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Code No: R21023

II B. Tech I Semester, Regular Examinations, Nov – 2012

ELECTRICAL CIRCUIT ANALYSIS - I (Electrical and Electronics Engineering)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Explain the difference between independent and dependent source with suitable examples.

b) The voltage waveform shown in figure 1 is applied to a pure capacitor of 60 µF. Sketch i(t)

and p(t) and determine Imax and Pmax .

2. a) For the circuit shown in figure 2, use nodal analysis to determine voltage across 3 Ω and 12 Ω

resistance. Compute power absorbed by 6 Ω resistor.

b) Calculate the mesh currents in the network shown in Figure 3.

3. a) Construct the phasor and impedance diagram and determine the circuit constants for the

following voltage and current.

) sin(5000ttV050150)( += V, )- sin(5000tti

0255)( =

b) A current of 4 A flows through a non-inductive resistance in series, with a choking coil when

supplied at 230 V, 50 Hz. If the voltage across the resistance is 100 V and across the coil is 180

V, draw the phasor diagram and calculate i) impedance, reactance and resistance of the coil

ii) the power absorbed by the coil iii) the total power.

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Code No: R21023

4. a) A series RLC circuit with R = 100 Ω, L = 0.5 H and C =40 µF has applied voltage of 100V

with variable frequency. Calculate the resonant frequency, current at resonance, voltage across

R, L and C. Also calculate the Q-factor, upper and lower half power frequencies and

bandwidth.

b) Construct an admittance locus and determine the variable inductance values, so that the phase

angle between the supply voltage and supply current is zero for the circuit shown in Fig. 5.

Assume ω = 5000 rad/sec.

5. a) Two coils with inductances in the ratio of 5:1 have a coupling coefficient k = 0.5. When these

coils are connected in series aiding, the equivalent inductance is 44.4 mH. Find L1, L2 and M.

b) In the network shown in figure 6, determine the value of the load impedance (ZL) for

maximum power transfer.

6. a) Draw the graph of the network given in figure 7, find tie test schedule and determine loop

currents.

b) Draw a graph of the network shown in figure 8. Select a tree with branches R1, R2, R5, R3 and

R4.Write fundamental loop matrix and cut set matrix.

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2Ω

2Ω

2Ω

2Ω 4 A 10 V

+

-

2Ω

Figure 7

R1

R3

R5

R2 R4 R6

R7

R8

R9

Figure 8

5 Ω

20 µF

7 Ω ~ 100 V

Fig. 5

XL

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Code No: R21023

7. a) Find the current in 10 Ω resistance of the circuit shown in figure 9 using Millman’s theorem.

b) In the network given in figure 10, impedance Ω∠=0

1 020Z be connected between the

terminals A and B. Find the power dissipated in the above impedance.

8. a) Find VL in the circuit shown in figure 11, using superposition theorem.

b) Verify the Tellegen’s theorem for the circuit shown in Figure 12.

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5Ω

10 Ω

j10 Ω

j5 Ω

5 Ω

A

B

50 00

V

Figure 10

5 A 2V

+

-

RL VL

1Ω

1Ω +

-

2Ω

5 A

Figure 11

50 V

+

-

2Ω 3Ω

5Ω

5Ω 2Ω

Figure 12

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Code No: R21023

II B. Tech I Semester, Regular Examinations, Nov – 2012

ELECTRICAL CIRCUIT ANALYSIS - I

(Electrical and Electronics Engineering)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Explain the principle of source transformation using suitable examples.

b) A pure inductance of 3 mH carries a current of the waveform shown in figure 1. Sketch the

waveform of v(t) and p(t). Determine the average value of power.

2. a) Using nodal analysis, find current i in the circuit shown in figure 2.

b) Find the source currents in the resistance network shown in figure 3 by using Y- ∆ transformation.

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1 3 5 7 8 4

t (milli-sec)

10A

-10 A

i(t)

Figure 1

1 KΩ 2 mA

12 mA

3 KΩ 6 mA

2 KΩi

Figure 2

d

2 Ω

5 Ω

3 Ω

a

b

c

5 V

8 Ω

5 Ω

Figure 3

+

-

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Code No: R21023

3. a) In an electrical circuit R, L and C are connected in parallel. R = 10 Ω, L= 0.1 H and C = 100

µF. The circuit is energized with supply at 230 V, 50 Hz. Calculate (i) the impedance ii)

current taken from the supply (iii) power factor of the circuit and power consumed by the

circuit.

b) Find the currents flowing through different elements in the circuit shown in figure 4.

4. a) In a series resonance circuit, the resistance is 5 Ω, the resonant frequency is 4×105 rad/sec and

the bandwidth is 104 rad/sec. Compute L and C of the network, half-power frequencies and Q

of the circuit.

b) Draw the admittance locus for the circuit shown in figure 5 and calculate C which results in

resonance when ω= 5000 rad/sec.

5. a) Discuss about the analogy between magnetic and electric circuits.

b) For the circuit shown in figure 6, find the voltage across j5 Ω reactance.

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Code No: R21023

6. a) Define the following.

i) Tree ii) co-tree iii) cut-set iv) Loop

b) Draw the graph of the network shown in figure 7. Find the tie set schedule, obtain

equilibrium equation on loop current basis and find the branch currents.

7. a) Find Norton’s equivalent circuit for the circuit shown in Figure 8.

b) Find the current through 15 Ω resistance using Millman’s theorem for the circuit shown in

Figure 9.

8. a) Find ‘i' using super position theorem for the circuit given in figure 10.

b) Verify the reciprocity theorem for the circuits given in figure 11.

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+

5Ω

10 V -

5Ω

5Ω

5Ω

5Ω

5Ω

1

2 3 Figure 7

2 A 6 V

+

-

1Ω Vx

5Ω +

-

+ -

5Vx

i

Figure 10

5 Ω

~

1 Ω 4 Ω

j2 Ω -j4 Ω

V 0

9010∠5 Ω

~

1 Ω 4 Ω

j2 Ω -j4 Ω

V 09010∠

Figure 11

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Code No: R21023

II B. Tech I Semester, Regular Examinations, Nov – 2012

ELECTRICAL CIRCUIT ANALYSIS - I (Electrical and Electronics Engineering)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Define Ohm’s law. Explain about ideal and non-ideal voltage and current sources.

b) The waveform given in figure 1 is the voltage across a linear time invariant inductor of 2H.

If iL(0) = 0, sketch the waveform of current i(t) up to 3 sec.

2. a) Write a set of node-voltage equations for the network shown in Figure 2 and solve all node

voltages.

b) Find the current in 3 Ω resistor and voltage across the current source in the network shown in

Figure 3 using mesh analysis.

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Code No: R21023

3. a) When a resistor and choke coil in series are connected to a supply of 240 V, a current of 3 A

flows lagging the supply voltage by 400. The voltage across the inductor is 180 V. Find the

resistance of the resistor and the parameters of the coil.

b) Determine the branch currents and the current supplied by the mains in the circuit shown in

Figure 4.

4. a) Show that in a series RLC circuit, 21 fff0 = , where fo is the resonant frequency and f1, f2

are half power frequencies.

b) For the circuit shown in figure 5, draw the admittance locus and sate whether resonance is

possible.

5. a) Explain the concept of mutual inductance and derive the expression for coefficient of

coupling.

b) Determine the voltage V across the 10 Ω resistor in the magnetically coupled circuit shown

in Figure 6.

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Code No: R21023

6. a) Calculate the source current for the circuit shown in figure 7 using network topology.

b) Draw the dual of the network shown figure 8.

7. a) Find the value of ZL to be connected between the terminals AB of the circuit shown in figure

9, for maximum power transfer. Find maximum power.

b) Find the voltage V using Norton’s theorem for the circuit shown in Figure 10.

8. a) Show the validity of reciprocity theorem for the circuits shown in figure 11.

b) Find V0 in the network shown in figure 12 using superposition theorem.

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10 Ω

5Ω

50 V

10Ω

+

-

10Ω 20Ω

10 Ω

5Ω

50 V

10Ω

+ 10Ω

20Ω

-

2Ω

1Ω

4 V 2Ω

+

- 1Ω

1Ω

Figure 7

Figure 8

S1

4 A

C2=4 F

L1=3H

R1=1 Ω

2V

+

-

R2=2 Ω

L2=2H

R3=3 Ω

S2

Figure 11

1 A 10V

+

- 2Ω

0.5V0 V0

5Ω

+

-

+ - 1Ω 4V

+

-

Figure 12

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Code No: R21023

II B. Tech I Semester, Regular Examinations, Nov – 2012

ELECTRICAL CIRCUIT ANALYSIS - I (Electrical and Electronics Engineering)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) The waveform shown in the below Figure 1 has a period of 10secs

i) What is the average value of the current over one period?

ii) How much charge is transferred in the interval 1 < t < 14 secs?

iii) If q(0)=0, sketch q(t), 0 < t < 16secs.

b) A current of the waveform shown in figure 2, flows through a capacitor C = 25 µF. Sketch

the voltage waveform and determine Vmax and qmax.

2. a) Use nodal analysis to find currents in different resistances of the circuit given in Figure 3.

b) Find the currents I1, I2, and I3 in the circuit given in Figure 4, using node voltage analysis

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-4

Time in sec

i(A)

2 4 6 8

10

12 14 16 18 -2

4

2

8

6

Figure 1

5A

-5A

i(t)

Time in macro secs

Figure 2

2

3

4 5 0

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Code No: R21023

3. a) A series combination of R and C is in parallel with a 25 Ω resistor. A 50 Hz source results in

a total current of 6.5 A, a current of 5 A through 25 Ω resistance and a current of 2.3 A in the

RC branch. (i) Draw the phasor diagram of the circuit and find values of R and C (ii) Find

apparent, active, reactive power and power factor of the circuit.

b) A resistance and inductance are connected in series across a voltage given by

t tv ω= sin283)( . The power drawn by the series combination is 400 W and the current has a

maximum value of 4 A. Determine the circuit parameters and the power factor of the circuit.

4. a) In a series RLC network, R = 50 Ω and C = 20 µF, and L = 50 mH. Find the voltage across

each element, when the voltage across the resistor is a maximum, given that the applied voltage

is 100 V with a variable frequency.

b) Using the locus diagrams, determine the value of RL for which the circuit shown in figure 5

will be under resonance.

5. a) Two coupled coils with L1 = 0.01 H and L2 = 0.04 H and k = 0.6 can be connected in four

different ways such as series aiding, series opposing, parallel aiding and parallel opposing. Find

equivalent inductance in each case.

b) For the circuit shown in figure 6, determine the currents i1 & i2 using loop method of analysis.

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10 Ω

-j 5Ω

j 10 Ω

~ RL

100 V

Fig. 5

j 2Ω

V2=10 00 V i2

i1

j4 j3 V1=10 0

0V

-j8Ω 2Ω

Figure 6

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Code No: R21023

6. a) For the network given in figure 6A, draw its dual and write KCL in matrix form of the dual

network.

b) For the network given in figure 6B, calculate the branch voltages and branch currents using

node- basis method.

7. a) Use the Thevinin’s theorem to find the deflection of galvanometer having a resistance of

100 ohm and a sensitivity of 0.5x10-5

A per mm connected to terminals AB of the bridge shown

in Figure 7.

b) Find the voltage across 10 Ω resistance in the network shown in Figure 8 using Norton’s

theorem.

8. a) Use superposition to determine voltage Vx in the network given in Figure 9.

b) Verify Tellegen’s theorem for the below circuit shown in Figure 10.

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40

10Ω

50Ω

20Ω

88V

+

-

10

Figure 10

L

R1 S

V

+

-

R2

C

Figure 6A

1Ω

1 V +

-

1Ω

2Ω

1Ω 1Ω 2Ω

Figure 6B