L-lIT-21EEE Date

.'~^~.

L-lIT-21EEE Date: 29/06/2015

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA 'L-l/T-2 B. Sc. Engineering Examinations 2013-2014

Sub:

EEE 105

(Electrical Circuits II)

- "",,-

Full Marks: 210 Time: 3 Hours

USE SEPARATE SCRIPTS FOR EACH SECTION The figures in the margin indicate full marks.

SECTION -A

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

Symbols bear their usual meanings.

1. (a) A voltage v={100sin(wt+300)-50sin(3wt+600)+30cos5wt} volt is impressed on a resistance of 6 ohm in series with a capacitance of 88.4 ~f and an inductance of 0.01061 henry. Find the ammeter value of the current, the power dissipated by the circuit, the power factor of the whole circuit, and the voltage drop across the capacitance

ifw = 377 radian per second. Also write down the complete equation of current.

(18)

(b) Determine the source and load currents in the circuit shown in Fig. 1(b).

(17)

2. (a) A balanced three-phase load requires 10 kVA at 0.5 lagging power factor. Find the kVA size of a condenser (capacitor) bank which may be paralleled with the load to bring

the power factor of the combination to 0.9 lagging and then to 0.9 leading.

(17)

(b) Consider the unbalanced circuit arrangement shown in Fig. 2(b). Derive the expression of ZanIan in terms of Vab, Vbe, Yea, Zan, Zbn and Zen' Also, comptue Zen len.

Now assume magnitudes of line to line voltages are 220 volts, Zan= Zen = 80 ohm and Zbn= -j40 ohms. Calculate Zan Ianand Zen len for both abc and acb sequences. Comment

on lamps brightness to sequences.

(18)

3. (a) Define a filter. Draw a four-terminal network terminated on the image impedance

basis. Define image impedance and characteristic impedance.

(7)

(b) Draw the symmetrical T- and 7t-sections of filter. Derive the characteristic

impedance for both sections.

(10)

(c) Find i(t) for t>O in the circuit shown in Fig. 3(c). Assume i(O) = O. Identify steady- state and transient terms in the expression of i(t). Plot the steady-state term and the transient term of i(t) for two cycles of steady-state variation under the following

conditions.

(18)

(i) The applied voltage is a 60-cycle sinusoidal variation, the maximum value of which is 311 volt.

(ii) R = wL = 4 ohm

Contd P/2

=2=

EEE l05/EEE

Contd ...Q.No.l(e)

(iii) The switch is closed at such a time as to make the transient term acquire a negative maximum value.

Sketch the resultant current iCt) on the same plot. Also comment on impact of transient term on resultant current.

4. (a) Write down the fundamental filter equation in terms of full series arm impedance (ZI) and the full shunt arm impedance (Z2). Now compute the cutoff frequencies of elementary low and high pas~ filters. Express the cutoff frequency of constant-k high pass filter in terms of Clk and L2k. Express characteristic impedance for constant-k high pass T- and 7t-sections in t~rms of f, fe, elk and L2k. What is infinite-frequency characteristic impedance?

(b) Design both T- and 7t-section, high-pass filters of the constant-k type which will have an infinite-frequency characteristic impedance of 173 ohm and a cut-off frequency of9l9 cycle. Draw the circuit arrangement in each cases indicating the particular values (in milihenrys or microfarads) of each circuit element.

SECTION -B

There are FOUR qu~stions in this section. Answer any THREE.

5. (a) Assume that the current i=lmcos(wt) flows through a given RLC series branch.

Show that the voltage across th.e branch is v

=

1m2 cos(wt +8)=7= Vmcos(wt +8)

~ ()'2

^{wL - ...L}

where z

=

R² + wL _.l, and 8

=

tan-l we

we .

R

(b) Determine the load impedance Zload to receive maximum power for the network shown in Fig. 5(b). Also calculate the maximum power.

I

(25)

(10)

(15)

(20)

:ii~~~~~~~':;~~'2:=----~=--_. -~~~===~=:: .••.•. ^-:'-~~I~~

'2fr fS, ..:.:t't-J1-:.rL:.:" -- ---,. --.-- - ..---.---- - - ----.-.--.-- -.- -.-~- ---..-

---91;=2-tJ1A1

___ ~ ~ F_,'tr..

S-(b)

Contd P/3

,^'

=3=

EEE l05/EEE

6. (a) Detennine the crest factor of the voltage across the inductor shown in Fig. 6(al) when the current shown in Fig. 6(a) flows through the circuit.

r'-'" .- "'... "- --'-"-"

ⁱ0 Sl..-_ ..~_... ..__._.,_:._!

~..:.._..-.- - .:. -- -.~..-.----..,-- -.-.._.._---.,-._-.:-:- ."--t '-""--'.

-r l-t-)"..t- --- -- .... 1.H-- ,- ---vet-i)

^I

.1

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

(18)

!

I

,

I, ...".."...

(b) Calculate I in Fig. 6(b) by the superposition theorem if E¹

=

lOOLO° and E²

=

50L60° volts.

~_••--:" ~ .- ••• - --. '-~ •,,_, _ •• _A."~~ •..-••~ .~~.~, •••~ ••,__ '"_~,,,_, __ ,_,_.

>'"'~I

. -...-"---..-...-.-.--~---..--.+:"i.~.

b--6b).--.----.---. ..__.. __... ..._

^j

7. (a) Draw the phasor diagram and show the locus of ILand I as XL is varied for a circuit shown in Fig. 7(a). Also briefly explain different operating points of the locus of!.

Contd P/4

(17)

(18)

•

=4=

EEE l05/EEE

Contd ...Q. NO.7

(b) Find the value of L or C in Fig. 7(b) which will make the overall power factor 0.8 if V

=

100L90° volts at 50 Hz.

8. (a) Prove that a circuit arrangement shown in Fig. 8(a) is in resonance for all frequencies and also offers an impedance =

.J

L /C to all frequencies when RL = Rc =

..Jil.

~.".i

(b) The per unit band width between the half-power points of a series RLC band selector is 0.02. Calculate the values of Rand C when the value of L is 10 mH and the resonant frequency is 20 kHz.

(17)

(18)

(~

'

.

.. ~ '1

\

I i

V

IgJL- 0,.2 Ii

f- .

Lb. io~Ob

fH~.

If

f,C9

N~ D'

^J

Ii

/

C0

I .

b a- -

^e

J b

, . !J

^A_~.f)

rX-. ^~''i

. .i

L-lIT-2/EE Date: 06/07/2015

, where 'a' is the radius of the ring.

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA L-l/T-2 B. Sc. Engineering Examinations 2013-2014

Sub:

PHY 165

(Electricity and magnetism, Modem Physics, Mechanics)

Full Marks: 210 Time: 3 Hours

The figures in the margin indicate full marks.

USE SEP ARA TE SCRIPTS FOR EACH SECTION

-'-'---~~---...,..~,-,....--...-- SECTION-A

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

1. (a) Discuss charge and matter, Discuss conservation of charge. Show using an example

that charge is quantized and conserved. (10)

(b) Discuss electric field. A particle of mass m and charge q is placed at rest in a

uniform

electric field as shown in the Figure below. Describe its motion. (15)

(c) An electron is constrained to move along the axis of the ring of charge as shown in the figure below. Show that the electron can perform oscillations whose frequency is (10)

. I .

given by ^OJ

= ./:

eq ³ V 47r&oma

~-'-'-'_."--"--'''-''''''''''''''_._''''-'''--i

..._.._,A...~~,

tS.._.~

'",' _-- _-,-_ ;- ---- ..--- ..--., ..i

I

.

-_

^..

_._-~_._

^{..~~--~~,'_..}

;_

•...••...

~--~

^{...•,-~.•.,..•}r

2. (a) Discuss Gauss's law in electrostatics. Show that the electric flux ~E through a cylindrical surface immersed in a uniform electric field E is Zero. (10) (b) Fig 2(b) shows a spherical charge distribution of radius R. (15)

I

I

I

I

I

flj z {1)i

Contd P/2

=2=

PIIY 165 (EF:)

Contd ... Q.No. 2(b)

The charge density p at any point depends only on the distance of the point from the center. Find an expression of E for points (i) outside and (ii) inside the charge distribution [Apply Gauss's law to solve this problem]

(c) A 100-ev electron is fired directly forward a large metal plate that has a surface charge density of -2.0 x 10,6 coul/m2• From what distance must the electron be fired

if

it

is to just fail to strike the plate? (10)

3. (a) Define capacitance of a capacitor. Discuss dielecttics from the atomic point of view.

When a dielectric medium is inserted in a parallel plate air capacitor the capacitance, th~

electric field and the potential change, Elaborate on this phenomenon of capacitor. (lO) (b) What are free charge q and induced surface charge q'. Show that the induced surface charge q' is given by

q' ⁼ q(

1- ~) where the symbols have their usual meaning.' Also shows that the surface induced charge q' is always less in magnitude than the free charge

q and q' = 0 when there is not dielectric medium. (15)

(c) A spherical capacitor consists of two concentric spherical shells of radii a and h, with b>a. Show the its capacitance is given by C

=

^41T6o b~a' where the symbols hElve their

usual meaning. (10)

4. (a) Using an example, prove that the speed of light for all observers in different inertial

frame of reference is the same. (7)

(b) Define relativistic mass and momentum for a body moving at a speed COl'l'll'Hlrable to the speed of light. From this, derive the mass~energy relation E

=

mc2, where the symbols

have their usual meaning. (20)

(c) Show that at low speed, relativistic kinetic energy of a moving body reduces to

the

classical one. [Use Binomial expansion if necessary]. (8)

SECTION~B

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

5. (a) What are the limitations of classical Physics in explaining photo-electric effect? How

does quantum theory explain it? (12)

(b) Define de Broglie wavelength and explain the teml "Wave particle duality", (10) (c) Sketch the relative probabilities of photo-electric effect, Compton scattering and

pair -

production as a function of energy of light in a same graph for carbon. (5)

Contd P/3

=3=

PRY 165 Qlli)

Contd ... Q.NO.5

(d) X-rays of wavelength lx10-11 ill are scattered by a target electron. (8) (i) Find the wavelength of X-rays scattered during head-on collision.

(ii) Find the maximum kinetic energy of the recoil electron.

6. (a) Explain why radioactivity is a time dependent property of a nucleus? (7)

(b) Describe the binding energy curve for a nucleus. (12)

(c) Explain nuclear fission and fusion reactions. In power production, which one ofthi8 is

more safe and viable, and why? (10)

(d) Atomic mass of ~~Zn is 63.929u. Find the binding energy per nucleon for 2n

where

mass of proton is 1.007825 u and that of neutron is 1.008665 u. (<5)

7. (a) Write down the fundamental postulates of quantum mechanics. (7) (b) Vf(x,t)=A

exp[-a{(m

x²

/n)+it}],

where 'A' and 'a' are positive real constants~

represents the state of a particle of mass m at any time t.

(i) Find the value of A.

(ii) Calculate the expectation value of x, and p

(c) Let Pab(t) be the probability of finding a particle in the range (a<x<b), at time 1.Show that

dPab(t) - J(a,t) -J(b,t) dt

J(

x,t

)-

^{=-. -}

in [

'1/ x,t

*

)alf/*(x,t)----If *(x,t ---)a If/(x,t)]

2m

ax ax

What are the units of lex, t)?

(l0)

(9)

8. (a) What do you mean by angular momentum? (3)

(b) Figure 8(a) shows a space hauler and cargo module, of total mass M, traveling aloni x axis in deep space. They have an initial velocity Viof magnitude 3725 kmlh relative to the sun. With a small explosion, the hauler ejects the cargo module, of mass 0.20M (Fi~.

8(b». The hauler then travels 1115 km/h faster than the module along the x-axis; that is, the relative speed Vrelbetween the hauler and the module is 1115 km/h. What then is the velocity ^ViiS of the hauler relative to the Sun?

(~ (~

~~=~.===-=~~-=E:=f-====.==~---,-==-]

. The

explosivo separation can change the momentum of the part~but not lhe momertum of the system.

~

Gi~"l:::.o

Vl, ..

t<.t>I~"'-"""'-;;"'+4

,1~~~'C~aUler

'-- cargo module .

- :r

a-goM

Contd P/4

•

=4=

~IIX.165 CEID

Contd ... Q. No.8

(c) State the kepler's law ofplfmetary motion. (15)

I

(d) A space shuttle 1110ving\yith an initial velocity as shown in Fig. 8(c) "Slingsl1Qts"

around the sun in order to reverse its direction. Let the mass of the sun is, m, ^SUIl,.< ~l.)J.dth@

sun remains stationary. (18)

(i) What is the minimum inittal speed required by the space shuttle to escape t11<:3 sun's gravitational field and move in a linear trajectory toward infinity?

(ii) If the maximum acceler~tion the astronauts can survive is 4g, how close can be shuttle come of the sun?

(iii) What is the minimum initial speed Vo that the shuttle must have to avoid

faIling

into the sun?

(iv) Write down the equations required to calculate the initial angle

e

in terms of ^VOl d;

mSun, G and r.

A

L-lIT

-2/EEE

Date: 01108/2015 BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-l/T-2 B. Sc. Engineering Examinations 2013-2014 Sub:

MATH 257

(Ordinary and Partial Differential Equations)

Full Marks: 210 Time: 3 Hours

USE SEP ARA TE SCRIPTS FOR EACH SECTION The figures in the margin indicate full marks.

SECTION -A

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

Symbols used have their usual meaning.

1. (a) Find the differential equation by eliminating the arbitrary constant c from the equation y

= e(x - e)2. .

(b) Solve the following:

(12)

(i) dy 2x- y+l dx

=

x+2y-3

(12)

2. (a) Solve the following equations.

. I 2 2

(i) xdy - ydx - Vx - y dx

=

0

(ii) y(2xy

+

1)dx

+

x(1+2xy - x3

i

^)dy

=

O.

(b) If an electric circuit contains a resistance R (ohms) and a condenser of capacitance C(farads) in series and an emf E(volts), the charge q (coulombs) on the condenser is given by the differential equation R dq

+!L =

E . If R ⁼ 10 ohms, C ⁼ 10-3 farad and

dt C

E

=

100 sin120n-t volts, find q, assuming that q=0 when t=O.

(11)

(12) (12)

(11) .

3. Solve the following differential equations.

(a) (D3+3D2 +3D) y =e2x (12)

(b)

(n4

^+2D2

⁺

^{l)y =x2 cos2 x (12)}

(c) (D2 - 6D

+

9)y =x2e3x cos 2x (11)

4. (a) Solve the differential equation [(x

+

2)2D2 -(x+2)D+IJy

=

3x+4 (12) (b) Solve the equation l(x

+

1)D^{2 -:} (3x

+

4)D

+

3

Jy =

(3x

+

2

)e

^3X by the method based on

.factorization of the operator.

d

²

{d ⁾²

(c) Solvey(l-lny

)---?+

(1

+

lny

2 =

O.

dx dx

Contd P/2

(12) (11)

=2=

MATH 257/EEE

SECTION-B

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

Symbols used have their usual meaning.

5. (a) Find the series solution of the following differential equation by using the method of

Frobenius:

(25)

.2x ---x-+2 d2y dy (x-5 )y=O

dx2 dx .

(b) Form a partial differential equation by eliminating the arbitrary function ~ from

~(tanx+sin-l y-logz,eX-secy+z3)=0. (10)

(12)

(ii) yzp2 ~q

=

0

(11)

6. (a) Find the integral surface of the linear partial differential equation

(12)

x(i + z )p - y(x2 + z)q= ^Z(x2 - y2 )which contains the straight line x+y = 0, z = 1.

(b) Using Charpit's method, find the complete and singular integrals of the following partial differential equations:

(i) 16p2z2 +9q2z2 +4z2 -4

=

0

7. Solve the following higher order partial differential equations:

(a) (D;

+

DXDy -6Dnz

=

ycosx

(b) (D; -DXDy -2D~ +2Dx +2Dy)z =e2x+3y +xy (c) (3D; +2D~+Dy +2)z =ex+2ysin(2x+ y).

(12) (12) (11)

8. (a) Solve the following higher order partial differential equation:

(x2D; - 2xyDxDy _3y2 D~ +xDx -3yDy)z = x2y sin (logx2 )

(b) The vibrations of an elastic string is governed by the partial differential equation

a2~

⁼

a2~ .

The length of the string is 'It and the ends are fixed. The initial velocity is

at ax

(15)

zero and the initial deflection is u(x,

0)

= 2(sinx + sin3x). Find the deflection u(x,

t)

^of

the vibrating string for t>0 .

(20)

---

L-l/T

-2/EEE

Date: 05/08/2015

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA L-l/T-2 B. Sc. Engineering Examinations 2013-2014

Sub:

HUM 127

(Sociology, Science and Technology)

Full Marks: 210 Time: 3 Hours

USE SEP ARA TE SCRIPTS FOR EACH SECTION The figures in the margin indicate full marks.

SECTION -A

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

1. (a) 'Sociological imagination is. an unusual type of creative thinking' - Justify this

statement with suitable examples.

(l0)

(b) Illustrate Emile Durkheim's contribution in the field of sociology.

(l0)

(c) Write the principles and properties of functionalist perspective of sociology.

(15)

2. (a) What do you understand by socialization? Evaluate different roles of agents of

socialization in global context.

(10)

(b) Critically discuss G. H. Mead's theory of self.

(10)

(c) What is social stratification? Explain different systems of social stratification with

suitable examples.

(15)

3. (a) What type of mass media you usually use in your everyday life? Explain how these

mass media influence to create your ideology as a whole.

(l0)

(b) 'Juvenile delinquency is nothing but abnormal and anti-social behaviour by a

juvenile'- Discuss.

(10)

(c) Who are poor? Illustrate various types of poverty you are observing in your society.

(15)

4. Write short notes on any three of the following:

(35)

(a) Sub culture and counter culture.

(b) Dominant ideology.

(c) Ethnocentrism and cultural relativism.

(d) Karl Marx theory of class differences.

Contd P12

f

=2=

HUM 127/EEE

SECTION -B

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

5. (a) What do you mean by environment?

(5)

(b) Briefly discuss the negative impacts of global warming.

(15)

(c) Discuss how can environmental destruction be brought under control?

(15)

6. (a) 'Private property is the terra ferma of capitalism'- explain this statement on the

basis of nature of capitalism.

(15)

(b) Critically discuss the evolution of cities.

(10)

(c) What functions does the family perform for society?

(10)

7. (a) In what ways is globalization just a friendlier term for neo-imperialism?

(15)

(b) Critically discuss the 'world system theory' of development.

(10)

(c) Define deviance. Identify Merton's types of deviance.

(10)

8. Write short notes on any THREE of the following

(35)

(a) Electronic media (b) Fatalism

(c) Cyber crime (d) Internal migration.

L-lIT-2/EEE Date: 09/0812015 BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-l/T-2 B. Sc. Engineering Examinations 2013-2014 Sub:

CHEM 101

(Chemistry - I)

Full Marks: 210 Time: 3 Hours

USE SEP ARA TE SCRIPTS FOR EACH SECTION The figures in the margin indicate full marks.

SECTION-A

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

1. (a) Discuss the mechanism of dissolution of ionic compounds in water? How does heat evolve or absorb during dissolution of the compounds in water?

(b) State and explain different forms of Henry's law. Mention the limitations of Henry's law.

(c) What types of liquid pairs are steam distilled? How steam distillation is useful in evaluating the molar masses of compounds?

(d) An aqueous solution containing 10.0 g of KOH and 90.0g of water has a density of 1.12 kg/dm^3. Find (i) ;( % of KOH, (ii) Molality, (iii) Molarity and (iv) Mole fraction ofKOH.

2. (a) What do you mean by colligative properties? Discuss its importance.

(b) With the help of a diagram, thermodynamically prove that the elevation of boiling point of a solution containing a non-volatile and non-electrolytic substance is proportional to the molality of the substance in the solution.

(c) Derive a relation between osmotic pressure and vapour pressure of a dilute solution of a solid in a liquid.

(d) A 35.0 g sample of haemoglobin is dissolved in water and the total volume of the solution is brought to 1.0 dm^3• The osmotic pressure of the solution is 10.0 torr at 25°C.

Calculate the molar mass of haemoglobin, Hb.

(10)

(9)

(8)

(8)

(6)

(12)

(8)

(9)

3. (a) Define the following terms with suitable examples: (8)

(i) Rate and Rate constant.

(ii) Order and Molecularity.

(b) Derive the integrated rate equation for a second order reaction, 2A -7 P. How does it

differ from first order behaviour?

(8+4=12)

(c) Describe the isolation method and differential method for the determination of order of a reaction.

Contd P/2

(8)

=2=

CHEM lOllEEE Contd ... Q.NO.3

(d) The graph of a chemical reaction is plotted as

[~l

vs time and the plot is a straight line. If the intercept is 2 x 10 mole-l.1it and slope 2 x 10-2 mole-2.1it.sec-l. Calculate the half-life of the reaction.

4. (a) Derive the rate law for a reaction at equilibrium.

(b) State and explain Hess's law of constant neat summation. Give its application.

(c) Define phase, component and degree of Freedom of a heterogeneous system in equilibrium.

(d) Derive the Gibbs phase rule thermodynamically. Draw the phase diagram of water

(7)

(6) (5+3=8)

(6)

system and describe its main features.

SECTION -B

There are FOUR questions in this section. Answer anyTHREE.

(7+8=15)

(10)

(13)

5. (a) With the help of potential energy diagram discuss how a combination occurs between two hydrogen atoms and the molecule becomes stable.

(b) Compare molecular orbital theory (MOT) with valence bond theory (VBT) for the formation of Covalent bond. Illustrate your answer with examples.

(c) What is coordinate Covalent bond? Discuss the Werner theory of coordination

compounds with its limitation. Explain effective atomic number rule with examples.

(12)

6. (a) Applying Bohr atom model derive an expression for the calculation of wave number of radiation obtained in the emission spectrum of hydrogen.

(b) Derive the equation ill.tiP ::::::h ,where ill =Uncertainty in position of an electron, tiP =uncertainty in momentum of the same electron. h =plank's constant.

Is the equation applicable in case of Bohr atomic model? Justify your answer.

(c) The uncertainty in velocity of an electron is 5.7 ^x 105 m.S-I. Calculate the uncertainty in position ofthe same electron.

7. (a)Deduce a generalized theory in which acids and bases have been defined on the basis of electronic structure.

(b) Classify the following substances as acids and bases and give arguments on your classification.

Contd P/3

(12)

(13)

(10)

(7)

(10)

=3=

CHEM lOl/EEE Contd ...Q.No.7

(c) Explain why hard and soft acids and bases principle is applicable in the following

fields:

(12)

(i) Ligand selection in metalloproteins and enzymes.

(ii) Redox reaction.

(iii) Quantitative analysis scheme for metal ions.

(iv) Medicinal Chemistry.

(d) You are supplied with H²S0⁴ of specific gravity (sp. gr.) 1.98. Calculate the amount

of distilled water required per liter to convert the acid solution of sp. gr. 1.75.

(6)

8. (a) State and explain Lechatelier Principle with suitable examples.

(6)

(b) The relationship between enthalpy change (~H) and equilibrium constant is exponential. Prove this statement through derivation of a mathematical model. What is

the significance of this model?

(10+3=13)

(c) Write down the equation showing the relationship between Gibb's free energy and

equilibrium constant. Point out the significance of this relationship.

(6)

(d) 35% of PCls is dissociated' at 373 K. If the total pressure is 1.5 atm., find out the

values of "K^p" and "Ke".

(10)