure 12 .

Figure 12:

(b) Construct the incidence matrix for the graph shown in f i gure 13.

Figure 13:

(c) Use nodal analysis, to determine the voltages V1 and V2 in the circuit shownthe f i gure 14 .

Figure 14:

7. (a) State and explain the Reciprocity theorem. Is this theorem valid for networkwith two sources? Subtantiate your answer.

(b) Verify the reciprocity theorem using the network given below the figure15.

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Figure 15:

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) the followingfigure16

Figure 16:

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1. (a) Find the equivalent resistance between the terminals Y and Z in the f i gure 17below

Figure 17:

(b) In the network shown in f i gure 18 , determine ix

Figure 18:

2. (a) Define MMF, flux and reluctance of a magnetic circuit.

(b) An iron ring has a mean diameter of 25 cms, and a cross sectional area of 4cm2. It is wound with a coil of 1200 turns. An air gap of 1.5 mm width is cutin the ring. Determine the current required in the coil to produce a flux of 0.48mwb in the air gap. The relative permeability of iron under this condition is800. Neglect leakage.

3. (a) Get the expression for complex power and the sign of the active power.

(b) Find I1, I2, I3 and I Find also the power consumed .Draw the phasor diagram(figure 19).

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Figure 19:

Figure 20:

4. (a) Obtain the Y-parameters for the following figure20 network in Laplace trans-form variables.

(b) A tuned circuit consists of a coil having an inductance of 200 micro henriesand a resistance of 15Ω the parallel with a series combination of a variablecapacitance and resistor of 80Ω. It is supplied by a 60v source. If the supplyfrequency is 1MHZ, what is the value of C to give resonance?

5. (a) Draw a schematic diagram for measuring the power in 3 phase circuit con-nected in star using Two wattmeters. Assuming a phase sequence ABC obtainthe expressions for the wattmeter readings. How do you determine the powerfactor using the wattmeter readings.

(b) A 3 phase, 3 wire, 208V CBA system has a star connected load with ZA =56 00Ω ZB = 5 6 300Ω and ZC = 10 6 − 600Ω. Obtain the line currents and thevoltages across each load impedance. Draw the phasor diagram.

6. (a) What is duality? Explain the procedure for obtaining the dual of the givenplanar network shown below the figure21.

(b) Construct the incidence matrix for the graph shown in figure22.

(c) Use nodal analysis, to determine the voltages V1 and V2 in the circuit shownthe figure23.

7. (a) State and explain the super position theorem.

(b) Is super position valid for power? Substantiate your answer.

(c) Using super position theorem find vab the figure24.

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Figure 21:

Figure 22:

Figure 23:

Figure 24:

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8. (a) For the circuit shown below find the initial conditions of i1, i2,di1dt

,di2dt

andvoltage across capacitor. The circuit was in steady state before t = 0 thefollowing figure25

Figure 25:

(b) Switch is opened at t = 0 find the current i (t) for t ≥ 0 the following figure26

Figure 26:

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1. (a) Find the equivalent resistance between the terminals Y and Z in the figure27below

Figure 27:

(b) In the network shown in figure28, determine ix

Figure 28:

2. (a) State and explain Faraday’s Law of electro magnetic induction. What arestatically and dynamically induced EMFS.

(b) An iron ring 15 cms in diameter and 10 cm2 in area of cross section is woundwith a coil of 200 turns. Determine the current in the coil to establish a fluxdensity of 1 wb/m2 if the relative permeability of Iron is 500. In case if an airgap of 2mm is cut in the ring, what is the current in the coil to establish thesame feat density.

3. (a) Explain the significance of J – operator ? What are the different forms ofexpressing the sinusoidal quarter in complex form?

(b) Find the components of Z such that the current drawn quantity by the circuitsame at all frequencies the following figure29.

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Figure 29:

4. (a) Define the following terms

i. Band width

ii. Q-factor

iii. half power frequencies(b) Obtain a Π-equivalent circuit for the following figure30 of 2 port network.

Figure 30:

5. (a) Derive the relationship between line and phase quantities in a balanced starconnected system.

(b) A 3phase 4-wire CBA system of phase sequence, with effective line voltage of100v has a star-connected impedances given byZA=3.0 6 00Ω ZB = 4.56 56.310Ω ZC = 2.246 − 26.570ΩObtain the line currents and current in neutral wire. Draw the phasor diagram.

6. (a) For the circuit shown below the figure31, find the currents & voltages in allthe branches of the circuit. Use Node Voltage method.

Figure 31:

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(b) Draw the dual of the network shown below the figure32. Explain the procedureemployed.

Figure 32:

(c) Obtain the expression for characteristic impedance of a symmetrical T net-work.

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

(b) Using super position theorem find the current in 2 ohms resistor. Verify yourresult by any other method the following figure33.

Figure 33:

8. (a) What are the initial conditions? Why do you need them?

(b) Explain why the current in a pure inductance cannot change in zero time.

(c) Switch is closed at t = 0. Find the initial conditions at t(o+) for i1, i2, vc,

,di1dt

, di2dt

,d2i2dt

and d2i1dt

(as show in the figure34)

Figure 34:

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