Electrical Circuits Analysis 6

8/4/2019 Electrical Circuits Analysis 6

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Code No: Z0222/R07 Set No. 1

I B.Tech Supplementary Examinations, November 2009ELECTRICAL CIRCUITS ANALYSIS

( Common to Electrical & Electronic Engineering and Instrumentation &Control Engineering)

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

All Questions carry equal marks

1. (a) Four resistances of equal value are available. Find

i. The total equivalent conductance and total equivalent resistance ratio

ii. The ratios of current drawn in each configuration

iii. The ratios of power drawn by each configuration in each element.Considering that the supply voltage is same when the configuration arein series and parallel.

(b) Find RAB in the network as shown in figure 1b. [10+6]

Figure 1b

2. (a) Derive an expression for the energy stored in an inductor and a capacitor.

(b) Obtain an expression for Co-efficient of coupling. [10+6]

3. Define RMS and Average values of an alternating quantity. Find the rms value,

average value, form factor and peak factor of a full wave rectified wave form. [16]4. (a) Three identical impedances of (3+j4) are connected in delta. Find an equiv-

alent star network such that the line current is the same when connected tothe same supply.

(b) Three impedances of (7+j4), (3+j2) and (9+j2) are connected betweenneutral and the R, Y and B phases. The line voltage is 440V, Calculate.

i. The line currents and

ii. The current in the neutral wire.

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iii. Find the power consumed in each phase and the total power drawn bythe circuit. [4+12]

5. In the network shown in the figure 5, find V2 such that the current in (1+j1) ohkmsbranch is zero. [16]

Figure 5

6. (a) Using Nortons theorem, find the current through the load impedance ZL asshown in figure 6a.

Figure 6a

(b) State and explain reciprocity theorem. [10+6]

7. In the circuit shown in the figure 7, the switch is put in position - 1 for 1 m secand then thrown to position - 2. Find the transient current in both intervals. [16]

Figure 7

8. Find the transformed Z - parameters of the n/w shown in figure 8: [16]



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Figure 8



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1. (a) Calculate the equivalent resistance of the combination of resistors as shown infigure 1a and also calculate the source current.

Figure 1a

(b) A battery of unknown emf is connected across the resistances as shown infigure 1b. The voltage across 8 resistor is 20V. What will be the currentthrough 13 resistor? What is the emf of the battery? [16]

Figure 1b

2. (a) An iron ring 10cm diameter and 15cm2 cross section is wound with 250 turnsof wire for a flux density of 1.5wb/m2 and permeability 500. Find the exciting

current, the inductance and the stored energy. Find corresponding quantitieswhen there is a 2mm air gap.

(b) Explain the terms reluctance, mmf, flux and flux density. [10+6]

3. Two impedances Z1=10+j31.4 and Z2=(10+R)+j(31.4-Xc) are connected in par-allel across a single phase ac supply. The current taken by the two impedancebranches are equal in magnitude and the phase angle between them is 90 0. Calcu-late the values of R and Xc and the phase difference of the branch currents withrespect to the applied voltage. [16]



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4. A symmetrical 3-phase, 3-wire, 440V supply is connected to a star connected load.The impedances in each branch are : Z1=(2+j3), Z2=(1-j2), Z3=(3+j4). Findits equivalent delta connected load. Hence find the phase and line currents and thetotal power consumed in the circuits. [16]

5. In the network shown in the figure 5, find V2 such that the current in (1+j1) ohkmsbranch is zero. [16]

Figure 5

6. (a) State Thevenins Theorem.

(b) Compare Thevenins Theorem with Nortons theorem.

(c) Explain the steps to apply Thevenins Theorem and draw the Theveninsequivalent circuit. [4+6+6]

7. In the circuit shown in the figure 7, the switch is put in position - 1 for 1 m secand then thrown to position - 2. Find the transient current in both intervals. [16]

Figure 7

8. For the two port n/w shown in the figure 8, the currents I1 and I2 entering at port1 and 2 respectively are given by the equations.I1 = 0.5 V1 - 0.2 V2I2 = - 0.2V1 + V2



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Figure 8

Where V1 and V2 are the port voltages at port 1 and 2 respectively. Find the Y, Z,ABCD parameters for the n/w. Also find its equivalent network. [16]



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1. (a) Four resistors are in parallel. The current in the first three resistors are 4A,5A and 6A respectively. The voltage drop across the fourth resistor is 200V.The total power dissipated is 5KW. Determine the values of resistances of thebranches and the total resistance.

(b) A coil of 5 resistance is connected in parallel with a coil of R1 resistance.This combination is then connected in series with an unknown resistor R2and the complete circuit is then connected to a 50 V d.c supply. Calculate thevalue ofR1 and R2 if the power dissipated by the resistor R2 is 150W with 5Apassing through it. [6+10]



3. (a) Derive an expression for the current, impedance, average power for a seriesRLC circuit excited by a sinusoidally alternating voltage and also find the

power factor of the circuit. Draw the phasor diagram.(b) In an ac circuit, the applied voltage is given by v=200sin314t and the current

is i=20cos314t. Find the circuit constants and also the power factor of thecircuit. Draw the phasor diagram. [10+6]

4. A symmetrical 3-phase, 3-wire, 440V supply is connected to a star connected load.The impedances in each branch are : Z1=(2+j3), Z2=(1-j2), Z3=(3+j4). Findits equivalent delta connected load. Hence find the phase and line currents and thetotal power consumed in the circuits. [16]

5. (a) Find the power delivered by the batteries shown in the figure 5a using meshanalysis.



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Figure 5a

(b) Set up the nodal equations for the n/w of the figure 5b. Hence find thepotential difference b/w nodes 2 & 4. [8+8]

Figure 5b

6. (a) Using Nortons theorem, find the current through the load impedance ZL asshown in figure 6a.

Figure 6a

(b) State and explain reciprocity theorem. [10+6]

7. In the circuit shown in the figure 7, the switch is put in position - 1 for 1 m sec



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and then thrown to position - 2. Find the transient current in both intervals. [16]

Figure 7

8. Find the transformed Z - parameters of the n/w shown in figure 8: [16]

Figure 8



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1. (a) A bridge network ABCD is arranged as follows:Resistance between terminals AB, BC, CD, DA and BD are 10 ohms, 30 ohms,15 ohms, 20 ohms and 40 ohms respectively. A 4V battery is connected withnegligible internal resistance between terminals A and C. Determine the cur-rent through each element in the network using network reduction techniques.

(b) Three equal resistances are available. Find

i. Two ratios of the equivalent resistances when they are connected in par-allel.

ii. The ratio of the current through each elements when they are connectedin parallel. [10+6]



3. A sinusoidal current wave is given by i=50 sin100t. Determine

(a) The greatest rate of change of current.(b) Derive average and rms values.

(c) The time interval between a maximum value and the next zero value. [16]

4. (a) Three identical impedances of (3+j4) are connected in delta. Find an equiv-alent star network such that the line current is the same when connected tothe same supply.

(b) Three impedances of (7+j4), (3+j2) and (9+j2) are connected betweenneutral and the R, Y and B phases. The line voltage is 440V, Calculate.

i. The line currents and

ii. The current in the neutral wire.

iii. Find the power consumed in each phase and the total power drawn bythe circuit. [4+12]

5. (a) Draw the oriented network graph from the incidence matrix given below.

BranchesNodes 1 2 3 4 5 6

A -1 0 0 +1 -1 0B +1 -1 0 0 0 -1C 0 +1 -1 0 +1 0D 0 0 +1 -1 0 +1



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(b) Draw the graph of the network shown in figure 5b. Obtain a tree thereof.What is the number of mesh currents required for the network. [8+8]

Figure 5b

6. (a) Use Thevenins Theorem and find the current through (5+j4) ohms impedanceshown in figure 6a.

Figure 6a

(b) State and explain reciprocity throrem. [10+6]

7. In the circuit shown in the figure 7, the switch is put in position - 1 for 1 m sec

and then thrown to position - 2. Find the transient current in both intervals. [16]

Figure 7

8. (a) Discuss about the relationship b/w Y parameters and Z - parameters.(b) How will you obtain h parameters from Z parameters. [8+8]

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Electrical Circuits Analysis 6