1411578278ECA-II-R10-AUGUST2014 (1)

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Code No: R22025

II B. Tech II Semester Supplementary Examinations, August - 2014

ELECTRICAL CIRCUIT ANALYSIS - II (Electrical and Electronics Engineering)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~

1. a) For a star connected three phase system, derive the relationship between the i) phase

voltages and line voltages ii) phase currents and line currents

b) A balanced delta connected load takes a line current of 15 A when connected to a

balanced three phase 400 V system. A wattmeter with its current coil in one line and its

potential coil between the two remaining lines read 2000 W. Determine the load impedance.

2. The following impedances are connected in the form of a star connected unbalanced system

and it is connected to a 400 V, 3-Ø supply: , 304 0 Ω∠=RZ , 205 0 Ω∠=YZ

. 010 0 Ω∠=BZ Calculate the line currents by using i) loop method ii) Star-delta

transformation technique.

3. For the circuit shown in Figure 3. Find i1(t) and i2(t) for t > 0. Assume zero initial conditions.

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

)sin(500t 20 φ+ applied at time when 0=φ . i) Find the expression for current ii) At what

value of φ must the switch be closed so that the current directly enter steady state.

5. a) Express y-parameters in terms of h-parameters and ABCD-parameters.

b) Find the y-parameters for the network shown in Figure 5.

1 of 2

V2

Figure 5

2Ω

1Ω 3V1

2Ω

+ -

V1

I1 I2

SET - 1 R10

+

-

t=0 0.6 H

0.4 H

0.6 H 8Ω

12 Ω

10 V

Figure 3

+

-

t=0 8Ω

8Ω 10 V

Figure

i1(t) i2(t)

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Code No: R22025

6. a) Two 2-port networks N1 and N2 are connected in parallel. The z-parameters of N1 and N2 are

=

43

311NZ and

=

87

752NZ . Determine z-parameters of combined parallel 2-port

network.

b) Derive the ABCD parameters for the network shown in Figure 6 as a connection of two

identical networks.

7. a) Explain about the exponential Fourier series.

b) Obtain the trigonometric Fourier series for the waveform shown in Figure 7. Write down the

amplitude and phase spectrum.

8. a) Explain the properties and applications of Fourier transform.

b) Determine the Fourier transform of the signum function.

2 of 2

Vm

Figure 7

t T T/2 0 T/4

T/2

T

Vm

SET - 1 R10

V2

Figure 6

2Ω 2Ω 4Ω

V1

I1 I2

1 F 1 F

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Code No: R22025





1. a) Explain how the reactive power is measured in a 3-phase balanced system.

b) In a three phase balanced load, each arm consists of a resistor of 20 ohms, an inductance of

0.5 H and a capacitor of 120 µF connected in series. The supply is a balanced 3-phase 415

V, 50 Hz. Calculate the line current, total power consumed in the load when the three arms

are connected in star and delta.

2. A 400 V, 3-phase supply is connected to an unbalanced load having three impedances

of , 34 Ω+= jZ R , 34 Ω−= jZY . 5.2 Ω=BZ Also . 13.0 Ω+= jZ N Find phase currents,

voltage across loads and neutral current.

3. a) In the circuit shown in Figure 3(a), the switch S is in position 1 for 0.01 seconds and then

changed to position 2. Find the time at which the current is zero and reversing its direction.

b) In the circuit shown in Figure 3(b), find the time when the voltage across the capacitor

becomes 25 V, after the switch is closed at t=0.

4. a) A sinusoidal voltage t100sin )( πVtv = is applied at t = 0.01 seconds to a series R-L circuit,

where R=10 ohms and L=0.1 H. Calculate the ratio of maximum value of current (to which

it rises) to the steady state value of current.

b) A series R-C circuit, with R=50 ohms, C=10 µF has a sinusoidal voltage of 314tsin 2230 .

Find the transient response.

1 of 2

SET - 2 R10

5Ω

Figure 3(a)

0.1 H 100 V

+

- +

-

S 1

2

20 V

20Ω

Figure 3(b)

1µF 100 V

+

-

S

t=0

i(t)

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Code No: R22025

5. a) Why Z-parameters are known as open circuit parameters and Y-parameters are known as

short circuit parameters? Explain.

b) Find the h-parameters of the following network shown in Figure 5.

6. Find the y-parameters for the network shown in Figure 6 by considering it to be a parallel

combination of a resistive network referred to as Na and a capacitive network referred to as Nb.

7. In the circuit shown in Figure 7, the input voltage is a periodic signal with period 2 as shown.

Determine: i) the exponential Fourier series representation of input signal ii) the trigonometric

Fourier series representation of input signal iii) the exponential Fourier series representation of

output signal

8. a) Determine the Fourier Transform of unit impulse function.

b) Determine the Fourier transform of the rectangular function shown in Figure 8.

2 of 2

f(t)

A

t a -a

Figure 8

SET - 2 R10

V2

Figure 5

CA

RA mI1

RB V1

I1 I2

Figure 6

1

-j1Ω

1Ω

-j1Ω

-j1Ω

11 21

2

Figure 7

1 H

Vin(t) +

- 1Ω Output

Vin(t)

1

t 2 1 3 4

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Code No: R22025





1. a) For a Delta connected three phase system, derive the relationship between the i) phase

voltages and line voltages ii) phase currents and line currents

b) Three identical coils each having a resistance of 20 ohms and a reactance of 20 ohms are

connected in star and delta across 440 V three phase supply. Two wattmeters are connected

in the system to measure power. Calculate line current and reading in each wattmeter when

the loads are connected in star and delta.

2. A three phase 400 V star connected balanced supply is connected to star connected three load

of ,0 25 0 Ω∠ ,02 11 0 Ω−∠ and ,01 15 0 Ω∠ Find line current, power and current in neutral

of the (i) four wire system (ii) three wire system. Assume zero neutral impedance.

3. For a network is shown in Figure 3, find the currents i1(t) and i2(t) after switching. Initial

potential of capacitor is 4 V and initial currents through the inductor and capacitor are zero.

4. a) Determine the transient and steady state currents through a series R-C circuit when it is

connected to a sinusoidal voltage source.

b) Find the expression for current at t > 0 when switch S is moved from 1 to 2 position at t=0 in

Figure 4(b). Assume a steady state current of 1 A in the R-L circuit when the switch is

moved from position 1 to 2.

1 of 2

SET - 3 R10

+

-

t=0 1Ω

Figure 3

+

-

1 H

1Ω

10 u(t)

i1(t) i2(t) 1F 4 V

+

-

1Ω

100 Ω

Figure 4(b)

0.1 H 100 sin 100πt

S

1

2

~

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Code No: R22025

5. a) Explain the concept of reciprocity and symmetry. Derive the above condition for h and

ABCD parameters.

b) Obtain the Z parameters of the network shown in Figure 5.

6. a) The h-parameters of certain two-port network are

−=

2.020

210h . Find the new h-parameters

that result, if a 1 ohm resistor is connected in series with i) input terminals of the network

ii) output terminals of the network.

b) Two 2-port networks A and B are connected in parallel. Each of these networks has their

own y-parameters. Show that resultant y-parameters of the combined parallel network is

sum of y-parameters of the individual networks A and B.

7. Determine the current i(t) flowing through the circuit shown in Figure 7.

8. a) Determine the Fourier transform of the triangular function shown in Figure 8.

b) State and explain four properties of Fourier transform.

2 of 2

f(t)

A

t T0

Figure 8

SET - 3 R10

Figure 5 - -

V2 V1 3Ω 2I1

1Ω + +

I1 I2

Figure 7

t

1.0

0

π

-1.0

2π ~

1F i(t)

V(t) 1Ω

V(t)

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Code No: R22025





1. a) Compare a three phase star connected system with a delta-connected system. Discuss merits

and demerits of the two systems.

b) Show that power consumed by three identical phase loads connected in delta is equal to

three times power consumed when phase loads are connected in star.

2. a) Explain how the three-phase power is measured using two-wattmeter method.

b) A 100 V, 3-Ø balanced supply is connected to an unbalanced delta load having three

impedances , 90106 0 Ω−∠=ABZ , 56.7125.63 0 Ω∠=BCZ . 100 Ω=CAZ Calculate line

currents and power consumed if (i) the phase sequence is ABC (ii) the phase sequence ACB.

3. In a series RLC circuit L=1 H, and C=1 F. A DC voltage of 20 V is applied at t=0. Obtain i (t)

when i) R=5 ohms, ii) R=2 ohms, iii) R=1 ohm.

4. Find the current i(t) in the network shown in Figure 4 for t>0. At t=0- the network was

un energized.

5. a) For a network, the equations are

212

211

2.0

2.05.0

VVI

VVI

+−=

−=

Find Z and ABCD parameters.

b) Find Y and Z parameters of the network shown in Figure 5.

1 of 2

V2

Figure 5

3Ω 2Ω

V2 2Ω

+ -

V1

I1 I2

SET - 4 R10

0.1 H

100 sin314t ~

2 F

10Ω

Figure 4

t=0

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Code No: R22025

6. Determine the Y parameters of the two-port network shown in Figure 6.

7. a) Explain about the trignometric form of Fourier series.

b) A voltage

∞++++= .....

5

10sin

3

6sin

1

2sin4)(

ttttv

πππ

πis applied to a circuit consisting

of resistance R=4 ohms in series with an inductance of π

1=L H. Calculate the current in the

circuit.

8. Determine the Fourier transform of the function shown in Figure 8.

2 of 2

SET - 4 R10

V2

2Ω 2Ω +

V1

I1 I2

1 F

2 F

Figure 6

1Ω

1 F

+

- -

f(t) A

t T -T

-A

0

Figure 8

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Code No: R22029

II B. Tech II Semester Regular/Supply Examinations August - 2014

ELECTRICAL CIRCUIT ANALYSIS - II

(Electrical and Electronics Engineering) Time: 3 hours Max. Marks: 75


1. a) A balanced delta connected three phase load absorbs a complex power of 100kVA with a

lagging power factor of 0.8 when the rms line to line voltage is 2400V. Calculate the

impedance of each arm of the delta connected load.

b) The three rms phase voltages of a balanced 3 ph supply are 00100∠=AnV ,

0120100 −∠=BAnV and 0240100 −∠=CnV . What are the magnitudes of line voltages? If a

balanced 3 phase star connected load of impedance 03010∠ ohms per phase is connected to

the supply, what are the line and phase currents. (8M+7M)

2. A delta connected load with impedance 03010∠=ABZ ohms, 0025∠=BCZ ohms, and

03020 −∠=CAZ ohms is connected to a three phase three wire 500V system. If the phase

sequence is ABC, calculate the line currents and the total power. (15M)

3. Derive the expression for transient response in series R-L-C circuit for DC excitation. Obtain

the solution using Laplace transforms. (15M)

4. In the Figure 1, determine complete solution for current, when switch K is closed at t = 0 for

applied voltage v (t) 400 cos (500t+π/4). Derive the expression for the current. (15M)

1 of 2

R10 SET - 1

~

i

400 cos (500t +4

π)

K

3 µF

15 Ω 0.2H

Figure 1

t = 0

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Code No: R22029

5. a) Find the ABCD parameters for the following network in Figure 2

b) Explain about reciprocity and symmetry in h-parameter representation. (8M+7M)

6. a) Synthesize the impedance function ( )( )3

682

24

+

++=

ss

sssz by Foster form I.

b) Determine where the function ( )133

423

2

+++

+=

sss

ssF is positive real or not. (8M+7M)

7. a) Determine the average power supplied to the circuit shown in Figure 3.

0 0i(t) 2 cos(t 10 ) 6cos(3t 35 )A= + + + +

b) Find the Fourier series of a rectified half sine wave is defined over one period (9M+6M)

f(t) = A sin wt for 0 < t < T/2 and f(t) = 0 for T/2 < t < T.

8. a) State and explain Fourier integral theorem.

b) Use the defining integral to find the Fourier transform of the following function (5M+10M)

( )A / 2 t 0

f t A 0 t / 20 elsewhere

− −τ ≤ <= < ≤ τ

2 of 2

SET - 1 R10

Figure 3

i(t) v(t)

+

-

2 F 10 ohm

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Code No: R22029





1. a) Prove that the line currents are equal to 3 times the phase currents in a delta connected

system and they lag by 300 to the respective phase currents.

b) Explain how reactive power can be measured in balanced three phase systems. (8M+7M)

2. A balanced 3 phase, 3 wire 50 Hz 100 volt supply is given to a load consisting of three

impedances (1+i1), (1+j2) and (3+j4) ohms connected in star as shown in Figure 1. Compute

the voltages across and currents in the three phases of the load using a) Milliman’s theorem

b) Loop current method. Phase sequence ABC. (15M)

3. a) A series RC circuit consists of resistor of 10Ω and capacitor of 0.1F as shown in Figure 2. A

constant voltage of 20V is applied to the circuit at t=0. Obtain the current equation.

Determine the voltages across the resistor and the capacitor.

b) In the Figure 3, determine the current i(t) when the switch is changed from position 1 to2 at

t = 0. (8M+7M)

1 of 2

SET - 2 R10

ZA=1+j1

VBn =100∟-120˚

VAn =100∟0˚

VCn =100∟-240˚

A

Figure 1

B

C

ZB=1+j2

ZC=3+j4

IA

IB

IC

n n'

10 Ω

0.1F

S

Figure 2

i 20 V

10 Ω

10 V

i (t)

50 V 0.5H

1

2

Figure 3

t=0

t=0

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Code No: R22029

4. Derive the complete solution for transient response in series R-L circuit for AC excitation

(15M)

5. a) The z-parameters of a two port network are z11=20Ω, z22=30Ω, z12=z21=10Ω. Find Y and

ABCD parameters.

b) Derive the condition of reciprocity for ABCD-parameters. (10M+5M)

6. a) Find the Foster form II of the given function ( )ss

sssZ

4

1582

2

+

++=

b) Synthesize the RL driving point impedance by using Cauer second form ( )148

4822

2

++

++=

ss

sssZ

(7M+8M)

7. The circuit shown in Figure 4, has a non-sinusoidal vs(t) source that has Fourier series

( ) ( )s

k 1

1 2 1v t sin n t

2 n

∞

=

= + ππ∑ for n = 2k -1. Find the voltage vo(t) at inductor and the

corresponding amplitude spectrum. (15M)

8. a) Determine the output voltage across the capacitor if the excitation is a current source

i(t) = e-t u(t) in below Figure 5.

b) Suppose the input given to a linear system is v = 2e-t u(t). Determine the response of the

system (9M+6M)

2 of 2

SET - 2 R10

+

V0 (t)

-

2 H

5 ohm

vs(t)

Figure 4

Figure 5

i (t)

+

V (t)

-

1 F 2 Ω

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Code No: R22029





1. a) Three impedances each of 3-j4Ω are connected as shown in Figure 1 across a 3ph 230V balanced supply. Calculate the line and phase currents in the delta connected load.

b) A balanced 3 ph load draws 100kW at a lagging power factor of 0.8 from a 400V 3 phase

50Hz main. Calculate the complex power and the line current. (9M+6M)

2. A three phase 4-wire 400volts a.c. system supplies a star connected load in which 0010∠=AZ

Ω, 03015∠=BZ Ω, and 03010 −∠=CZ Ω. The phase sequence is ABC. A wattmeter W1 has

its current coil in phase A and its pressure coil across A and B. Another wattmeter W2 has its current coil in phase C and its pressure coil across B and C. Calculate the wattmeter readings and the current through the neutral wire. Also calculate the voltage between supply neutral and load neutral. (15M)

3. a) In an RL circuit of Figure 2, the switch closes at t = 0. Find the complete current response if R =10Ω, L=0.01H;

b) A 200Ω resistor is in series with an inductor L. The initial value of the inductor current is 5 mA and its value 5ms later is 3mA. Find the time constant and the inductance. (8M+7M)

1 of 2

SET - 3 R10

IA

Figure 1

A

B

C

IB

IC

IBC ICA

3 –j4

3 –j4 3 –j4 IAS 230V, 50Hz

3ph Supply

Sw

v(t) = 10 V

i(t)

t= 0 R

L

Figure 2

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Code No: R22029

4. In the Figure 3, determine complete solution for current, when switch K is closed at t = 0. For

applied voltage is V(t) which is given as 100 cos (103t+π/2). Derive the expression for the

current. (15M)

5. Find z-parameters for the given network shown in figure 4 using interrelations. (15M)

6. a) Synthesize the function Z(s) using first Foster form of realization ( )( )

( ) ( ).164

1022

2

++

+=

ss

sssZ

b) Synthesize the LC impedance function ( )( ) ( )

( ).2

312

22

+

++=

ss

sssZ in II cauer form.

7. a) Determine the complex Fourier series for the waveform shown in Figure 5. b) In a two-element series network voltage and current are given as v = 40+30 sin 314 t + 30 sin 942 t i = 8 sin (314 t +600) + 15 sin (942 t + 450) Determine the power consumed and the network elements. 8. a) Use the defining integral to find the Fourier transform of the following function

≥

<=

− atte

ttf

at ,)(

0

00

b) For the circuit shown in Figure 6, find v0 (t) if v0 (t) = 5 e-3t u(t).

2 of 2

SET - 3 R10

K

100 cos (103 t +2

π)

t= 0

R = 20Ω

L

Figure 3

i

L = 0.1H ~

Figure 4

L L

C C

C

I1 I2

V1 V2

L

+ +

_ _

f(t)

T/2

A

- A

0 t

-T/2

Figure 5

T/4

Figure 6

vi (t)

+

V0 (t)

- 4 Ω

1 H

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Code No: R22029





1. a) A balanced three phase inductive load is connected to a balanced 3ph power system. The line

voltage is 480V and the line current is 10A. The angle of the phase impedance of the load is

600. Find the complex power S and real power P absorbed by the load.

b) Three inductors each of resistance 2 ohms and an inductive reactance of 8 ohms are

connected in star and supplied from three phase 230V 50 Hz supply .What are the line and

phase currents and voltages? Also calculate the power input and power factor. (7M+8M)

2. For the network of Figure 1, calculate the line currents and power consumed if a) the phase

sequence is ABC and b) the phase sequence is ACB. (15M)

3. a) The circuit shown in Figure 2 consists of resistance, inductance and capacitance in series

with a 100V constant source when the switch is closed at t=0. Find the current transient.

b) In the circuit shown in Figure 3, obtain the equations for i1(t) and i2(t) when the switch is

closed at t = 0 (7M+8M)

4. Derive the expression for transient response in series R-L-C circuit for AC excitation using

Laplace transforms (15M)

1 of 2

SET - 4 R10

IA

Figure 1

A

B

C

IB

IC

IBC

ICA

5Ω

2 –j2 Ω

3 +j4 Ω

IAB 100V, 50Hz

3ph Supply

R

20 µF

S

Figure 2

i

100 V

0.05 H L

C

20 Ω t=0 t=0

1 H

10 Ω

S

Figure 3

i1 50 V 20 Ω i2

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Code No: R22029

5. a) Derive z-parameters in terms of y and ABCD parameters.

b) Determine h-parameters after writing transformed network for the given circuit in Figure.4

(10M+5M)

6. a) Synthesize the RC impedance using first Foster form ( )( ) ( )

( ).4

624

+

++=

ss

sssZ .

b) Test whether the function

+

+

ss

s

4

13

2

is positive real. (8M+7M)

7. Find the response io(t) in the circuit shown in Figure 5 if the input voltage v(t) has the

Fourier series expansion ( ) ( )n

2n 1

2( 1)v t 1 cos nt n sin nt

1 n

∞

=

−= + −

+∑

(15M)

8. a) For the circuit shown in Figure 6, find v0 (t) if vi (t) = cos 2 t.

b) List out any six properties of Fourier transform. (9M+6M)

2 of 2

SET - 4 R10

1F 1F I2 I1

V1 V2

1

11 21

2

1H

Figure 4

4 ohm 2 ohm

2 ohm2 H v(t)

i0(t)

Figure 5

Figure 6

vi (t)

+

V0 (t)

- 5 Ω

1 H

1411578278ECA-II-R10-AUGUST2014 (1)

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