EEE209 - Bangladesh University of Engineering and Technology

L-2/T -2/EEE Date: 17/02/2018

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-2/T -2 B. Sc. Engineering Examinations 2016-2017

Sub: EEE 209 (Engineering Electromagnatics)

Full Marks: 210 Time: 3 Hours

1.

2.

USE SEPARA TE SCRIPTS FOR EACH SECTION

The figures in the margin indicate full marks.

SECTION -AThere are FOUR questions in this section. Answer any THREE.

All symbols have their usual meanings.

(a) State Gauss law and Gaussian surface. By applying Gauss's law show that theelectric field intensity at a point due an infinite sheet of charge does not depend on the

distance of the point from the sheet.

(b) Define Electric Scalar Potential. Show that E =Wand V2V = _ Pv .E

(c) Two conducting cones (0 = !!..- and 0 = lr) of infinite extent are separated by an10 6

infinitesimal gap at r = O. If V( e = 1~) = OV and V( e = ~) = 50 V, find VandE

between the cones. Consider the co-axial cone as shown in Fig. 1 (c) .

.-..----:..--~~~-.--Iz . -::::'"::::::::::-:v-~

-:-----' .....••

. "r

· ... 1

I

, I~l. I

\ .•. I

(a) Explain image theory.' Mention the conditions that are to be satisfied in applyingthis theory. Determine the system of image charges that will replace the conductingboundaries that are maintained at zero potential for an infinite line charge of density

CPJ) located midway-~ -----.- -I

----- ~--~.~._----~---~"-~-----~.

---_ --- ........--_.:-..-_-----. _.,- __ .~-~~.~._-,'. ." .-...:::o.--'-~.f:J;----.--------.-.--.-.--.- ..-.---.- ---:--..--:-__--it . b o ._._...£j~(t:-.~c.~)-:

/' ""..r . I

.- I'. __ ~ ..__ -....-...._=....,... ._._ :.-":_.:....._ .. --:.:~~=:.=.- -_.__ .__._~ .. ~~__. ~.__'"...__._~1

Contd P/2

(10)

(10)

(15)

(10)

=2~EEE 209Contd ... Q. No. 2(a).

between two large intersecting conducting planes farming a 60° angle as shown in

Fig.2(a) .

(b) Calculate the energy expended in moving a point charge 500 (PC) from

P{2,;,-1) to P2(4,-~,-1) in an electric field E=ar6Jrsin9+a(63rcos9(Vlm)

by (i) first moving from 9 = Jr to Jrat r = 2 then from r = 2 to 4 at 9 = - Jr .322

(c) For an electric dipole having dipole moment P, show that V = P.ar .~ (volt)4Jr Eo R

where P = qd.

From the above expression show that lEI = -P-.-4-.J3 cos2 e+1 V1m.4Jr Eo R

3.. (a) Show that the force on a current element I dl due to a magnetic field B is equal to

F=fl dlxB.

Also, show that Torque experienced by a current carrying circuit in a magnetic field Bis given by

T=mxB(b) A semicircular loop of radius 0.25m and carrying current ?O A in clockwisedirection is situated in a uniform magnetic field. It is on the x-y plane with its center atthe origin and the diameter along the x axis as shown in the figure. Calculate the forceon the circular part and on the diameter of the loop. Also calculate torque on the loop.

The flux density is given by B = OAax + 0.3ay + .05azT .

~;::

______..._ ... .____ ..-----.f-C~-:--3Tb)-,---"-~-~- -~._-*-- ...-. -------._--~~--"--- - ....

----.--.:.-~-- . i

(c) If B = 0.5aJ , compute the magnetic flux passing through a hemisphere of radius 10

cm centered at the origin and bounded by the plane z = 0 as shown in the figure.

z

(10)

(15)

(12)

(15)

(8)

y

x

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EEE209

(12)4. (a) The magnetic vector potential of two parallel infinite straight current filaments in

free space carrying equal current I in opposite directions is

A= JLllnd-r a21! r Z

where d is the separation distance between the filaments (with one filament placed

along the z-axis). Find the corresponding magnetic flux density B .(b) The interface 2x+y = 8 between two media carries no current. If medium 1

(2x+y~8) is nonmagnetic with HI =-4ax+3ay-azA/m, find (i) the magnetic

energy density in medium 1 (ii) B2 in medium 2 (2x + y ::;;8) with P = 10Po' (iii) the

angles HI andH2 make with the normal to the interface. (12)(c) By using stored magnetic energy determine the inductance per unit length of a two-wire transmission line with separation distance d. Each wire has radius a as shown in

the figure. (11)- ~--- ~~----------~.-

F-t~.. 1 Cc..)

•... '\..,

1r,

" ".t-' . :_,

d---'-~'-"-"""-"""'=-----T-"---"'-~-=--'~----~'-"--=~--

.~

SECTION-BThere are FOUR questions in this section. Answer any THREE questions.

5. (a) Write down Maxwell's equations in both differential and integral forms. Use theseequations to derive the expression of non-homogenous wave equation for scalar

potential V in a homogenous medium.

(b) The conducting bar shown in the figure below can slide along :t y directions over a

conducting rail of negligible resistance.-- ------- -----

(13)

(12)x x x x x

~. H' ~~ ,- )

l'~. ,

~x

xB

x

x

x

x

x

x

x x x

x

x (

X'f

x

• x

z

/ y

Figure for question 5(b)

Contd P/4

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EEE 209Contd ... Q. No. 5(b)

If the conducting bar is 5 cm long, calculate the voltage induced in it while it slides at avelocity of v = 15 ay m/s through a magnetic flux density ofB=2sin (105t - y) az mWb/m2• Also calculate the induced voltage if the magnetic flux

density is changed to B = 5 aymWb/m2•(c) Define conduction, convection and displacement currents. For a parallel platecapacitor connected to a sinusoidal input voltage, show that the displacement current in

the capacitor is the same as the conduction current flowing through the wire. (10)

6. (a) The electric field component of a plane electromagnetic wave in a lossless medium

is given by the expression: (13)

E(z)=ay(E;e-Jkx +E;eJkx)If the permittivity and permeability of the medium are Band Il, respectively, derive the

instantaneous expression of the magnetic field component of the EM wave.

(b) For two arbitrary shaped conductors separated by a lossy dielectric medium, show

that ,RC = Bla. Use this expression to derive the leakage resistance per unit length

between the inner and outer conductors of a coaxial cable, which has an innerconductor of radius 1'1 and outer conductor of radius 1'2. The medium separating the two

conductors has a conductivity of a and dielectric permittivity of B. (11)(c) A lossy dielectric has an intrinsic impedence of 100L25° Q at an angular frequency

of co. The magnetic field component of a plane wave propagating through this

dielectric is given by: (11)H = 25 e-aycos(cot-OAy) az Aim.Calculate the value of skin depth in this medium.

7. (a) Define Poynting vector. Derive the expression of time averaged Poynting vector fora uniform plane wave propagating in a lossy medium having intrinsic impedence

of1Jc = l1JcleJ8 . Assume that the wave is propagating along the +z direction with a

magnetic field intensity ofH(z) = ay Ho e-(a+j13)z. (14)(b) Based on the principle of conservation of charges, derive Kirshoff's current law.Also write down the boundary conditions for normal and tangential components of

current density at the boundary of two ohmic media having conductivities al and a2. (12)(c) Define loss tangent in a medium. For a plane wave of 1.5 GHz frequency, theamplitude of electric field intensity is 120 Vim. If this wave exists in a medium having

relative permittivity of 2.5 and a loss tangent of 0.002, calculate the average power

dissipated in the medium per cubic meter. (9)

8. (a) A plane transverse electromagnetic wave of 30 MHz frequency is propagating in airalong the +z direction with a y-polarized electric field component of 15 V1mamplitude. Suppose this wave is incident normally on a lossless medium (located at

z ~ 0 as shown in the figure below), which has a dielectric constant of 3. Calculate the

following: (13)Contd PIS

=5=EEE209Contd ... Q. No. 8(a)

air losslessmedium

. Figure for question no 8(a)

(i) standing wave ratio of the wave in air

(ii) instantaneous expression of magnetic field intensity in the lossless medium

(iii) time averaged power densities in both air and the lossless medium.

(b) 'An electromagnetic wave propagates faster in a good conductor than in a low-loss

dielectric' - do you agree with this statement? Justify with necessary derivations.

(c) In phasor domain, write down the expression of a linearly polarized E field

propagating along +z direction and resolve it into two circularly polarized components.

Under what condition superposition of two linearly polarized waves results in elliptical

polarization?

(12)

(10)

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L-2/T-2/EEE Date: 22/02/2018. BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA


Sub: EEE 205 (Energy Conversion II)


USE SEPARATE SCRIPTS FOR EACH SECTION

SECTION-A

There are FOUR questions in this Section. Answer any THREE.

The questions are of equal value.

1. (a) Describe the constructional details of stator and rotor of high power non-salient and

salient pole synchronous generators. With diagrams of stator and rotor mention the

purposes of their different parts.

(b) Explain how from test the EA, RA and Xs are found out. Explain why the short circuit

characteristic of the synchronous generator is a straight line.

2. (a) Explain how synchronisation of an alternator to the bus-bars is carried out by using dark lamp

and bright lamp methods, and by phase sequence indicator and synchroscope.

(b) Two 3-phase 6.6 kW Y-connected alternators supply a load of 3000 kW at 0.8 power factor

lagging. The synchronous impedance per phase of machine A is (0.5 + j 10) n and of machine B

is (0.4 +j 12) n. The excitation of machine A is adjusted so that it delivers 150 A at a lagging

power factor and the governors are so set that load is shared equally between the machines.

Determine the current, power factor, induced e~m.f and load angle of each machine.

3. (a) Derive the phasor diagram of salient pole synchronous generator at lagging power factor

condition. Explain the terms Xd and Xq• Derive also the expression of power for a salient pole

synchronous generator neglecting the armature resistance. What is reluctance power?

(b) Explain the normal, under and over excitations of synchronous motor. With necessary phasor

diagram explain what V-curves are. What is hunting of synchronous motor? How hunting can be

damped?

4. (a) Using phasor diagram explain the effects of load change on synchronous motor. How proper.

direction of reactive power flow is maintained during load increasing?

(b) A 480 V, 50 Hz 4-pole synchronous motor draws 50 A from the line lit unity power factor and

full load. Assuming that the motor is lossless, answer the following questions:

(i) What is the output torque of this motor?

(ii) What must be done to change the power factor to 0.8 leading? Explain your

answer, using phasor diagrams.

Contd P/2

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EEE205Contd •••Q. No. 4(b)

(iii) What will be the magnitude of line current if the power factor is adjusted to 0.8

leading at full load.

(iv) If the motor is V-connected with synchronous reactance 1.1 Q per phase and

negligible armature resistance find the value of EA and load angle 8 at full load 0.8

leading power factor.

SECTION-B

There are FOUR questions in this Section. Answer any THREE.

The figures in the margin indicate full marks. All the symbols have their usual meaning.

5. (a) Answer the following to-the-point.

(i) Why in a DC shunt motor speed adjustment below the rated one is not done usingfield current control?

(ii) Why in a DC shunt motor speed adjustment above the rated one is not done usingarmatm:e voltage control?

(iii) What will happen if a loss of field event occurs while a DC shunt motor isrunning?

(iv) Why a series DC motor shaft should be firmly coupled with its load?

(b) A 10 hp 120 V DC shunt motor has a no load rpm of 1200. Its total armature

resistance is 0.06 ohms and total field circuit resistance is 60 ohms.

(i) What will be the rpm if its line current at full load is 70 Amps?

(ii) Determine the rated output power, rotational loss, convertible power loss, copperloss and efficiency.

(20)

(15)

6. (a) Explain with necessary figures cross-field and double revolving field theorems for the

operation of a single phase induction motor? (20)

(b) A single phase induction motor with split winding is designed to operate from 240volts 50 Hz supply. Its main winding impedance is 2+j3.5 ohms and auxiliary winqingimpedance is 9.l5+j8.40 ohms. The proportionality constant for torque is 1 N-m/Amps2.

Determine the following in locked-rotor condition. (15)

(i) The locked rotor torque developed.

(ii) How much external resistance to be put in series with the auxiliary winding sothat two windings' currents have a phase difference of 30°?

(iii) The percentage change (increase or decrease) in the locked rotor torque with the

added resistance mentioned in (ii) above.

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EEE 205

7. (a) Explain the major problems that occur in the commutation process in a DC machine? (15)

(b) Explain the remedies to the problems mentioned in (a) above. (12)

(c) A single loop armature DC machine shown in Fig. for Q. No. 7(c) has the following

parameters: B = 0.4 T, VB = 48 V, 1= 0.5m, r = 0.25 m, R = 0.4 n

Will it work as a generator or motor if its speed is 500 rad/sec?

8. (a) What are the major difference between solar thermal and solar photovoltaic power

generation?

(b) The Figure for Q. No. 8(b) shows the I-V and P-V characteristics (respectively solid

curve and dotted curve) of a solar cell. The solar cell has an area of 1 cm x 1cm and is

illuminated with a light intensity of 1000 W1m2. Determine using the Figure.

(8)

(5)

(i) fill factor (FF) of this solar cell. (4)

(ii) load resistance and efficiency when the cell operates at Maximum Power point. (6)

(iii) load resistance when the cell operates at 9% efficiency and at a voltage of 0.6 V. (5)

(c) Describe using block diagrams the applications of photovoltaic panels in a solar

electric vehicle and a solar hybrid electric vehicle.

Fig. for Q. 7(c)

(15)

10

I-V Characteristics and P-V Characteristics of a Solar CellI , • I ",1' ,'", ,.,' ,.,' I " I

TiiH! .•!H::!TlI:iHTri!rlJJJlTI;.;;;.t~~v;.-~-~--:-~-~--r-:~~--;-:--:-:-:-T-i-i-~--i-~--:-:w--:~---:""'.-:, , I •• "-."--~--i.-;- ..i.-i--i.t--f. -r.-: t -- ~- - t _. ~- - i---l- - i_.-i-. i- --;---~--;---f. -f - - f ~ - f - - t _. i.-t - - i-.i..-;---;---;---i- ~ -,l- - -f - -f - I - -r - -.t .. i.-i --i~__ I- _. ~ •• to ••• - _ •. - - • - - ~_ - ~. _ •• __ .• _ •••••••• - _t- - -I- - _o. - _ •• _ ••.• _ •. .: _ •• - _. - _ •• - _ •• - _ .•••.• _ •••••.•• - _t_ - -I- - _t- __ •..• _o. - -.. -I- - _. - _0< ••••• ".

: : : ":. : : : : :.: :.: : : : : : : : : : : : : : : : : : : : : . : : : :--~--~ --~- -~--r - - r- "1--~.-;- -;- -T-;-'--:- --r--f .. r .. f •. r - -r.- - r - -1--~-- ;--;- .'r-;-- -r --f- -f--f. -r .or.-, - -r--; .. ~--;--:~::~::~~:~::~::~:.:~::~~:~::1::~::~~::~::~::~::~::~::~~:~:~i: ~~~~~::~:~.~~.~~:~~::~:::~:~~~~~~:~:~~::~--t ~:1~~1~~~-~~t~~t::t::!:: t::!~:j:: j~:j::j:: J::t:j: ::t::t :~t~:t::t:: t: :.1:: j:: j:: j:: j:: t:j:: J:::t::t::t::t:: t::t:: ::j:: 1::j:

, , I , .' , , , I I • I , • , •• , , , • , • , , , I , , • , , I , , • ,

15

25

20

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5

Fig. for Q. 8(b)I

\1

oo 0.1 0.2 0.3 0.4 .Voltage in Volts

0.5 0.6 0.7 \I

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L-2/T-2/EEE Date: 27/02/2018BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-2/T-2 B. Sc. Engineering Examinations 2016-2017

Sub: ME 267 (Mechanical Engineering Fundamentals)


(15)1.



SECTION-AThere are FOUR questions in this section. Answer any THREE.

Necessary graphs and ~bl~s are attached.

(a) Show that the theoretical pressure head rise across a centrifugal pump is given by-

H = u~ _ u2 Vn2 cot ~2

I g g

The notations have their usual meaning.

(b) A centrifugal water pump rotates at 2500 rpm. The impeller has uniform blade

widths bl = 11 mm, b2 = 5 mm, and radii rl = 21 mm, r2= 66 mm. The blade angles are

PI = 44°, P2= 30°. Assuming ideal conditions (frictionless flow, negligible vane

thickness, perfect guidance), with UI = 90° (no pre-rotation), determine (i) the

discharge, theoretical head, required power, and pressure rise across the impe~ler, and

(ii) the theoretical head-discharge curve. Use water as the fluid. (15)(c) "A pressure relief valve should be mounted at the outlet of a positive displacement

pump as a safety measure", is it true? Briefly explain you answer. (5)

2. (a) "Low density of refrigerant is always preferable", is it true? Briefly explain your

answer.

(b) A vapour compression refrigeration machine of 12 ton of refrigeration capacity has

evaporator and condenser temperatures of -28°C and 26°C. The refrigerant R-12 is

subcooled by 4°C before entering the expansion valve and the vapour is superheated

by 5°C before leaving the evaporator. The compression is isentropic and the expansion

is isenthalpic. The properties ofR-12 are given below:

Sat. Temp, Pressure, Sp. volume Enthalpy, kJ/kg Entropy, kJ/kg.K

°C bar of vapour,Liquid Vapour Liquid Vapourm3/kg

-28 1.093 0.1475 10.64 175.11 0.0444 0.7153

26 6.697 0.0262 60.67 198.11 0.2271 0.6865

The specific heat of liquid R-12 is 0.963 kJ/kg.K and of vapour R-12 is 0.615 kJ/kg.K.

Determine:

(i) Theoretical power required.

(ii) Mass of refrigerant to be circulated per min.

(iii) The coefficient of performance (COP) of the cycle.

Contd P/2

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(15)

(15)

=2=ME 267/EEEContd ...Q. No.2

(c) The operating temperatures of a lithium bromide-water absorption system are as

follows: (15)

Generator 100°C

Condenser 35°C

Evaporator 5°C

Absorber 30°C

The mass flow rate delivered by the pump is 0.4 kg/so The specific heat of water

vapour is 1.86 kJ/kg.K. Calculate-

(i) The heat supplied to the generator.

(ii) . The heat rejected at the condenser and absorber.

(iii) The cooling produced by the evaporator.

(iv) The coefficient of performance (COP) of the cycle.

3. (a) How can the efficiency of an ideal Rankine cycle be increased? Describe with the

help of a T-s diagram.

(b) A power plant operates on a regenerative vapor power cycle with one close feed

water heater. Steam enters the first turbine stage at 12 MPa, 520°C and expands to

1 MPa, where some of the steam is extracted and diverted to the close feed water

heater operating at 1 MPa. The remaining steam expands through the second turbine

stage to the condenser pressure of 6 kPa. Assume that the feed water leaves the heater

at the condensation temperature of the extracted steam and that the extracted steam

leaves the heater as a saturated liquid and is pumped to the line carrying the feed water.

Show the cycle on a T-s diagram, and determine (i) the thermal efficiency and (ii) the

mass flow rate into the first turbine stage, in kg/h, for a net power output of 330 MW. (20)

4. (a) Show that in a Pelton turbine the power delivered by the fluid to the turbine runner

can be expressed as- (15)

The notations have their usual meaning.

(b) Briefly describe the working principle of an evaporative condenser with neat \. )

sketch. (16)(c) Neatly sketch a schematic diagram of a steam condensing plant and label it. (10)

Contd P/3

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ME 267/EEE

SECTION-B

There are FOUR questions in this section. Answer any THREE.

Symbols have their usual meanings.

Assume a reasonable value of any missing data if necessary.

. "

5. (a) Discuss some applications of electronics in a modem internal combustion engine.

(b) With the help of a schematic diagram briefly explain how the engine cooling

system works.

(c) In a Diesel cycle, the compression ratio is 15. Compression begins at 0.1 MPa,

40°C. The heat added is 1.675 MJ/kg. Find (i) the maximum temperature in the cycle,

(ii) work done per kg of air, (iii) the cycle efficiency, (iv) the temperature at the end of

the isentropic expansion, (v) the cut-off ratio and (vi) the MEP of the cycle. Take

Cv = 0.717 kJ/kg.K, cp = 1.005 kJ/kg.K and Ru = 8.314 kJ/kg.mole.K.

(5)

(10)

(20)

6. (a) Show the gas power cycles (Otto, Diesel and Brayton cycle) on the P-v and T-s

diagrams. Also distinguish between them in a table. (Assume all the cycles as air

standard cycle.)

(b) Present a gas turbine with three stage compressors with intercoolers and two stage

turbines with a reheater in a schematic diagram and T-s diagram.

(c) Ashuganj Power Station Company Ltd. operates their power plant unit GTI using a

gas turbine whose capacity is 56 MW. The following are maintained during the

operation of their gas turbine unit:

Turbine inlet air temperature 27°C

Turbine inlet air pressure 0.1 MPa

Pressure ratio 6.25

Maximum temperature inside the turbine 800°C

Using air standard Brayton cycle analysis, find:

(i) the compressor work per kg of air,

(ii) the turbine work per kg of air,

(iii) the heat supplied per kg of air, and

(iv) the cycle efficiency.

Take Cv = 0.717 kJ/kg.K, cp = 1.005 kJ/kg.K and Ru = 8.314 kJ/kg.mole.K.

Contd P/4

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(8)

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ME 267/EEE

7. (a) What do you understand by critical radius of insulation? Show necessary

mathematical formulation to obtain a critical radius of insulation for an electric wire

insulated using a plastic covering.

(b) Four identical power transistors with aluminum casing are attached on one side of a

I-cm-thick 20-cm x 20-cm square copper plate (k = 386 W/m.K) by screws that exert

an average pressure of 5 MPa (Fig. for Q. No. 7(b)). The base area of each transistor is

8 cm2, and each transistor is placed at the center of a IO-cm x lO-cm quarter section of

the plate. The interface roughness is estimated to be about 1.5 !-Lm.All transistors are

covered by a thick Plexiglas layer, which is a poor conductor of heat, and thus all the

heat generated at the junction of the transistor must be dissipated to the ambient at

20°C through the back surface of the copper plate. The combined convection/radiation

heat transfer coefficient at the back surface can be taken to be 25 W/m2.K. If the case

temperature of the transistor is not to exceed 70°C, determine the maximum power

each transistor can dissipate safely, and the temperature jump at the case-plate

interface. (Consider the thermal contact conductance of copper-aluminum interface as

he= 42,000 W/m2.K)

.•~

(10)

(15) .

II

, 70°C

Fig. for Question no. 7(b)L----

(c) Mention five major sources of renewable energy. Discuss them in the context of

Bangladesh. In your discussion, construct a table"showing their relative advantages and

disadvantages, their present application status in Bangladesh and whether they are

feasible or not in case of Bangladesh.

Contd PIS

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=5=ME 267/EEE

8. (a) Classify the following boilers based on working pressure, boiler axis, installation

type and tube containment (water/fire) in a table.

(i) Cochran Boiler,

(ii) Lancashire Boiler,

(iii) Cornish Boiler,

(iv) Locomotive Boiler,

(v) Babcock and Wilcox Boiler.

(b) Identify the following components as boiler mountings or accessories and mention

their two important featllfes.

(i) Steam stop valve,

(ii) Feed water pump,

(iii) Air preheater,

(iv) Economiser.

(c) Show a nuclear power plant III a schematic diagram and mention its major

advantages and disadvantages.

(b) High pressure boilers are normally water tube boilers. Why?

(10)

(10)

(10)

(5)

.- .- .~ _ .•••, •••• j •. -

~.,tv\E 2.6=1IF:. 'tt: -6-- -

,/~if., ~aturated water-Temperature table~~ -- Qt ' .r~,. Specific volume, Internal energy, Enthalpy, Entropy,

.m3/kg kJ/kg kJ/kg kJ/kg . K, .1 Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat.

.Temp., press., liquid, vapor, liquId, Evap., vapor, liquid, Evap., vapor, liquid, Evap., vapor,TOG Psat kPa v, vg u, U'g ug hf htg h Sf Sfg Sgg

0.01 0.6117 0.001000 206.00 0.000 2374.9 2374.9 0.001 2500.9 2500.9 0.0000 9.1556 9.15565 0.8725 0.001000 147.03 21.019 2360.8 2381.8 21.020 .2489,1 2510.1 0.0763 8.9487 9.0249

10 1.2281 0.001000 106.32 42.020 2346.6 2388.7 42.022 2477.2 2519.2 . 0.1511 . 8.7488 8.899915 1;7057 0.001001 77.885 62.980 2332.5 2395.5 62.982 2465;4- 2528.3 0.2245. 8.5559 8;780320 2.3392 0.001002 57.762 83.913 2318.4 2402.3 83.915 2453.5 2537.4 0.2965 8.3696 8.666125 3.1698 0.001003 43.340 104.83 2304.3 2409.1 104.83 2441.7 2546.5 0.3672 8.1895 8.556730 4.2469 0.001004 32;879 125.73 2290.2 2415.9 125.74 2429.8 2555.6 0.4368 8.0152 8.4520

5.6291 25.205 146.63 2276.0 2422.7 146.64 2417.9 2564.6.;..

35 0.001006 0.5051 7.8466 8.35.1740 7.3851 0.001008 19.515 167.53 2261.9 2429.4 167.53 2406.0 2573.5 0.5724 7.6832 8.255645 9.5953 0.001010 15.251 188.43 2247.7 2436.1 188.44 2394.0 2582.4 0.6386 7.5247 8.163350 12.352 0.001012 12.026 209.33 2233.4- 2442.7 209.34 2382.0 2591.3 0.7038 7.3710 8.074855 15.763 0.001015 9.5639 230.24 2219.1 2449.3 230.26 2369.8 2600.1 0.7680 7.2218 7.989860 .19.947 0.001017 7.6670 251.16 2204.7 2455.9 251.18 2357.7 2608.8 0.8313 7.0769 7.908265 25.043 0.001020 6.1935 272.09 2190.3 2462.4 272.12 2345.4 2617.5 0.8937 6.9360 7.829670 31.202 0.001023 5.0396 293.04 21l5.8 2468.9 293.07 2333.0 2626.1 0.9551 6.7989 7.7540

75 38.597 0.001026 4.1291 313.99 216L3 2475.3 314.03 2320.6 2634.6 1.0158 6.6655 7.681280 47.416 0.001029 3.4053 3~4.97 . 2146.6 2481.6 335.02 2308.0 2643.0 1.07~6 6.5355 7.611185 . 57.868 0.001032 2.8261 355.96 2131.9 . 2487.8 356.02 2295.3 2651.4 1.1346 6.4089 7.543590 70.183 0.001036 2.3593 376:97 2117.0 .2494.0 377.04 2282.5 2659.6 1.1929 6.2853 7.478295 84.609 0.001040 1.9808 398.00 2102.0 2500.1 398.09 2269.6 2667.6 1,2504 6.1647 7.415:]:

100 101.42 0.001043 . 1.6720 419.06 2087.0 2506.0 419.17 '2~56.4 2675.6 1.3072 6.0470 7.3542105 120.90 0.001047 1.4186 440.15 2071:8 2511.9 440.28 2243.1 2683.4 1.3634 5.9319 7.2952110 143.38 0.001052 1.2094 461.27 205i5.4 2517.7 461.42 2229.7 2691.1 1.4188 5.8193 7.2382115 169.18 0.001056 1.0360 482.42 2040.9 2523.3 482.59 2216.0 2698.6 1.4737 5.7092 7.1829120 198.67 0.001060 0.89133 503.60 2025.3 2528,9 503.81 2202.1 2706.0 1.5279 5.6013 7.1292

125 232.23 0.001065 0.77012 524.83 2009.6 2534.3 525.07 2188.1 2713.1 1.5816 5.4956 7.0771130 270.28 0.00i070 0.66808 546.10 1993.4 2539.5 .546.38 . 2173.7 2720.1 1.6346 5.3919 7.0265135 313.22 0.001075 0.58179 567.41 1977.3 2544.7 567.75 2159.1 2726.9 1.6872 5.2901 6.9773140 361.53 0.00.1080 . 0.50850 588.77 1960.9 2549.6 .589.16 2144.3 2733.5 1.7392 5.1901 6.9294145 415.68 0.001085 .0.44600 610.19 1944.2 2554.4 610.64 2129.2 2739.8 1.7908 5.0919 6.8827,150 476.16 0.001091 0.39248 631.66 1927.4 2559.1 632.18 2113.8 2745.9 1.8418 4.9953 6.8371155 543.49 0.001096 0.34648 653.19 1910.3 2563.5 653.79 2098.0 2751.8 1.8924 4.9002 6.7927.160 618.23 6.001102 . 0.30680 674.79 1893.0 2567.8 675.47 2082.0. 2757.5 1.9426 4.8066 6.7492165 700.93 0.001108 0.27244. 696.46 1875.4 2571.9 697.24 2065.6 2762.8 1.9923 4.7143 6.7067170 792.18 0.001114 0.24260 718.20 1857.5 2575.7 719.08 2048.8 2767.9 2.0417 4.6233 6.6650

4.5335.. t'

175 892.60 0.001121 0.21659 740.02 1839.4 2579.4 741.02 2031.7 2772.7 2.0906 6.6242180 1002.8 0.001127 0.19384 761.92 1820.9 2582.8 763.05 2014.2 2777.2 2.1392 4.4448 6.5841185 1123.5 0.001134 0.17390 783.91 1802.1 2586.0 785.19 1996.2 2781.4 2.1875 4.3572 6.5447190 1255.2 0:001141 0.15636 806.00 ' 1783.0 2589.0 807.43 1977.9 2785.3. 2.2355 4.2705 6.5059195 1398.8 0.001149 0.14089 828.18 1763.6 2591.7 829.78 1959.0 2788.8 2.2831 4.1847 6.4678200 1554.9 0.001157 0.12721 850.46 1743.7 2594.2 852.26 1939.8 2792.0 2.3305 4.099.7 6.4302

rt'ob\e do~ &,N()-02.~)

~- ,,_ .. _~.......• '~~.;;- ,.~~ .

•. .". "~

FIGURE B3 Equilibrium chart for aqueous lithium bromide solutions

"-U

"

~rt1

~0"

~tiT\i1rrr

, I,.."0

'ia~III

I

V:>

30 ~•.g"

20 ""-a~'(l

?;;•.

:I

10 ;9

40

l~O

100

180

I- 50

I" 'r-, 5rt -.

170

I

~

tiISO .60

I

.1_1." .__1- ....• .4__

f-'I.

'40'30

i,Tif

'20

'l'

f?jy.

"0! '

i-toI

100I

~

17.

90

~c-V>

v

&0

v/y/

f.-'-'"-\ -

~

70

,..-/Y}~/./(A

'/

(/

60

+-+-+-.+-!-I I I I I.L

C = 7.05

o = --1596.49E,= -104 095S

SO4030

2. l' = IT _ ~~B)("}/~~A.x" Refrigerant temp., .C

3.\og P=C+Drl + Err'. F =kl'a; r=K

4.1'= ~'2ED+[D2~4E(C - logP}flS

"" = HlO7 55 B. = 124.937A, = 0.169 76 8, = -7.716 49", = -3.133 326 E-03 B, = 0.152286A, = 1.97668 E-05 B; = -7.950 90 E-04

RANGE: -IS < T < IlO'CS< T< 175'-(;

'45 < X < 70% LiBr

Solution temperau-'re. 'C

£QUA-nONS

I . T = l:~8)(" + .,..l:~A.x'Solutio" temp., .C

Reprinted by pennissioil from ASHRAE, 1997 (page 19.85).

'~:.:~~;~.':.."~~.,..._....,;;:,.,..;,~-~~;~~~;;,.:~~:;;"~;~:::,.;>..".",~~~ ~;;';'-;~;~~:;:;:"'':;;;':;::;'~;;;:'':;'-';7"~.:;;,~:;:,:;-;..>:::_~~~.;:;;;.;;.:;;.;;:-;.::.:..-;;;:~~~~/;?+;::''''.;{;-::~~-:tc!:.''V:!''£'''~''~~~~';.~'''''~-'';''=~~' __'_~~_'.-".-

8=

,Lithium: bromid~ concentration. mass percent

Conce.ntration range Temperature range40 < X < 'j()% LlBr 15 <1' < 165°C

r r:c"x" in kJlkg. where T = °C and X ,. %LiBrBo 18,2829 Co -3.7008214E-2B, -1.1691757 Cj 2.8877666E~3BI 3,24804]E-2 C2 = -8.1313015E-5B3 -4.0341 84E-4 C) 9.9116628E-7B. J.8520569E-6 C4 = .;.4.4441207E~9

.~

.2o.,

Equations

h;;" I::A"Xi, + Tr..:B"x" +Ao'.:'7, - 2024.33'A, <=' 163.309~2 -4.8816]"

'~:i = 6.302948E~2A4:,,:-:2,913705E-4

FIGUREB4 Enthalpy-concentration diagram for waterl1il~ium bromide solutions.

Reprinted by permission from ASHRAE, 1997 (page 19.84).

~_ [-:.:-A-p~pe-n-d-iX-'-B-':-,' -Re-fl-'i-ge-'-an-[-':'-P-ro-p-e-r[-;e-S----- __ -_-_'_--_-_.-_'-=--=-~~=~::::::--:--:-----~:-,------.---- -_-,-j

I

A! -'I

!~ :

1.'

,.

.,;.--,-.-:- .•...-::.., ... ~.' ,

'.

..~_:-~-_..-....,.:=::~:;:~~"~*:~~~~.•'----...~.. . -. . '.

.._ ••••• M ••• ,.# ••• __ •••••••

.:...:.~.'_.,..: •••••.:...:.:.:.:..-: .••.••..•~"'>J~ " _.~.

: ,.... .:.:. ~ " ',. ...•., .

0.14 109.3. 0.001051 1,237 458.2 2517.3 458.4 2232.0 2690,4 1.4112 .. 5:8360 7.2472

0:16 113.3 0.001054 1.091 475.2 2521.8 .. 475;3 2221.2 . 2696.5 1:4553 .' 5,7472 .' 7.2025

0.18 116.9 0.001058 0.9775 490.5 2525.9." 490.7 2211.1 2701:8 1.4948' 5.6683 . 7.1631

Table C.2b Saturated Water, Pressure Table (Metric Units)

zc:>I

o(,).D~

-? - -""':.

':..:,["

SZ>

. ..:.-)5>.er .~(\)

,~

.(,.

",

. . . - . - ~.'~" ..:~.. -:- '. ".-

..

.".'.' o:~.

0.0016110.0017110.0018400100203I~

'--•••-.l ••.~'~I~~-.i.MiD-:s~~'t,~!~~J";::'~~~,~.>..~*,,:fr..;:-~.,,:;,::,.;,:::-.•.."?.4~~?';~.J:>_;;,~~,:,~.";_~.;,.-...••••.,..,.;>"',"')I~~:t!~j-;""",,,,":';"~.r""""""''''',_~-.''''''''-_M~ n' .,_~.". T"

Note: Saturated liquid entropies have been adjusted to make the Gibbs functions of the liquid and vapor phases exactly equal. For this.reason, there are some smali'differences.between'valuespresented here and the original tables. . . . . . .... ,.. .: .Sources: Reprinted by permission from Reynolds, W. C., Perkins, H.C. Engineering ThermOdynamics, second ed., 1977, McGraw-Hili, New York. Recalculated frOm'equations.giVen in Keenan, J. H,Keyes, F. G., Hill, P. G., Moore, J. G. Steam Tables. Wiley, New York, 1969. Reprinted by permission of John Wiley & Sons, Inc. . ... . .

.: .... ; -_.

..",'.;

zo1

oIN

/iY'C/

.$2'::>' ..

.~ .

?7SL

' ..~

.....

-~~ . u,kJlk; 2564.5 ;~;6.~ 2726.1 ;~:~ ;~~~ ~~~ ;;;;6'.~ 3129.2 ;;1~.~ ;;;'2 .~~~;'.9 ~~.5.;;9 ~I:~W"I$ t~0.4 143.6 ,;-''',",''. ~

( ) h, kJlkg 2752.8 2860.5 2964.2 3066.7 3169.6 3273.4 3378.4 3484.9 3592.9 3702.4 3926.5 4157.4 -4395.1 r:~ '11

- 5, kJ/(kg.K) 6.9307 :7.1714 7.3797 7.5670 7.7390 7.8992 8.0497 8.1921 8.3274 8.4566 8.6995 8.9253 9.1370 ~}~'t:'" r.~!.'\ ~,c _. » "'~~._ 1. - _ - ~~ - ,':0- ~_ ,'="'~'_~""""'" ",.... _...••.•..JIo••.•.'~ ••". .•. ~':!e""'''''''''''''~ ,..., •..,..". '. ~ .• '.~c:r.~.. _ ~~'_~ _ ~ ••.••1~'::'~ • '_ ~ _' ::tr~ .•.'!"=t''+o~-:; • >!'.tJ?: ""'""_ :~. l,~'''''''_.'' -'~~. - •.- .m3"i<.?('> •.~41""l~~<}~3 •.•..$~&~~c.,'t~,~~~.("~"~n~"~~An''>Cl.,<>~'''''';n'"~ ••~~,A~"''''<'~''<~.,~.;w&;n'''''~~!iirt'...w:i.''n~~.'''''"'1i:O~,,~~ ..~~'~.m.''''M~~".''''''n.7A7~Vrr;&'l;'n.MA~~~~A7~ "~H'''.~ l

( \.-:-' .li~f'~~~-ii.tffi~stkj/(I!9.O!5J""1"W'<r~:..._."':<";1t:>~i\;\i~..L~6..9673£j,,;\%,~E~'182(r.~J"!"'l,9i7~3732~~~7;5!l7:2~i~~~~7.;1Q85;~...';i¥i~z;:86db~4i"\'iWe:tti2.9:i";tr,~t{8;:!386~!tf~..c82682t\~}k"'.e:$1j$':"*..:~";$~fEfI375.~~~8~g;494~1 tI&.,..9~.f..~:ttS~.' I': ~~ ~.••..~_~~~_ ••~wr~\i~ .•~ ..••....•.,.••..,.".••.2,)'~l:"~~ ~~,';"~>(.~~."':t'.-~ •.•.~:"~.."•..~,;p;$;.~~:,,>:_.~~~~<ie=;:.--.~~~~~#"<lG<:r.-'V:- .••.,,~,..,,_,.~~~.~ ..••__ i.~~ ••.""-~....::: ••~~~.~!; ••••~:,i~.__~' .•••..,:;••••..••~:M~~;.,~l:.M ••~<jm,::-:.:nl'flr~.J',~~~;.~l4Ir").;.7:l'~a:~_ ••:"r.}-~ •.••..•••.~... '~r~ ....--< " '.' .' V, m3~g . ,- '.. 0.2608 0.2931', 0.3241 .' 0.3544 . . 0.3843 . . 0:4139 •O.~ 0.4726,' 0.5018 ,0:5601 . 0.6181 '. 0.6761.'. l~]:.~~ u •,

~ .1 >~~-=<;_~J3~,9..~~~""".""."~~~,,•.,""",,~~~2~;~'".,.""''',::.:~;~"";=<>.~~.,:~~7.~:.;.~=1;~~~"~-!~;.,~._""~;.~;"....•,.,..~.~.~,.'"',~~;;9~,~~~1 m,~~~,~1 ~~~~ if.><J "'~"'\"""'"*<.'~l'*ii"'m J1iti'",c••',!;<f"~"~*'t~'~,~s:.;;'~""J;iLn:?MO~.",.",,...'irr?~?7.::i'!\.,,<);'''''n'?<;7Q"••...,Cl""n?A?<;''','''''~n.~.',;;.''',;,''b''.~'U\A$''' ••>'K\' •••.'.,'''''".,1''''M~n'''77'''~~'''''''''<''.""'i'",,,,'''''.'AA7<>. '" ,.,m .•a".,' ...• "ltn".n.,,,, IPM'.,O?~ I~ '.iii:~~"~~;':;'!~';m'."~ghll5lRg'-;~~(t<..~~g\\\'~.~!¥2827r9~f:;'f,..' ~~'29.'42!6~""I,~¥JI'.355f2r''''.~'I'~~.3f57.f7rli~~~~~.>~326fr91'l;r,..v.'''''.,i337Qi.l~)~~3'<I78%~f~~~.35;l'7':'51j;~{'l\.~.'369Z;9r;.\{;r-~3923~1'tW.'~.~fI'~~~t'.4tS;1'E~.:.~~~~..~r9~.;~ ~~W.~!;.-~' I~ %>~~-f~.l\!:1"~.'~'.;~~~~ij;;<:,~~.,j,.~tf;¥~~",<.!~~~~1:Jfu"&~.~,,~~",!h,'~t~:c~(""f".:if,'."'~&W,'!;'~fli.,."""N.~l@t1(~'''.•;I!i,j,.~~,,~~~~..,,~~~.~~;"'~~"'''''~~''"?t-~~,'f-i''ffi'~~~:~''''''';S.;-~:. '>'f ••'i''''''''~i~~'-'1.~"""~ "".;".:.,..~..<".,1.,II;;l:. IO ~","'t'('l,f. ,'It:.:o.'I',S,11<J/(kg,;~ "''' .•••1'••73''f"'''' •• "'~6.6948~~""t6.925S ;"<1':i!i'h1237&;~""'~".7'.3019~i\",~;it'%'7,;'I6S8;tt,,,",,,-,,,,"',7;;6188,~",••••,,,7;:,:I630""",,'tlc.8~..5'>,,~,,,,!8:0298Jm'1;'.8Z~40~~"'. 'c 8:SOOS.,'f5,~"1!!;8!1,127.E; ~~ .••••

,~ •.~~oi!t.oo_-'~.~~~,}..o,..!I:'~~h4_~ ...•.•,.... ~,,r-,~~!'iV"~~." ~~<'Il:""~,..:.._""i''':'l~;or.!"W~~.''' '",",. ~~~~ ~:;jy~,,,.~,.6.::~-.v .•.•."l;;~:l'.'lf.,,*,~ __ ;, ~••",~~~:r •.•.~",...,."..,~ ,.;-n:'r~~ •.•••.W'dilt"l;!..~,,;o;.,.:,,_~. • ;.f,.;.~::b?,!.?i:1 •..•••••r.;.~~ ••••~t'l'.i3\~""".ot',;;o;r., ~~~~,"",'

\ v, m3lkg - 0.1325 0.1520 .0.169.7 0.1.866 0.203.0'. 0.2192 0.2352 0.2510 0.2668 . 0.2981 .0~3292 ..0.3603 I>~~.'~"u, kJlkg - 2598.1 2695.3 2783.1 2867.6 2951.3 .3035.3 3120.3 3206.4 3293.9 34.73.2 3658.7 3850.8 .•..•ffi .,D 1.5(198.3) '. '. . .•...•~~~ '1(Jo /:I, kJlkg - 2.796.8 2923.2 .3037;6 3147.4 325S./l 3364.1 3473.0 3562.9 .3694.0 3920.3 4152.6 4391.2 ffl'a;;>~'.

r-;:- (Continued)~.'

." '

\~":~~~

r

" ~

. '.,

. ,,~~1r,il

"';";,.~, ':t'

~j,{-'r"l'f:f, ,if.:

II:l'

f,l'j! a,~! 1

!~1:L, i'Iji!:~

~.~(t).

't~

:2o\c

... (,)

.....f?.~

,}' .

~..,"~~.>-,'.~', I;. ,

';',

,.

Table C.3b Superheated Water Vapor (Metric Units) .

12 (324.8)

'.. ..

, .r-,.",i~~~"':""-'-:-";"---~::~"~~"""_~-, ..,. ;-': ;~;~'--" '; -. f • - t.;. h~' __ :::::-"::-; ;_~::"",,-~':. ~:~_~~~~~, ~;: " ,;. 'OM" ,,- ••• ~.: '.' _.... G ._ •.•• ~--.'.n ,__ .:""_ _ :....-". '., ~

< .

-L-2/T -2/EEE Date: 05/03/2018


L-2/T-2 B. Sc. Engineering Examinations 2016-2017

Sub: EEE 207 (Electronic Circuits II)



The symbols have their usual meanings.


SECTION-A


1. (a) Draw the circuit diagram whose output voltage is directly proportional to the

logarithm of its input voltage. Also derive the expression of its output voltage.

(b) Calculate Va, 10 and IL for the circuit shown in Fig. for Q. 1(b).

\0 U./l..

\OV

F\'~~' ~. 1. (10) -~

j

(8)

(12)

'+,?>V

(c) Calculate the value of output voltage Va for the circuit shown in Fig. for Q. I(c). (15)

V\u./l.. + .'1>

-+4V .-~----. -~v-".."R:;:---_"'"'-s_v __._. _

\ u..tL\" 1.(..It.

-"---

r--2. (a) Design a circuit using ideal Op-Amps so that the output voltage is

where, VI, V2 and V3 are input voltages.

Contd P/2

(10)

=2=

EEE 207

eouid ... Q. NO.2

(b) For the circuit shown in Fig. for Q. 2(b), Vio = 3 mY, Ip - = 0.4 ~A and Ip+ = 0.1

~A. (15)

'\

._--_.i,

---_._-,----~--_... ''::'5. ~ 6!.. 2(b)

(i) What is the best value ofR if the source internal resistance is 10 Q?

(ii) Calculate the individual error in Vo due to Vio,18+, 18- and los.

(iii) What is the actual value of Vo when both input offset voltage and currents

are present along with Vs?

(c) The slew rate of a 741 Op-Amp. is 0.5 V/~s. For an inverting amplifier with a gain

of 10, find the maximum peak to peak input signal that can be applied without

distorting the output at a frequency of 40 kHz. (10)

3.

4.

(a) Explain the different types of filters. Mention the advantages of active filters over

passive filters.

(b) Show the design procedure of a -60 dB/decade low pass Butterworth filter and

derive the expression of its cut off frequency with necessary diagram.

(c) A bandpass filter has a resonant frequency of 950 Hz and a bandwidth of 2700 Hz.

Find its lower and upper cut off frequencies. Also, calculate the quality factor of the

filter and comment on whether the filter is narrowband or wide band.

(a) Write down the Barkhausen criteria for sinusoidal oscillation.

(b) Draw the circuit diagram of a Wien Bridge Oscillator and derive the expression of

oscillating frequency.

(c) Design a phase shift oscillator having an output frequency of 1 kHz. Assume

R = R) = 5.6 KQ and R2 = R3. Also draw the designed circuit.

Contd P/3

(7)

(18)

(10)

(5)

(18)

(12)

•

=3=

EEE207

SECTION -B


5. (a) With necessary diagrams, derive the expressions of input resistance (Rif) and output

resistance (Ref and R~f ) of a current shunt feedback amplifier.

(b) Identify the topology of feedback amplifier given in Fig. for Q. 5(b)(i). Using the

small signal ac model of the Op-amp given in Fig. for Q. 5(b)(ii), ealculate-

(i) the voltage gain, Avf

(ii) input resistance, Rif

(iii) Output resistance, Ref and R~f .

Given that J.! = 104, Rid= 100 kQ, ra = 1 kQ, RL = 2 kQ, R1 = 1 kQ, R2 = 1 MQ and

Rs= 10kQ.

(18

(17)

___ i__-__ L_.--.-----~L~B ...

_____ f(~-,.-~~<1~~(~)_(i)---------9-\d~_lrra~~\!i )_0"')-J

6. (a) A particular amplifier has a voltage transfer function,

Sketch Bode plot for both the magnitude and phase.

From the plot estimate the magnitude and phase at ~ = 1,100 and 106 rad/sec (use

graph papers).

(b) Derive the approximate equation for the upper 3 dB frequency WH of an amplifier if

a dominant pole does not exist. Also show that the equation is valid even if the

dominant pole exists.

(c) What is cross-over distortion in power amplifier? How can it be overcome?

Contd P/4

(20)

(10)

(5)

•

=4=

EEE207

7. (a) With proper connection diagram, briefly describe the operation of non-sinusoidal

oscillation circuit using 555 Timer.

Also derive the expression of frequency of oscillation.

(b) Derive the expressions of high frequency amplifier gain AH(s) and upper 3-dB

frequency, WHfor the amplifier shown in Fig. for Q. 7(b).

(17)

(12)

~~ .. ~~.

C2.._. ..__ . . ._-' '. :Yb-' ~-' .,.~ .....-_.f...-r::::s-'---' -

~ C>O -----. .4;....- _--_.'-.__._~--q'-..-_. , ,_ ._* -:L ... ~~ .• ~ &.1fJ.) :l~v(ra..* - -i.-tf~) ----' _I

(c) The low frequency response of an amplifier is characterized by the transfer

function,

F (s)- s(s+15)(s+200)L - (s +100) (s + 500) (s + 2000)

(6) -l

. ft,

Determine the lower 3-dB frequency approximately. Also, check whether the dominant

pole approximation is valid or not. If valid, determine the lower 3-dB frequency using

the dominant pole formulae too.

8. (a) Design a transformer-coupled class-A amplifier to drive an 8-0 load if Vee= 20 V,

VSE = 0.7 V, 13 = 100, Rin = 2 kQ, and the transformer has a turns ratio of 10:1.

Determine the current gain Ai, voltage gain, Av, power output and maximum

undistorted voltage output swing. (Take necessary assumptions)

(b) Derive the expression of minimum power rating of each transistor for a class-B

push-pull power amplifier.

(c) Showing Q-point on load line, classify BJT power amplifiers.

With necessary diagram, prove that the maximum converSIOn efficiency of an

inductively coupled class-A amplifier is 50%.

(15)

(8)j

(4+8)

\

L-2/T-2/EEE Date: 11/03/2018



Sub: MATH 357 (Probability and Statistics)



Symbols used have their usual meaning.


SECTION -A


(iO) ~.

1. (a) Suppose that a system consists of components connected in a series, so the system

fails if anyone components fails. If there are 10 mutually independent components and

each fails with probability 0.05, what is the probability that the system will fail?

(b) A population starts with one member; at time t = 1, it either divides with'

probability p or dies with probability 1 - p. If it divides, then both of its children

behave independently with the same two alternatives at time t = 2. What is the

probability that there are no members in the third generation? For what value of p is

this probability equal to 0.5? (10)

(c) An important factor in solid missile fuel is the particle size distribution. Significant

problems occur if the particle sizes at~etoo large. From production data in the past, it

has been determined that the particle size (in micrometers) distribution is characterized

by (15)

f(x) = {3X-4

, X > 10, elsewhere

(i) Verify that this is a valid density function. Plot the density function.

(ii) What is the probability that a random particle from the manufactured fuel

exceeds 4 micrometers?

(iii) Give-the mean and variance of the particle size.

2.-11 x

(a) Find the mean and variance for the Poisson distribution p(x,!-L) = ~ .x. (12)

(b) Service calls come to a maintenance center according to a Poisson process, (ind on

average, 2.7 calls are received per minute. Find the probability that (13)

(i) no more than 4 calls come in any minute.

(ii) more than 10 calls come in a 5 minute period.

Contd P/2

=2=MATH 357/EEEContd ... Q. NO.2

(c) Let X and Y have the joint density function.

f(x,y)= {k(X- y), 0 ~ y < x ~ 10, elsewhere

(i) Sketch the region over which the density is positive and use it In

determining limits of integration to answer the following questions.

(ii) Find k.

(iii) Find the marginal densities of X and Y.

(iv) Find the conditional densities of Y given X and X given Y.

3. (a) Find the density function f(x) for the Weibull cumulative distribution function

defined as

(b) The time to failure (in hours) of a bearing in a mechanical shaft is satisfactorily

modeled as a Weibull random variable with p = ~ and 0= 5000 hours.

(10)

(10)

. (8)

(i) Determine the mean time until failure.

(ii) Determine the probability that a bearing lasts at least 6000 hours.

(c) Assume that the heights of 3000 male students at a university are normally

distributed with mean 68.0 inches (in) and standard deviation 3.0 in. If 80 samples

consisting of 25 students each are obtained, what would be the expected mean and

standard deviation of the resulting sampling distribution of means if the sampling were

done (i) with replacement and (ii) without replacement? (iii) In how many samples

would you expect to find the mean between 66.8 and 68.3? (Necessary table attached). (17)I

4. (a) Show how to select 20 random samples of 2 students each (with replacement) from

the following table by using random numbers. (Necessary table attached)

Height (in) Frequency

60-64 5

65-69 18

70-74 42

75-79 27

80-84 8

(b) Find the mean and standard deviation of the sampling distribution of means in part

(a) and compare the results, explaining any discrepancies.

Contd P/3

(20)

(15)

=3=MATH 357 IEEE

SECTION -BThere are FOUR questions in this section. Answer any THREE.

5. (a) A number of particular articles have been classified according to their weights.

After drying for two weeks the same articles have again been weighted and similarly

classified. It is known that the median weight in the first weighting was 20.83 gm,

while in the second weighting it was 17.35 gm. Some frequencies 'a' and 'b' in the first

weighting and x and y in the second weighting are missing. It is known that x = 3a and

y = 2b . Find out the values of the missing frequencies.

Class 0-5 5-10 10-15 15-20 20-25 25-30

151 weighting a b 11 52 75 22

2nd weighting x y 40 50 30 28

(b) An analysis of production rejects resulted in the following table:

No. of rejects 21-25 26-30 31-35 36-40 41-45 46-50 51-60per operator

No. of 5 15 28 42 15 12 3operators

Calculate Karl Pearson's coefficient of skewness and comment on its value.

(18)

(17)

(20)"

-_.~---

6. (a) Distinguish between the following concepts: (i) Simple and multiple regression, (ii)

Linear and curvilinear regression; (iii) curvilinear and polynomial regression and

(iv) correlation and regression analysis. (8)(b) What does a coefficient of correlation measure? Discuss the situations when r = -1,

l' = 0, l' = +1. (7)(c) A researcher is interested in predicting the average value of the length of time (Y)

in minutes that an individual can continue a physical exercise, on the basis of two

predictor variables, the average number of cigarettes smoked per day (Xl) and the ratio

of weight in kilogram to height in meters (X2). Data for 20 individuals were recorded

as in the table below. Estimate the regression ofY on Xl and X2.

..•. .•. .:...•.

81. no. 1 2 3 4 5 6 7 8 9 10X1 24 0 25 0 5 18 20 0 15 6X2 53 47 50 52 40 44 46 45 56 40Y 11 22 7 26 22 15 9 23 15 24

81. no. 11 12 13 14 15 16 17 18 19 20X1 0 15 18 5 10 0 12 . 0 15 12X2 45 47 41 38 51 43 18 36 43 45y 27~. 14 13 21 20 24 15 24 12 16

- .•. -~ .•..__ J.

Contd P/4

=4=

MATH 357/EEE

7. (a) Write short notes on (i) Null and Alternative hypotheses, (ii) Level of significance

and Degrees of freedom, (iii) Type-I and Type-II errors, (iv) One-tailed and two-tailed

test.

(b) A manufacturer intends that his electric bulbs have a life of 1000 hours. He tests a

sample of 20 bulbs, drawn at random from a batch and discovers that the mean life of

the sample bulbs is 990 hours with standard deviation of 22 hours. Does this signify

that (at 1% level of significance) the batch is not up to the standard? (Given that v =19,to.01 = 2.539).(c) American theaters know that a certain hit movie ran an average of 84 days in each

city and the corresponding standard deviation was 10 days. The manager of the

southeastern district was interested in comparing the movie's popularity in this region

with that in all of America's other theaters. He/she randomly choose 75 theaters in

his/her region and found that they run the movie an average of 81.5 days. State

appropriate hypothesis for testing whether there was a significant difference in the

length of the movie run between theaters in the southeastern district and all of

American other theaters (Given that at 1% level of significance; z = ::1:2.58)

8. (a) Four salesmen were posted in different areas by a company. The number of units of

commodity X sold by them are as follows:

A 20 23 28 29B 25 32 30 21C 23 28 35 18D 15 21 19 25

Is there a significant difference in the performance of these Salesmen at 1% level of

significance? (Necessary chart is attached)

(b) Seeds of four different types of corn are planted in five blocks. Each block is

divided into four plots, which are then randomly assigned to the four types. Determine

at the 0.05 significance level, whether the yields in bushels per acre as shown in the

following table, vary significantly with differences in (i) the soil (i.e. the five blocks)

and (ii) the type of corn. (Necessary chart is attached)

Types of corn

I II III IV

Block A 12 15 10 14Block B 15 19 12 11Block C 14 18 15 12Block D 11 16 12 16Block E 17 17 11 14

(8)

(12)

(15)

(15)

(20)

Appendix IIAreas

Under theStandard

Normal Curvefrom Otoz

z 0 1 2 3 4 5 6 7 8 9

0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359

0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0754

0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141

0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517

0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879

0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224

0.6 .2258 .229\ .2324 .2357 .2389 .2422 ,.2454 .2486 .25\8 .2549

0.7 .2580 .2612 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852

0.8 .2881 .2910 .2939 .2967 .2996 .3023 .3051 .3078 .3106 .3133

0.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389

1.0 .3413 .3438 .346\ .3485 .3508 .3531 .3554 .3577 .3599 .3621

l.l .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .38\0 .3830

1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015

1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177

1.4 .4192 .4207 .4222 ' .4236 .4251 .4265 .4279 .4292 .4306 .4319

1.5 .4332 .4345 .4357 .4370 :4382 .4394 .4406 .4418 .4429 .4441

1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545

1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633

1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706

1.9 .47IJ .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767

2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817

2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .•4857

2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890

2.3 .4893 .4896 .4898 .4901 .4904 ' .4906 .4909 .4911 .4913 .4916

2.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .4936

, 2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952

2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964

2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974

2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981 .

2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 4986

3.0 .4987 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990

3.1 .4990 .4991 .4991 .4991 .4992 .4992 .4992 .4992 .4993 .4993

3.2 .4993 .4993 .4994 .4994 .4994 .4994 .4994 .4995 .4995 .4995

3.3 .4995 .4995 .4995 .4996 .4996 .4996 .4996 .4996 .4996 .4997

3.4 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4998

3.5 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998,

3.6 .4998 .4998 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999

3.7 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999

3.8 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999

3.9 .5000 .5000 .5000 .5000 .5000 . .5000 .5000 .5000 .5000 .5000

562Copyright@2008, 1999, 1988, 1961 by The McGraw-Hili Companies, Inc. Click here for terms of use.

Random Numbers

.

51772 74640 42331 29044 46621 62898 93582 04186 19640 8705624033 23491 83587 06568 21960 21387 76105 10863 97453 9058145939 60173 52078 25424 11645 55870 56974 37428 93507 9427130586 02133 75797 45406 31041 86707 12973 17169 88116 4218703585 79353 81938 82322 96799 85659 36081 50884 14070 74950

64937 03355 95863 20790 65304 55189 00745 65253 11822 1580415630 64759 51135 98527 62586 41889 25439 88036 24034 6728309448 56301 57683 30277 94623 85418 68829 06652 41982 4915921631 91157 77331 60710 52290 16835 48653 71590 16159 1467691097 17480 29414 06829 87843 28195 27279 47152 35683 47280

50532 25496 95652 42457 73547 76552 50020 . 24819 52984 7616807136 40876 79971 54195 25708 51817 36732 72484 94923 7593627989 64728 10744 08396 56242 90985 28868 99431 50995 2050785184 73949 36601 46253 00477 25234 09908 36574 72139 7018554398 21154 97810 36764 32869 11785 55261 59009 38714 38723

65544 34371 09591 07839 58892 92843 72828 91341 84821 6388608263 65952 85762 64236 39238 18776 84303 99247 46149 0322939817 67906 48236 16057 81812 15815 63700 85915 19219 4594362257 04077 79443 95203 02479 30763 92486 54083 23631 0582553298 90276 62545 21944 16530 03878 07516 95715 02526 33537

570

Copyright@2008, 1999, 1988, 1961 by The McGraw-Hili Companies, Inc. Click here for terms of use.

~

--~~;/

• iF'j

,i[ .t~ppendiX VI .

/ 99th Percentile Values.. for the F Distribution

('1'1 degrees of freedom in numerator)('1'2 degrees of freedom in denominator)

F.99

~ 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120/.12

00

1 4052 5000 5403 5625 5764 5859 5928 5981 6023 6056 6106 6157 6209 6235 6261 6287 6313 6339 6366

2 98.5 99.0 99.2 99.2 99.3 99.3 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.5 99.5 99.5 99.5 99.5 99.5

3 34.1 30.8 29.5 28.7 28.2 27.9 27.7 27.5 27.3 27.2 27.1 26.9 26.7 26.6 26.5 26.4 26.3 26.2 26.1

.4 21.2 18.0 16.7 16,0 15.5 15.2 15.0 14.8 14.7 14.5 14.4 14.2 14.0 13.9 13.8 13.7 13.7 13.6 13.5

5 16.3 13.3 12.1 11.4 11.0 10.7 10.5 10.3 10.2 10.1 9.89 9.72 9.55 9.47 9.38 9.29 9.20 9.11 9.02

6 13.7 10.9 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.72 7.56 7.40 7.31 7.23 7.14 7.06 6.97 6.88

7 12.2 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.47 6.31 6.16 6.07 5.99 5.91 5.82 5.74 5.65.

8 II.3 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.67 5.52 5.36 5.28 5.20 5.12 5.03 4.95 4.86

9 10.6 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 5.11 4.96 4.81 4.73 4.65 4.57 4.48 4.40 4.31I

10 10.0 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.71 4.56 4.41 4.33 4.25 4.17 4.08 4.00 3.91

11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.40 4.25 4.10 4.02 3.94 3.86 3.78 3.69 3.60

12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.16 4.01 3.86 3.78 3.70 3.62 3.54 3.45 3.36

13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 3.96 3.82 3.66 3.59 3.51 3.43 3.34 3.25 3.17

14 8.86 6.51 5.56 5.04 4.70 4.46 4.28 4.14 4.03 3.94 3.80 3.66 3.51 3.43 3.35 3.27 3.18 3.09 3.00

15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.67 3.52 3.37 3.29 3.21 3.13 3.05 2.96 2.87

16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.55 3.41 3.26 3.18 3.10 3.02 2.93 2.84 2.75

17 8.40 6.lf, 5.19 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.46 3.31 3.16 3.08 3.00 2.92 2.83 2.75 2.65

18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.37 3.23 3.08 3.00 2.92 2.84 2.75 2.66 2.57

19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.30 3.15 3.00 2.92 2.84 2.76 2.67 2.58 2.49

20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.23 3.09 2.94 2.86 2.78 2.69 2.61 2.52 2.42

21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 3.17 3.03 2.88 2.80 2.72 2.64 2.55 2.46 2.36

22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.12 2.98 2.83 2.75 2.67 2.58 2.50 2.40 2.31

23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 3.07 2.93 2.78 2.70 2.62 2.54 2.45 2.35 2.26

24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.03 2.89 2.74 2.66 2.58 2.49 2.40 2.31 2.21

25 7.77 5.57 4.68 4.18 3.86 3.63 3.46 3.32 3.22 3.13 2.99 2.85 2.70 2.62 2.54 2.45 2.36 2.27 2.17

26 7.72 5.53 4.64 4.14 3.82 3.59 .3.42 3.29 3.18 3.09 2.96 2.82 2.66 2.58 2.50 2.42 2.33 2.23 2.13

27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 2.93 2.78 2.63 2.55 2.47 2.38 2.29 2.20 2.10

28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.90 2.75 2.60 2.52 2.44 2.35 2.26 2.17 2.06

29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 2.87 2.73 2.57 2.49 2.41 2.33 2.23 2.14 2.03

30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.84 2.70 2.55 2.47 2.39 2.30 2.21 2.11 2.01

40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 2.66 2.52 2.37 2.29 2.20 2.11 2.02 1.92 1.80

60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2.50 2.35 2.20 2.12 2.03 . 1.94 1.84 1.73 1.60

120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56. 2.47 2.34 2.19 2.03 1.95 1.86 1.76 1.66 1.53 1.38

00 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 2.32 2.18 2.04 1.88 1.79' 1.70 1.59 1.47 1.32 1.00

Source: E. S. Pearson and H. O. Hartley, Biometrika Tablesl'or Statisticians, Vol. 2 (1972), Table 5, page 180, by permission.

566Copyright @ 2008, 1999, 1988, 1961 by The McGraw-Hili Companies, Inc. Click here for terms of use.

AppendixV

-,' -

95th Percentile Valuesfor the F Distribution

(VI degrees of freedom in numerator)(V2 degrees of freedom in denominator)

,iI

I

~ 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 00V2

1 161 200 216 225 230 234 237 239 241 242 244 246 248 249 250 251 252 253 254

2 18.5 19.0 19.2 19.2 19.3 19.3 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.5 19.5 19.5 19.5 19.5 19.5

3 10.1 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.70 8.66 8.64 8.62 8.59 8.57 8.55 8.53

4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.63

5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4.37

6 5.99 5.14 4.76 4.53 ,4.39 4.28 4.21 4.15 4.10 4.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3.67

7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3.23

8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.28 3.22 3.15 3.12 3.08 3.04 3.01 2.97 2.93

9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01 2.94 2.90 2.86 2.83 2.79 2.75 2.71

10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.5411 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.4012 4.75 3.89 3.49 3.26 3.11 300 2.91 2.85 2.80 2.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.3013 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.60 2.53 2.46 2.42 2.38 2.34 2.30 2.25 2.2114 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.1315 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.48 2.40 2.33 2.29 2.25 2.20 2.16 2.11 2.0716 4.49 '3:63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.0117 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.38 2.31 2.23 2.19 2.15 2.10 2.06 2.01 1.9618 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.9219 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.8820 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.28 2.20 2.12 2.08 2.04 1.99 1.95 1.90 1.8421 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.8122 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.7823 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.20 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.7624 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.18 2.11 2.03 1.98 1.94 \;89 1.84 1.79 1.7325 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.7126 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.15 2.07 1.99 1.95 1.90 1.85 1.80 1.75 1.6927 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 2.13 2.06 1.97 1.93 1.88 1.84 1.79 1.73 1.6728 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.12 2.04 1.96 1.91 1.87 1.82 1.77 1.71 1.6529 4.18 3.33 2.93 2.70 255 2.43 2.35 2.28 2.22 2.18 2.10 2.03 1.94 1.90 1.85 1.81 1.75 1.70 1.6430 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.6240 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.00 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.5160 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.92 1.84 1.75 1.70 1.65 1.59 1.53 1.47 1.39120 3.92 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.61 1.55 1.50 1.43 1.35 1.2500 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.00

Source,' E. S. Pearson and H. O. Hartley. Biometrika Tables/or Statisticia/ls, Vol. 2 (1972), Table 5, page 178, by permission.

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EEE209 - Bangladesh University of Engineering and Technology

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