Electrical Circuit Analysis - II 2 Question Papers

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Code No: R22029

II B. Tech II Semester Supplementary Examinations January - 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 balanced - connected load with phase impedance of 33.3 + j197.2 at 60Hz is supplied from a Y - connected generator. The supply has 115.5V phase voltage and a 60Hz frequency. Calculate the line current magnitude and its phase with respect to phase voltage.

2. a) Show that in two-wattmeter method, the sun of the meter readings equals the total power dissipated in the load, whether the load is balanced or unbalanced, Y connected or - connected.

b) Determine: i) phase currents and ii) line currents for the unbalanced connected load shown in Figure 1. The load impedance ,100=abZ ,60= jZbc and

.6030 += jZ ca Assume a positive sequence voltage for the balanced supply system with a line line source voltage of 230V.

3. a) In the network shown in Figure 2, the switch is open for a long time and at t = 0, it is closed. Determine V2(t).

b) The network shown in Figure 3 is under steady state with switch at the position 1. At t = 0, switch is moved to position 2. Find i(t).

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SET - 1 R10

Figure 3

1

2

10 V i (t)

40

50 V 20 mH

Figure 1 A

B

C

IA

IB

IC

Zbc

Zab

Zca

0.5 6 V

0.25

0.3 F

V2 (t)

Figure 2

t=0

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Code No: R22029

4. A sinusoidal voltage V(t) = Vm sin(t+) is applied to a RL circuit at time t = 0. Find the complete solution for the current in the circuit using Laplace transform method and differential equations.

5. a) Derive ABCD parameters in terms of Y parameters. b) A two-port network whose h-parameters are known is energized by a voltage source of Vg

volt and internal impedance of Zg . It the output port of the network is terminated in impedance of ZL, determine, using the constraint equations, expressions for input impedance , voltage gain and current gain.

6. a) Test the given functions for positive real property

i) F(s) = )9(185

2

2

+

+

ss

s ii) F(s) = )2(

82

2

+

+

ss

s

b) Determine the carrer from I network for the RL impedance function given below. Z(s) = )6)(3(

)5)(2(3++

++

ss

ss

7. a) Find the exponential Fourier series expansion of the periodic function F(t) = et , 0 < t < 2pi with f(t+2pi) = f(t).

b) In a two-element series network voltage and current are given as V = 50 + 60 sin 314t + 60 sin 942t

i = 10 sin (314t + 60) + 15 sin (94t + 45) Find the network element series network voltage and compute the power consumed.

8. a) Discuss about the similarities and differences between Fourier and Laplace transforms. b) For the circuit shown in Figure 4, for an input voltage Vi(t) = 2e-3t u(t) find V0(t).

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Figure 4

Vi (t) +

V0 (t)

-

1 F

2

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Code No: R22029




1. a) Sketch the phasor diagram of load currents and voltages for a balanced Y connected load with = 20 lagging. Show that the phasor sum of load currents is zero.

b) There - connected 155 resistors are supplied from a - connected generator with a line voltage of VL = 400V. Calculate the current in each resistor and the line currents.

2. An unbalanced Y connected load is supplied from a three-wire supply with a line voltage of 200V at 60Hz frequency. The load components are R1 = R2 = R3 = 50, and L3 =398mH. Calculate the line currents IA, IB and IC.

3. a) A series RL circuit with non-zero initial energy is driven by a 1V DC switched source. The inductor current is found to be (2-e-t) A. What are the values of inductance and resistance?

b) In the network shown in Figure 1, the switch is closed. Assuming all initial conditions as

zero, find i, dtdi

and 22

dtid

at t= 0+.

4. a) Determine the current in a series R-L circuit, when a voltage V(t) = 50 sin 25t is suddenly applied by closing a switch where R = 10 and L= 5H.

b) A sinusoidal voltage V = 250 sin 500t is applied suddenly to a series RC circuit with R = 100 and C = 25F. Assuming zero initial charge on capacitor, find the expression for current in the circuit.

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10 V

10

Figure 1

1 H

1 F

i (t)

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Code No: R22029

5. a) The following equations give the voltages V1 and V2 at the two ports of a two- part network: V1 = 5I1 + 2I2 V2 = 2I1 + I2

A load resistor of 3 is connected across port 2. Calculate the input impedance. b) Two identical sections of the network shown in Figure 2 are corrected in cascade obtain the

transmission parameters of the overall connection.

6. Realize foster forms of the following LC impedance function.

Z(s) = )4)(2()3)(1(

22

22

++

++

sss

ss

7. a) Discuss the general procedure of determining the exponential Fourier series of a periodic waveform.

b) A square wave symmetrical above and below ground has a peak amplitude of 6V, as illustrated in Figure 3. Determine the amplitude of each component up to the seventh harmonic.

8. a) Determine the Fourier transforms of the functions F(t) = et [u(t) u(t-1)] and g(t) = te-t u(t)

b) Discuss about time scaling, duality and time shifting properties of Fourier transform.

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+

V2

-

+

V1

-

2 2 I1 I2

1 2

Figure 2

Figure 3 - 6 V

wt

6 V

pi 2pi

v (t)

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Code No: R22029




1. A Y connected three-phase balanced voltage source having a phase voltage of 127V supplies a connected balanced load with an per phase impedance of 120 60 through a distribution circuit. If the impedance of each line is (0.25+j1.0), and the per phase impedance of the voltage source is (0.25+j1.6). Calculate (a) the line current, (b) phase voltage at the load terminals, (c) load current per phase.

2. a) Explain the application of Millmans theorem for analysis of three- phase unbalanced circuit.

b) Explain three- wattmeter method to measure power in an unbalanced Y connected four- wire load.

3. a) In the network show in figure1, the switch is initially at the position 1. When the steady state is reached the switch is changed to position 2. Find current i(t).

b) A series RC circuit is excited by a pulse of amplitude 1V and duration 1S. Compute the voltage across the capacitor. Assume R= 1, C = 1F, and zero initial change on the capacitor.

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SET - 3 R10

Figure 1

1

2

i (t) R2

V

L

R1

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Code No: R22029

4. In the circuit shown in figure 2, determine the complete solution for the current when switch

K is closed at t = 0. Applied voltage is V(t) = 50 cos3

10[ 3 pi+t ]

5. a) A two port network has the following parameters: Z11 = 150, Z22 = 250, Z12 = 50, Z21 = 50. Calculate the required input voltage to produce a 2.5 mW dissipation in a 2.2 k load connected at the network output.

b) The following test observations were recorded on a two-port network in a laboratory: Port 1-11 on open circuit Port 2-21 on short circuit

V1 = 25mV V1 = 15mV V2 = 40mV I1 = 15A

I2 = 10A I2 = - 5A

Determine the hybrid parameters of the network from the test data. Compute the open-circuit impedance parameters and verify the result.

6. Realize the RC-impedance in courier -I and Foster I forms

Z(s) = )6)(2(4

++

+

ss

s

7. a) A series RLC circuit has R=10, L=2mH and C=40F. Determine the effective current and average power absorbed when the applied voltage is

V(t) = 100 cos 1000t + 50 cos 2000t + 25 cos 3000t V.

b) A 400 Hz sinusoidal voltage wave with an rms value of 10V is half-wave rectified. Calculate the amplitude of each component of the wave up to the sixth harmonic.

8. a) Calculate the fraction of the total energy dissipated by a 1 resistor in the frequency band -10 < < 10 rad/s when the voltage across it iw V(t) = e-2t u(t). b) Find the Fourier transform of the following functions. i) e jwot ii) coswot.

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c = 2F

20

Figure 2

V (t) i (t)

K

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Code No: R22029




1. a) Sketch the phasor diagram of line voltage, phase currents, and line currents for a balanced - connected load with = 20 leading.

b) Find the power and power factor of the balanced circuit in which the wattmeter readings are 5 kW and 0.5kW, the latter being obtained after the reversal of the current coil terminals of the wattmeter.

2. A star connected load whose phase impedance are ZA = 10, ZB = j10, and ZC = (14.4 + j10.8) is connected to a three-phase four-wire supply. Chose effective line voltage is 380V. Taking VCA as the reference voltage, calculate (a) line currents (b) phase currents and (c) current through the neutral conductor. Determine the total power consumed by the load.

3. a) Derive an expression for the current in an RL circuit excited by a unit step voltage. b) In the network shown in figure 1, the switch is opened at t = 0, solve for

.022

1+

=tatdt

vdand

dtdv

v

4. In the series RL circuit shown in figure 2, has a sinusoidal voltage source V(t) = 100 sin (1000t + ) voltage. It the switch is closed when (a) = 0 and (b) = 90, find current in the circuit.

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1F 1 k

Figure 1

V (t)

10 A

V (t)

50

Figure 2

0.1 H

t = 0

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Code No: R22029

5. a) Derive Z parameters as a function of ABCD parameters. b) A two-port network has the following admittance parameters: Y11 = 7.14 milli-Siemens,

Y22 = 4.29 milli-Siemens, Y21 = -1.43 milli-Siemens, Y12 = -1.43 milli-Siemens. Determine the power dissipated in a 620 load connected at the network output when a 5V input is applied.

6. a) Test whether F(s) = 14956

2

2

++

++

ss

ss is positive real function.

b) Determine the Foster I form of realization of the RC impedance function. Z(s) = )4)(2(

)3)(1(++

++

sss

ss

7. For the waveform shown in figure 3, time period T =

21

, f = 2Hz, and 0=4pi rad/s. the

mathematical expression of the waveform is given by

V(t) = 40t V for st

810 . And V(t) = (- 40t + 10) V for st

41

81

8. a) Determine the Fourier transforms of functions i) g(t) = u(t) u(t-1) and ii) f(t) = te 2t u(t)

b) Determine the current i(t) in the circuit of Figure 4a, given the voltage source shown in Figure 4b.

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Figure 3 1/8

5

V (t), V

t 1/4 1/2 5/8 3/4

Figure 4a

V (t) 1 F

2 i (t)

Figure 4b 1

1

V (t)

2 t ww

w.jntu

kfastu

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Electrical Circuit Analysis - II 2 Question Papers