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Page 1

PAPER – I

Time Allowed: 3 Hours Maximum Marks: 200

Candidates should attempt SIX questions, selecting TWO questions from Section - A, ONE from Section - B, ONE
from Section - C and TWO from Section – D.


SECTION A

1. (a) For the circuit shown in Fig. 1, find the Thevenin and Norton equivalent circuits looking in at
terminals ‘a’ and ‘b’

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(b) In the R-L-C circuit shown in Fig. 2, Is = 10 A, R =1 , L = 1 H, C = 1 F and iL (0-) = 0.

Determine v(0+)    
2

2
0 0

dv d v
and

dt dt
  after the switch is closed at t = 0.


(c) An industrial consumer is operating a 3-phase 10 kW induction motor at a tagging power

factor of 0.8 and at a source voltage of 400 V r.m.s. He wishes to raise the power factor to
0.95 lagging by connecting a circuit element in parallel to the load (motor). Indicate the type
of circuit element (inductive or capacitive) and find its value if the operating frequency is 50
Hz. Give your comments on the new line and motor currents.

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2. (a) A 415 V, three-phase generator supplies power to both a delta- and a star-connected load in
the manner shown in Fig. 3. All the phase impedances are identical and specifically equal to
(5 + j 8.66). Compute the total generator current in each line.

I.E.S. (Conv.) - 2005

EELLEECCTTRRIICCAALL EENNGGIINNEEEERRIINNGG

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(b) Show that the resonant frequency w0 of an R-L-C series circuit is geometric mean of w1 and

w2, the lower and upper half-power frequencies respectively.

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(c) Prove that for BIBO stability, the roots of the characteristic equation or the poles of the
system transfer function cannot be located in the right half of s-plane or on the jw-axis,

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3. (a) A system is described by the following state variable equations:


where U(t) is Unit step input and the output


Determine y(t), t  0 when the initial values of the states at time t = 0 are x1(0) = x2(0) = 1.

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(b) A unity feedback system has an open-loop transfer function

 
 2
10000

10
G s

s s





Determine the phase margin of the system in degrees.

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(c) The transfer function of a phase-lead controller is given as   1 , 1
1

c

aTs
G s a

Ts


 


and T is a

constant depending on the circuit parameters.

Determine the maximum value of the phase lead which can be obtained from this controller.

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SECTION B
4. (a) Explain the concept of wave impedance for plane waves travelling in a lossless medium and

show how this may be extended to cover the case of a conductive medium. Show that the
reflection coefficient for plane waves travelling in a vacuum and falling with normal
incidence upon a medium having wave impedance  is given by

( - 0)/ ( + 0)

Show that when a plane wave is incident normally upon a medium with permeability 0
permittivity 0 and conductivity  the fraction of power absorbed is approximately
2(20/)

1/2.

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(i) error in registration and

(ii) error in r.p.m. of energy meter.

How error in r.p.m. can be rectified?

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(b) Explain the working of binary ladder digital to analog converter using R-2R ladder network
with four input voltages.

If in the above DAC a reference voltage of 12 V is used, what will be its resolution and full
scale output?

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(c) The inductance of a moving iron instrument is given by L = (0.01 + k1)
2 H

where  is angular deflection in radians from zero position. The angular deflection in radians
corresponding to currents of 1.5 and 4.S Amps. are /6 and /3 respectively. Find the value
of k.

10

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Page 10

Two MOSFETS which are connected in parallel similar to the above figure, carry a
total current, IT = 25 A. The drain to source voltage of M1 is VDS1 = 2.0 V and that of
M2 is VDS2 = 35 V. Determine the drain current of each transistor and difference in
current sharing if the current sharing series resistances are (i) RS1 = 0.35 ohm, RS2 =
0.2 ohm, and (ii) RS1 = RS2 = 0.5 ohm.

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(b) Describe with necessary diagrams

(i) an Integrator, and

(ii) a differentiator using operational amplifier circuits. How the offset voltage can be
minimized in an Integrator at the

8. (a) Draw the symbols and characteristics of the following devices

(i) Diode,

(ii) Thyristor,

(iii) GTO,

(iv) Triac and

(v) IGBT.

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(b) A single-phase thyristor converter with a resistive load is shown below:


Supply voltage Vs is sinusoidal at a fixed frequency.

(i) Draw the waveforms of VS, V0 and VT1 at the firing angle

 = 45°. Neglect leakage current.
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(ii) If the supply voltage is 230 V (rms) at 50 Hz, calculate for

 = 45° and R 100 ohms.
(a) Average output voltage and current.

(b) R.M.S. value of supply current.

(c) Ripple factor.

Derive the formulae used.

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SECTION D
9. (a) Draw the circuit diagram of a single-phase semi converter and derive an expression for the

average voltage across the load in terms of supply voltage and firing angle a. Explain the
semi convener operation and show the waveforms for the input voltage, output voltage and
current through different diodes and thyristors.

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(b) A semi converter is connected to a 240 V 50 Hz supply. The load current Ia can be assumed
to be continuous and its ripple current is negligible. Calculate the harmonic factor of input
current for  = /2. Derive all the relevant formulae used using Fourier series analysis.
Obtain also expressions for r.m.s. value of supply current and r.m.s. value of fundamental
current in terms of Ia and .

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10. (a) Define “amplitude modulation” and “modulation index”. Write down the equations for (i)
amplitude, and (ii) the instantaneous voltage of the amplitude modulated wave. Sketch the
graph of an amplitude modulated wave.

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(b) The current in an Antenna of an AM transmitter is 8.0 A when only the carrier is sent, but it
increases to 9.0 A, when the carrier is sinusoidally modulated. Find the percentage
modulation. Determine also the Antenna current when the depth of modulation is 0.77.

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(c) An 18 MHz carrier is modulated by a 400 Hz audio sine wave if the carrier voltage is 50 V
and the maximum deviation is 12 KHz. Write down the equations of this modulated wave for
(a) F.M., (b) P.M. If the modulating frequency is only changed to 1.6 KHz all other data
remaining constant, write down the new equations for (c) F.M. and (d) P.M.

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