C.S.

E-Mains 2003

ELECTRICAL ENGINEERING
PAPER – I
Candidates should attempt questions 1 and 5 which are compulsory and any three of the remaining
questions selection at least one question selecting at least one question from each Section.
SECTION A
1. Attempt any THREE of the following
(a) For the circuit given below,
(i) Find the frequency w0 at which the impedance across X, Y reaches a maximum.
10
(ii) Find the impedance across X, Y at frequency w0 and the current through the network
at that condition.
5+5

(b) (i) Solve the difference function given by

y(K + 2) - 5y(K + 1) + 6y(K) = 3x(K + 1) + 5x(K)
If the initial conditions are
11 37
y  1  and y  2  
6 36
and the input function is x(K) = 2. u(K).
10
(ii) Enumerate different properties of the ROC for Laplace
1
transform and find out the I.L.T of X  s   for
 s  1 s  2 
the different ROC’s Re(s) > -1, Re(s) < -2, -2 < Re(s) < -1
10
(c) (i) A full-pitched coil having N turns rotates with an angular velocity of wr rad/sec with
respect of field flux. Obtain an expression for the flux Linkages with the coil as a
function of time t. Derive there from an expression for the emf generated in the coil.
Discuss about the two components of the emf expression so obtained.
10
 (ii) Show that, in case the field flux is time-invariant, the generated emf lags by 90° the
flux that generates it.
10
(d) (i) Can you detect a DSBSC signal using an envelope detector? By a suitable analysis,
compare the same with coherent detection
(ii) A modulating signal, m(t) is given by cos 100t + 2 cos 300t. Determine the LSB and
USB relations + LSB and USB if the carrier frequency is 1000 rad.
15+ 5
2. (a) (i) The following two amplifier circuit is a generalized immitance converter (GIC).

Analyze the above circuit to get an expression for Zin. Assume the two op-amps to be
ideal.
(ii) With Z1 = R1, Z3 = R3, Z2 = 1/C2s, Z4 = R4 and Z5 = R5, what does the GIC circuit
above realize?
(iii) Z1 and Z5 are capacitors, Z2, Z3 and Z4 are resistors. How does the input impedance
Zin, behave?
(iv) What are energy and power signals? Compute the energy and power contents of the
following signals and indicate whether they are energy or power signals
xT(n) = {(-0.5)n u(n) 0.01s}
yT(n) = {2e3jn u(n) 0.2s}.
10 + 2 + 2 + 6
(b) (i) Discuss why forward break over in a thyristor occurs at a lower anode-cathode
voltage if its gate current is increased.
(ii) What are the advantages of IGST over BJT, MOSFET and thyristor?
(iii) Discuss why the speed control with constant supply voltage and reduced supply
frequency is rarely used in practice in a three-phase induction motor.
(iv) A dc machine has total armature ampere conductors of 4500 and total flux in the
machine is 0.14 Wb. Calculate the torque developed in the machine.
5+5+5+5
(c) A three-phase full-converter feeds a resistive load of 150. For a firing-angle delay of 75°, the
load takes 6 RW. Find the magnitude of per phase input supply voltage to the three-phase
kill-converter.
Derive the relevant expression used if any.
20
3. (a) (i) A rectangular pulse g(t) exists between T = - (T/2) and t = + (T/2). Sketch the pulse
obtained by convoluting g(t) with itself. The Fourier transform of g(t) is a sine
function Write down the Fourier transform of the pulse obtained by the above
convolution.
(ii) Find the Laplace transform L(t) of the following function
f(t) = t cos wt.
w
Given L(sin wt) =
s  w2
2

Using the result of L(t cos wt), find

 
1
L1  
  s 2  w2  2 
 
10 + 10
(b) Explain the development of electromagnetic torque in a three-phase squirrel-cage induction
motor through the interaction of stator and rotor mmf waves. Hence introduce the concept of
load angle.
Show that rotor must rotate in the direction of rotating field. Discuss the conditions under
which optimum torque is developed in a 3-phase induction motor.
20
(c) A 12-V battery feeds a single-phase full-bridge inverter whose output is connected to an ideal
1-phase transformer. Its primary has 10 turns and the load voltage is 230 V. For a load
resistance of 100, calculate
(i) the number of turns in the transformer secondary winding,
(ii) rms value of primary current, and
(iii) rms value of thyristor current.
Consider only the fundamental component of inverter output voltage.
20
4. (a) In the circuit shown below the switch ‘S’ closes at t = 0, and open after 10 ms. What will be
the currents in R, and L1 and L2, and voltage across C1 8 ms after switch ‘S’ opens? Assume
D, to be an ideal diode and a 0.7 V drop across D2 whenever it conducts.

(b) Show that the field strength at a point close to the antenna (at distances of unto 200-300 miles
from the transmitting antenna) in terms of the power is given by
 9.49 P
 volts / m
r
Where:
 is the field strength in volts/m
P is the power radiated in watts
r is the distance in meters.
Calculate the field strength at 20 km away from a transmit- ting station of 50 kW power
20
(c) (i) A sine wave carrier is frequency modulated by a triangular modulating signal m(t) as
shown in figure below. If the carrier frequency is 100 MHz and modulating signal
frequency is 5 kHz, determine the bandwidth of the FM signal. Assume frequency
deviation constant, Kf = 105 Hz/r.

(ii) In a commercial FM broadcast system, the modulation index is 5, the 3 dB frequency

of the pre-emphasis/de-emphasis filter is 2100 Hz and message signal frequency is 15
kHz. If the average to peak power ratio of the message signal is 05, what is the
improvement in output SNR of FM with pre-emphasis and de-emphasis filtering
compared to a baseband system?
10 + 10

SECTION B
5. Attempt any THREE of the following:
(a) (i) What are the criteria for a material to be an imperfect di-electric or a good conductor?
Write Maxwell’s equations in terms of phasors for sinusoidally varying
electromagnetic fields. Consider a uniform plane wave in an isotropic and
homogeneous medium, and show that the electric and magnetic field are not in time
phase.
15
(ii) A uniform plane wave is traveling at a velocity of 3.0 10 m/s in a non-magnetic good
conductor and its wavelength is 0.35 mm. Find the frequency of the wave, and the
conductivity and the intrinsic impedance of the conductor.
5
(b) A series resonant circuit has its impedance
20  s  1  j10  s  1  j10 
Z s 
s
Find
(i) Resonant frequency
(ii) Q factor
 (iii) A and width
(iv) Impedance under resonance condition.
5+5+5+5
(c) Two single-phase full converters are used for control ling the speed of a separately-excited dc
motor. One full-converter in the field circuit has zero degree firing-angle delay. Both the
converters are connected to 1-phase, 220 V, 50 Hz source. DC motor armature resistance is
0.6 and field circuit resistance is 150 and its constant is 0.6 V-s/A-rad. Armature and
field currents are ripple free. For a firing angle delay of 40° and armature current of 40 A,
determine
(i) The motor speed in rpm,
6
(ii) Power factor of the armature converter, and
6
(iii) Power factor of the drive scheme.
6
(d) (i) Define sensitivity, selectivity and fidelity with reference to a radio receiver. What is
double spotting and its effects on a receiver?
(ii) A superhet receiver having no RF amplifier, the loaded Q of the antenna coupling
circuit is 100. If the superhet is to be improved for HF reception so that its image
rejection at 25 MHz is as good as at 1100 kHz, determine the loaded Q which an RF
amplifier for this receiver would have to have and the new IF that would be needed in
the absence of the RF amplifier. (Assume IF of 455 kHz).
8 + 12
6. (a) Discuss the criteria for a circuit to oscillate. Explain the operation of a phase shift oscillator
and derive an expression for the frequency of oscillation of an RC phase shift oscillator.
20
(b) (i) A rectangular hollow metal waveguide of internal cross-section 7366 cm × 3.556 cm
carries a 3 GHz signal in the TE10 mode. Calculate the maximum power handling
capability of the waveguide assuming the maximum permissible electric field inside
the waveguide to be 30 kV/cm.
10
(ii) Explain how a PLL can be used for demodulation of FM signals. Define capture range
and lock range of a PLL.
10
-12 2
(c) (i) White Gaussian noise of two sided spectral density 10 V /Hz is applied to a low
pass (RC) filter having a 3 dB cut-off frequency of 1 kHz. Find the output noise
power.
(ii) The received signal is r(t) = s(t) + n(t) where s(t) is the signal and n(t) is the noise
signal. The signal process is random with an autocorrelation Rs() = 2e-||. The noise is
a sample function of a random process with auto-correlation Pn() e-2||. If the two
processes are having zero mean value and are independent of each other determine the
autocorrelation and total power of r(t).
5 + 15
7. (a) What is uniform plane wave? Define all the parameters associated with it. What is meant by
group velocity?
 A uniform plane electro-magnetic wave travelling in region 1(1, 1, 1) is incident normally
on a plane boundary separating the region 2(2, 2, 2), How are the reflected and the
transmitted waves at the interface related to the incident wave?
10 + 10
(b) Distinguish AM and NBFM signals. Obtain an expression for NBFM and WBFM signals.
Determine the approximate band of frequencies occupied by an FM wave with carrier
frequency of 5 kHz, Kf = 10 Hz/V and f(t) 100 cos 200 t volts.
(c) Distinguish between envelope detection and synchronous detection. Explain a Costas loop
receiver for demodulating a DSBSC signal. Explain how the squaring circuit can also be used
for synchronous detection.
20
8. (a) (i) Using multiplexers, implement a full adder circuit.
(ii) It is desired to generate the following three Boolean functions

F1  abc  abc  bc

F2  abc  ab  abc

F3  abc  abc  ac
By using an OR gate array as shown in Figure, where P1 to P5 are the product terms in one or
more of the variables, a, a , b, b , c and c . Write down the terms P1, P2, P3, P4 and P5.
10 + 10
(b) A 50 kW, 440 V, 50 Hz, star-connected synchronous generator with per phase impedance of
0.8 + j 4.5 is working with rated terminal voltage. It is required to supply a power of 25 kW
to the bus. Estimate the minimum excitation emf. Find out the corresponding stator current.
20
(c) Consider the circuit shown below. Main thyristor T1 and auxiliary thyristor TA are off and
capacitor is charged to voltage Vs with upper plate positive. Sketch the waveforms for io, ic,
iT1, vc and vT1 (assuming constant toad current), after
(i) thyristor T1is turned on
(ii) steady slate is reached in part (i) and then thynistor TA is turned on
From these waveforms, obtain the expressions for circuit turn-off time for both SCRs.
In case Vs = 220 V, R = 10  and maximum value of current through main SCR is 3
times the load current, calculate the value of commutating inductance L for C = 20F and the
circuit turn-off time for the auxiliary SCR.
20
C.S.E-Mains 2003

ELECTRICAL ENGINEERING
PAPER - II
SECTION A
1. Select any three of the following statements, read them carefully and identity the correct and the
incorrect ones. Justify your answer using not more than 200 words in each case:
20 × 3 = 60
(a) Routh-Hurwitz criterion is an algebraic method that provides information on the absolute
stability of linear time invariant system that has a characteristic equation with constant co-
efficient.
(b) If a polyphase, load is supplied through ‘m’ conductors, the total power consumed is
measured by adding the readings of ‘m’ wattmeters so arranged that current coil of a
wattmeter is in each line and the corresponding pressure coil is connected between that line
and a common point. If the common point is located on one of the lines, then the power may
be measured by (m - 1) wattmeters only, irrespective of balanced/unbalanced load.
(c) For economic operation, the generator with highest positive incremental transmission loss
will operate at the highest positive incremental cost of production.
(d) Considering state of the art, the communication links of satellites for weather forecasting are
at present very effective.
2. (a) Explain the effects of negative feedback in control systems on the following
20
(i) Stability (ii) External disturbances
(b) Define surge impedance of a line and discuss the advantages and disadvantages of operating
an overhead line corresponding to surge impedance loading. Also explain the terms infinite
line, flat line.
20
(c) Describe a few features of a wind wheel for efficient generation of electrical energy and
discuss economic viability of this form of energy vis-a-vis conventional method. Which
generator do you recommend and why?
20
3. (a) Discuss briefly the architecture of 8086 microprocessor with special reference to the
following
20
(i) Memory organization
(ii) Register structure
(iii) Addressing modes
(b) Explain with reasons the connection of C.T.s for protecting a detta/star transformer Justify
your scheme of protection for (i) internal fault and (ii) external fault, using Merz-Price
protection.
20
(c) What is solar power? Describe very briefly with neat diagram the scheme for (i) residential
cooling and heating and (ii) solar power plant, using solar energy.
 20
4. (a) Describe the factors on which the conductivity of intrinsic semiconductor depends.
A semiconductor is made of ‘n’-type germanium. From the following data, calculate the
conductivity of ‘n’-type germanium:
(i) Density of Ge = 5.32 × 103 kg/m3
(ii) At. wt. of Ge = 72.6 kg/k.mol
(iii) Charge of electron = 1.6 × 10-9 C
(iv) Mobility of holes = 0.18 m2/V.s
(v) Mobility of electrons = 3.8 m2/V.s
(Assume one donor atom in each 108 atoms)
20
(b) Describe the basic modulation schemes in digital data transmission.
20
(c) Explain what is meant by saying that a satellite is stationary. Why are such satellites used for
worldwide communications in preference to any other kind?
20

SECTION B
5. Select any three of the following statements, read them carefully and identify the correct and the
incorrect ones. Justify your answer using not more than 200 words in each casa
20 × 3 = 60
(a) If the roots of characteristic equation of a linear digital control system lie within unity circle
in z-plane, the system is stable.
(b) The magnetic property of a material is completely lost above its characteristic Curie
temperature.
(c) The chances of arc interruption in subsequent current zero increase in case of air blast CS. but
decrease in oil C.B.
(d) The bandwidth of a PCM signal is much larger than that of original base band.
6. (a) Explain how frequency can be measured using four arm bridge arrangement. Derive balance
condition for such a bridge. Mention the range of frequency measurement and accuracy of
such measurement. If applied voltage is non- sinusoidal, will it be possible to balance this
bridge?
20
(b) Describe a communication circuit using modem and explain how modems are classified,
20
(c) Explain the significance of blind speed in moving target indicator (MTI) by radar.
A MTI operates at 5 GHz with a pulse repetition frequency (PRF) of 400 pps. Calculate the
lowest blind speed of radar.
20
7. (a) Discuss the performances of proportional plus derivative and proportional plus integral
controllers.
20
 (b) Describe radar beacons and their application.
20
(c) What do you mean by bandwidth of single mode fibre and describe the factors on which it
depends?
20
8. (a) Explain the following
(i) Gain margin (ii) Phase margin
How are they determined from Nyquist plot and Bode plot?
20
(b) A generator is connected to a motor through a Y/ transformer. The generator is connected
to the star side of the transformer. A fault occurs between the motor terminal and the
transformer. The symmetrical components of the sub-transient current in motor flowing
towards the fault are I a1 : - 0.8 - j2.6 p.u., I a2 : -j2.0 p.u. and I a0 -j3.0. From the transformer
towards fault I a1 : 0.8 – j0.4 p.u., I a2 -j1.0 p.u. and I a0 : 0 . Assume X” = X2 for both the motor
and the generator. Describe (i) the type of fault, (ii) the prefault current, if any, in line ‘a’.
20
(c) Explain the terms energy management, energy audit and energy economics. Explain how
these techniques can be used to improve the performance of an energy starved inter
connected power system.
20