C.S (MAIN) EXAM, 2009

ELECTRICAL ENGINEERING

Paper-I

Time Allowed Three Hours Maximum Marks 300

INSTRUCTIONS

Each question is printed both in Hindi and in English.

Answers must be written in the medium specified in the Admission Certificate issued to you, which must be stated clearly on the cover of the answer-book in the space provided for the purpose. No marks will be given for the answers written in a medium other than that specified in the Admission Certificate.

Candidates should attempt Question Nos. 1 and 5 which are compulsory, and any three of the remaining questions selecting at least one question from each Section.

The number of marks carried by each question is indicated at the end of the question.

Assume suitable data if considered necessary and indicate the same clearly. Symbols/ notations carry their meanings, unless otherwise indicated.

Section-A

The current <img src='./qimages/21-1a1.jpg'> is passed through a capacitor of 0·5 farad. Find the expression for the voltage across the capacitor in the time interval 1 t 2. 5
In the circuit given below, A and B are mutually coupled coils. Determine coefficient of coupling K between them so that the circuit is in resonance. <img src='./qimages/21-1a2.jpg'>

Three identical impedances of SL 30° ohms are connected in star to a 3-phase, 4-wire, 400 volts cba system. Express the current in phase in phasor form, assuming V bc as a reference phaser. 5

For the circuit shown in the figure,
assume t3 hFE 100.
Find if the silicon transistor is in cut-off, saturation or in the active region. 10

find v0
<img src='./qimages/21-1b2.jpg'> 5

Explain differential compounding of
a d.c. machine. 5
Which type of compounding is not commonly used? Why? Explain with relevant characteristics for a motor and a generator. 10

Explain the mathematical expressions for statistical average, mean, variance and correlation coefficient of a random variable. 6
Explain, using analytical expressions, stationarity, time averages 6 and ergodicity. 9

Using Fourier transforms, find the
impulse response of the system
described by the equation
3.x(t)
where x is an input and y 1s an
output. 10

Using z transforms obtain the convolution sum of two sequences, x1 x2 where Xl 1 2 1 0 x2 u(n is a unit step sequence.

The figure below shows a d ivide-by-N
counter.
Find N. Assume initial value of Q0 Q1 0 and Q2 0. 1 0
Repeat Part if initially Qo
01 0 and 02 1 . 10
<img src='./qimages/21-2b2.jpg'>

A d .c. series motor 1s powered by a d . c. chopper. The armature resistance is Ra 0 · 03 ohm and the field resistance Rf 0 · 05 ohm. The back e.m.f. constant of the motor 1s Ku 1 5 -27 mV/A-rad/s. The average armature current Ia 45 0 A. The armature current 1s continuous and has negligible ripple. If the duty cycle of the chopper is 7 d etermine- 1. the input power from the source; 2. the equivalent input resistance of chopper drive; 3. the motor speed. 10

Give the circuit of a single-phase half-bridge inverter. Draw the load current waveform for a highly inductive load. Explain the purpose of the feedback diodes. 10

Constrnct circuits using diodes which exhibit terminal characteristics as shown 1n Part and Part of the figure below. Assume diodes to be ideal. 20
<img src='./qimages/21-3a.jpg'>
Explain the phenomenon of hunting in a synchronous machine. 1 0
A 3-phase, star-connected alternator is rated at 1600 kVA, 1 3·5 kV. The effective armature resistance and synchronous reactance are 1 · 5 ohms and 30 ohms per phase respectively. Find the regulation for a load of 1 280 kW at rated voltage and 0·8 lagging power factor. 1 0
A plane wave m free space 1s incident normally on a large block of material with Er 12, µr 3 and cr 0 which occupies z 0. If the incident electric field is E 30 cos(wt z)ay V determine- the standing wave ratio; the reflected magnetic field. 0 =4nx 10-7

For the circuit shown below, determine the numerical value of i1, using nodal analysis. 12
<img src='./qimages/21-4a1.jpg'>
For the network shown below, write mesh equations in vector-matrix form for the loop currents i1 and i2. <img src='./qimages/21-4a2.jpg'> Assume mutual inductances between coils L1 L 3 and coils L2 L3 as .l.113 and M23 respectively.
How are choppers classified, based on direction of current and voltage? Indicate with v L -iL diagrams.
For a step-down chopper, derive an expression for peak-to-peak ripple current in terms of supply voltage V5 output voltage V0 frequency of 8 operation and inductance. 12
An AM wave 15(1 0 · 4cos2n103 · cos21tl06 t is to be detected by a linear diode detector.
1. Find the time constant, -r.
2. Find the value of if the capacitor used is 100 pF.
An FM signal defined as <img src='./qimages/21-4c2.jpg'> is applied to a high-pass RC filter, where for w representing the FM frequency band. Show if an envelope detector after the filter can 8 demodulate the FM signal. 12

Section-B

5. Sketch the function f u(n and express it as a sum of shifted unit impulses. is a unit step sequence.

A senes RC circuit with R 1 .Q, C 1 F 1s excited by input e -2t Obtain the expression for voltage across the capacitance in time domain, using the impulse 5 response of the system. 5

Determine Laplace transform of the
function f shown below. 5
<img src='./qimages/21-5a3.jpg'>

Realize a half-adder circuit using only NOR gates.

With a neat circuit diagram, explain the operation of a 1 80° variable half-wave rectifier along with its gate trigger circuit.

Define the following 2x5= 10 Skin depth Intrinsic impedance Phase velocity Group velocity Surface impedance.
In a medium <img src='./qimages/21-5d2.jpg'>
A Bridge-T network is made up of four capacitances, each having a value of 1 farad. Determine y parameters of this network, assuming that this Bridge-T netv.rork can be treated as parallel interconnection of two two-port networks. 1 2
For the network shown below, determine R L which will receive maximum power. <img src='./qimages/21-6a2.jpg'>
An silicon transistor is used in a common-collector circuit as shown in the figur e below. The circuit component values are V cc 3 · 0 Re l <img src='./qimages/21-7b1.jpg'>
Three identical cascaded stages have an overall upper 3-dB frequency of 20 kHz and a lower 3-dB frequency of 20 Hz. What are f L and f H of each stage? Assume non-interacting stages. 8

Explain how a separately excited d.c. generator and a d.c. shunt generator be operated below the knee of its magnetization curve. 10
A series motor has an armature resistance of 0·7 ohm and field resistance of 0·3 ohm. It takes a current of 15 A from a 200 V supply and ru 11.s at 800 r.p.m. Find the speed at which it will run, when connected in series with a 5-ohm resistance and taking the same current at the same supply voltage. 1 0

Design a combinational logic circuit which produces an output equal to l the input variables have more in the sequence than O's. The output is zero otherwise. Design the circuit for three variable inputs. Draw the realization. 10
The waveforms shown in the figure below are applied 1 . positive edge-triggered SR flip-flop; 2 . master-slave SR flip-flop. Draw the output waveforms in each case. <img src='./qimages/21-7a2.jpg'>
Distinguish between voltagecon trolled power devices and current-controlled power devices with examples.
What are the characteristic features of a GTO in relation to a thyristor? 8

Distinguish between the rrurumum current required to turn-on a thyristor and the minimum current to keep the thyristor in conduction. Explain with reference to the static characteristics of a thyristor. 6

Explain sensitivity, selectivity, fidelity and tracking m superheterodyne receiver with relevant diagram.

What 1s tracking error m superheterodyne receiver? How 1s receiver aligned to achieve three- point tracking? 6

Bring out the SSB spectrum with modulating signal cos2n 1500t cos2rr3000t and carrier is cos2n1 5000t

A signal 1 cos 1001t t 1s sampled with sampling interval of 0·02 second. Can the original signal 8 be recovered from these samples? 5

Find z transform of the function fin) a" cos( Sketch its RoC. 8

Determine Fourier transform of the function f e -al ti . Sketch its magnitude spectrum. Assume a 0. 7

A single-phase, 50 Hz, 1200 1 2 0 V transformer gave the following results of open- circuit test with high-voltage winding open circuited-applied voltage 1 2 0 current 1 6 power input 400 W. Find magnetizing and core-loss components of no-load current. 8

The power input to a 50 Hz, 4-pole induction motor running at 1 442 r.p.m. is 60 kW. Find the total mechanical power developed and the rotor copper loss per phase, if the total stator loss is 1 kW. 12

What 1s characteristic impedance of a transmission line? Write the expression of characteristic impedance of lossless line and distortionless line in terms of the primary constants C of the transmission line. What 1s the relation between characteristic impedance and input impedance of a matched line? 8
Explain the use of quarter-wave transformer for transmission line matching. 6

A lossless transmission li ne having characteristic impedance of 500 .Q is connected to a load Z L . Determine the ref lection coefficient and transmission coefficient.

Note English version of the In structions 1s printed on the front cover of this question paper.