USN

T whcre u6 is constant

'/ ,''

1OMAT31

Marks)

0

(07 Marks)

(07 Marks)

s equation, u** *uo = 0

(07 Marks)

,< / under the following

(07 Marks)

(06 Marks)

to fit most closely to the

(07 Marks)

subject to the

(06 Marks)

the constraints,

(07 Marks)

().9(.)

!

Cn

a

(.)

0)

oX

J>

-:r)

troo.=&

9;ioCs()

a:

o()

boc

-o>6

or:

o-Xo..o ._:

9iE,c)a(EG:!o

5.e>' (Foooc 01)

o=soF>iioVLo

(r<-Noo

iio

Third Semester B.E. Degree Examination, Dec.2013 lJan.20l4

Time: 3 hrs.Engineering Mathematics - lll

Max. Marks:100Note: Answer FIVEfull questions, selecting

at least TWO questions from each part.

- PART_A .

1 a' Find the Fourier series expansion of the function f(x) = lxl m Gn,n), hence deduce thatG- 6 I,,1 E- I

; = L; .,2. (06 Marks)o n tl/.n-l)

b. Obtain the half-range cosine series for the function, f(x) = (, - 1)' in the interval 0 < x < 1

and hence show that ^' = r{} * * * +. } (07 Marks)[t J J )

c. Compute the constant term and first two harmonics of the Fourier series of (x) given by,(07 Marks)

2 a. Obtain the Fourier cosine translorm of l(x) = J -I+x2'

b. Find the Fourier transform of f(x) - {t - x' for

l"l = t

[ 0 forlxl >l

c. Find the inverse Fourier sine translorm of #3 a. obtain the various possible solutions of two dimensional Laplace'

by the method of separation of variables.

b. Solve the one-dimensional wave equation, C' lI=! . . t.t0x' cfr.'

conditio-nS (i) u(0, t) : u(/, 0 : 0 (ii) u(x, 0) :au(ur) ^ (x.0)=9.dt

c' Obtain the D'Almbert's solution of the wave equation un - C'u,* subject to the conditions

and evaluate

<x

.auu(x" 0) : flx) and

fr(x.0) = 0.

a. Find the best values of a, b, c, if the equation y=a+bx+cx2 isfo llo wing observations.

Solve the following by graphical method to maximize z = 50x+ 60yconstraints, 2x+3y <1500, 3x+2y < 1500, 0( x < 400 and 0 < y < 400.By using Simplex method, maximize p=4xr -2xr-x. subject toxr +x2 *X-. (3,2xr+2x, *X, ( 4, xt-x, <0, X,)0 and x, )0.

x 0 7C

-)

2n

-:iJ

1l 4n;J

5n;

.,)

2n

(x) 1.0 t.4 1.9 t.7 1.5 t.2 1.0

Le

x I 2 1J 4 5

v 10 l2 13 t6 l9

1OMAT31PART _ B

Using Newton-Raphson method, find a real root of xsinx+cosx =0 nearer to n, carryoutthree iterations upto 4-decimals places.

Find the largest eigen value and the corresponding eigen vector of the matrix,lz -1 oll-, 2 -11

Io -r ,)By using the power method by taking the initial vector as [t t t]'

Solve the following system of equations by Relaxation method:t. 12x+y+z:31 ; 2x+8y-z=24; 3x+4y+l0z=58

6 a. A nducted in a slum localit eals the followine informat classified below,survev conductecl m a slum locallty reveals tne Iollowmg lnlormatlon as

lncome per day in Rupees 'x' Under 10 t0 -20 20-30 30-40 40-50Numbers of persons 'y' 20 45 115 274 115

Estimate the probable number of persons in the income group 20.to 25. (07 Marks)b. Determine (x) as a polynomials in x for the data given below by using the Newton's divided

difference formula. (07 Marks)difference formula.x 2 4 5 6 8 10

f(x) 10 96 t96 350 868 t746

5a.

b.

74.

(07 Marks)

c.

carryout 5 -iterations"(07 Marks)

(06 Marks)

c.I / r \td

Evaluate l- AO* by using Si*pson's [ ] I rule by taking 6 - equal strips and hencejl+x \3/deduce an approximate value of log; 2'. (06 Marks)

^) ^?

Solve the wave equation. + = 4{4, suUlect to u(0, t) : 0, u(4, t) : 0, u1(x, 0) : 0 anddt- dx'u(x, 0) : x(4 - x) by taking h - 1, K: 0.5 upto 4-steps. (07 Marks)

Solve numericallythe equatio, 4 =* subject to the conditions, u(0, t):0: u(1, t),^a0x't > 0 andu(x,0): sirfi*, 0 < x <1, carryout the computation fortwo levels taking h:+

andK- 1

36

Solve u* *u,, =0 in the following

indicated in the Fig. Q7 (c).

b.

c.

5oo I t]o 1oo 50

lI l2

li

Fig. Q7 (c)

0000Find the z-transform of (r) sinh n0 (ii) coshn0

^)Find the inverse z-transform or" 2z' +32

(z+2)(z-47Solve the difference equation, y n+2

-t 6yn*r -l9y , = )n

with yo = Yl = 0 by using z-transform.****>'r

(07 Marks)

square region with the 'bundary conditions as

' (06 Marks)

(iii) n2 (07 Marks)

(06 Marks)

(07 Marks)

20

8a.b.

c.

USN

Time: 3

.....I a.'

b.

c.

2a.b.

c.

3a.

b.

t.

4a.

b.

c.

MATDIP3Ol

Max. Marks:100

,',(06 Marks)

(07 Marks)

(06 Marks)

(07 Marks)

(07 Marks)

(06 Marks)(07 Marks)

(07 Marks)

-1, 0).

(07 Marks)

(06 Marks)

Third Semester B.E. Degree Examination, Dec.20l3 lJan.20l{

Advanced Mathematics - I

oooLa

():C)

E9

du

oo ll

Eoo.=N

oYYOE:-o

o>

o(.)odO

h0qcg6

a6

-o€

O.j=

^Xo'"oj

o=

AE!o5Ev,-^oECOo=o. iitr>=o

\J<_No

Z

Loo.

hrs.Note: Answer any FIYEfull questions.

Express the complex number q#+A

in the form x + iy.

E;.2. (3_42i)-Find the modulus and amplitude of trExpand cos8 0 in a series of cosines multiples of 0.

Find the nth deiivative of sin(ax + b). '."

If y: lsin-l x)2. show that (1- x')yn ,z-(2n+ 1)xyn*, - n'yn = 0.

FindthenthderivativeofI r *, . -?'' ).Is(x - l) (7 - lf 2x + 3)]

Using Taylor's theorem, express'lhe polynomial 2x3 + 7x2 + x - 6 in powers of (x - 1).

Using Maclaurin's series, expand taa x,,,upto the term containing x).^ ) ;)

If Z =rt + y' - 3axy then prove 1116 !J- = : : .ayax AxAy

-duIf u=xlogxy where x'+-y3+3xy=1,616 -'. (06Marks)

' """ - ., ,Az Oz Oz AzIf z: (x, y) and x"ff1e-' andy =e-" -eu, provethat i_-;= x';-Vf .tOzMarks)

du, dY dx 0y

lf u=x+3y2 -z'.v=4x'yz. w= 222-xy"findthevalueof a=(,''""*,). ur,1.. a(x,y"z\

5 a' Obtain the reduction formula for Jsin" x dx .

, u, x'dxb. Evaluate J--.ilu'-"'

, a. Evaluate IIft + ev)dydx.l3

t1l6 a. Evaluate JJJe'.'.'axdydz.ooo

r,.b. Find the vatue or l[+iLLrv \rr

l\ 2 / .

c. Prove that B(m-n', = @

:. -"(02 Marks)

,,,,,,,,,,,,,,,,

(07 Malt<o)

(06 Marks)

(07 Marks)

(07 Marks)

MATDIP3Ol

a. Solve I - .'*-" + x2 .e-2Y .

dx(06 Marks)

(07 Mary,ks)

".T'(3(07 Marks)

&te.,%; ,

-a'q, (06 Marks)

(07 Marks)

(07 Marks)

"1" -"'r

2 of2

10ES32

+Ya

+-v;

\(_

dooLa

oado

3e

6v

-o ,,

ooltroo.= c.i6$i: OOYd)oE-O

o>

a*oo)

o0i

-sEd

OE

p- 5.

oj

o=ad!o

Y,^=50vca0o=o. iiVL9-

rJ<J6i(J

oZ

o

Third Semester B.E. Degree Examination, Dec.2013/Jan.20l4Analog Electronic Gircuits

, Time: 3 hrs. Max. Marks:100N ote :

1 : : ::: I!.Y^u *'! Iy:"'fi i: "! :::': s .

PART _ AI a. Explain the following with respect to a semi conductor diode :

(i) Diffusion capacitance. (ii) Transition capacitance (iii) Reverse recovery time.(06 NIarks)

b. Explain the"working of bridge rectifier. (08 Marks)c. Design a suitable circuit represented by the box shown below which has input and output

waveforms as indicated. (06 Marks)

USN

2a.b.

\r;o'{

o

-ro{

**t;lcU*j,^t3\\i t fr.

%3v

-toY

Derive an expression for Ie, Ic and Vce for vohagg divider bias using exact analysis.(10 Marks)

For the circuit shown below; determine (i) Ie (ii) Ic (iii) VcE. (06 Marks)

Ycc -\5vRc-

c' Determine Rs and Rc for the transistor inverter of Fig. Q2 (c) if I61s,11 : 10 mA,Ie : 1500% Is1,nu*). (04 Marks)

3 a. Derive an expression for Av, ZiandZo for CE fixed bias using r. equivalent model.(10 Marks)

Fig. Q1 (c) - (ii)

C- to

lo/qI

nlg. qz iu;

u,m//*"/3-

.\\'2 \.

ifi \q)

4 a. Determine the lower cut off frequency forCs : 0.1 Pf, Rs =' 1 Kf), Rr : 120 Kf), Rr-

f0:6, Vcc: 15 V, Var: 0.7 V.

3 b. For the circuit shown in Fig. Q3 (b), calculate ta, Zi, Zo, Ay, A1.

Fc

ttol{.rL

rJct q V

1_.1F..Jt-

10ES32

(10 Marks)

[-- rI\ roto/+

f =roe J \ItE; o'-fY

-fo = 6O !t su

Fig. Q3 (b)

the emitter follower using BJT amplifier with: 4 Kf), Re : 1.5 KO, Cc : 0.1 ptf 0 : 100,

(12 Marks)(08 Marks)

(10 Marks)

Ipss: 5 mAVp:-6V

Yos :40 ps

b. Derive equations for Miller input and output capacitance.

, PART _BDerive an expression for Zi, Ay, Ar for Darlington emitter follower circuit.34.

b. What are the effects of negative feedback in amplifier? Show how bandwidth of an amplifier(10 Marks)

6a.b.

7a.b.

8a.

b.

With a neat diagram explain the working of complementary symmetry push pull amplifier.(10 Marks)

Explain the operation of class B push pull amplifier and show that its efficiency is 78.5Yo atmaximum power dissipation. (10 Marks)

With a neat diagram; explain the working of RC phase shift oscillator. (08 Marks)With a neat diagram, explain the working of series resonant crystal oscillator. A crystal has

L : 0.334^H, C : 0.065 pt CM : 1 pf, R : 5.5 kQ. Calculate its series and parallelresonating frequency. (12 Marks)

Draw the JFET amplifier using fixed bias configuration. Derive Zi, ZO and AV using smallsignal model. (10 Marks)For the JFET amplifier shown in Fig. Q3 (b), calculate (i) g. (ii) 16 1111) Zi (iv) Zs(v) Av. (lo Marks)

t95 2or{2-*n-

F---YOz.o/t

€-l

I

*8*E{<

2 of2

Fie. Q8 (b)

+F*r'y*

USN10ES33

(08 Marks)

(06 Marks)

(06 Marks)

19, 20. 22, 25, 27, 28, 30) + >d(8, 10, 24, 26).Marks)

Marks)active

(08 Marks)

(06 Marks)

(06 Marks)Map for each output

(08 Marks)

Third Semester B.E. Degree Examination, Dec. 20l3lJan.2Ol4Logic Design

Time: 3 hrs. Max. Marks:100Note: Answer FIVEfull questions, selecting

. atleust TWO questions from each part.

1 a. Design a three -input, one - output minimal tow-level gate combinational circuit which has

an output equal to 1 when majority of its inputs are at logic 1 and has an output equal to 0

d)oo

o()

(JX50-

,=63^^lgco.=N

oi-o

o2

o=

o()

<\

26

'Eaor=

:9

o:

A,i6E!O

>'!ofr "

.-cE=o-Btr>og(.) -\r<-l 6i

o-7

o

when majority of its inputs are at logic 0.

b. Minimize the expression :

Y=[Be D+ABe p+A Be D+A Bc D+ABe p+ABcD.c. Reduce the fbllowing function using K - Map technique

(A, B, C, D) : n M (0,3,4,7, 8, 10, 12,14) + d(2,6).

2 a. Obtain all the prime implicaats of the following Boolean function using Quine - Mccluskeymethod,(a, b, c, d): >(0,2,3, 5, 8, 10, l1)verify the result using k - Map technique. (10 Marks)

b. Simplify the given function using MEV technique taking the least significant variable as the

map entered variable(a, b, c, d, e) : t(1, 3, 4, 6,9, 11, 12,14, 77,

3 a. Implement the multiple functions :

f,(a, b, c, d) : >(0,4,8, 10, 14, 15) and

f2(a,b, c, d) : >(3,7,"9,13) using two 3 to 8 decoders. ,, .b. Implement the following with a suitable decoder with active

high output :

(w, x, y,z)=2(3,7,9)g(a, b, c): x(2, 4, 7).

4 a. Configure a 16 to 1 MUX using 4 to 1 MUX.

,r b. Implement the following Boolear"i function with 8 : 1 multiplexer(A, B, C, D) : Xr(0, 2,6,10,11,12,13) + d(3, 8, 14).

c. Write a truth table for two - bit magnitude comparator. Write the K -of two - bit magnitude comparator and the resulting equation.

c. Draw the interfacing diagram of ten key keypad interface to a digital system using decimal

to BCD encoder. (06 Marks)

PART - B

5 a. What do you mean by sequential circuit? Explain with the help of block diagram? (04 Marks)

b. Explain with timing diagram, the working of SR latch as a switch debouncer. (06 Marks)

c. Explain the working of a master - slave JK flip-flop with the help of logic diagram, function

tr$

table, logic symbol and timing diagram. (10 Marks)

6 a. Obtain the characteristic equation for a SR flip-flop.b. Design a 4-bit register using positive edge triggered D

the table below :

108S33

(04 Marks)flip-flops to operate as indicated in

(08 Mark$Mode select

Register operation&r AO

0 0 Hold0 1 Synchronous clearI 0 Complement contents

1 Circular shift riehtc.

la.b.

8a.

b.

Design a synchronous Mod - 6 counter using JK flip - flop.

Explain mealy. and Moore models.of a clocked synchronous sequential circuits.Analyse the synchronous sequential circuit shown in Fig. Q7(b).

(08 Marks)

(08 Marks)(12 Marks)

Write the basic recommended Steps for design of a clocked synchronous sequential circuit.(06 Marks)

Construct the excitation table, transition table, state table and state diagram for the Mooresequential circuit showri in Fig. Q8(b). (14 Marks)

{<*{<**

2 of2

Fig. Q7(b)

Fie. Q8(b)

USN l0ES34

Third Semester B"E. Degree Examination, Dec. Z0l3lJan.2014Network Analysis

Time: 3 hrs. Max. Marks:100Note: Answer FIVEfull questions, selecting

utleast Tl4/O questions from each port,

PART _ A

1 a. Find the equivalent resistance at AB using Y - A transformation technique for the circuitshown in Fig. Ql(a). (All the resistors connected are 30 Q each). (05 Marks)

b' Find 'i"' and 'v,' lbr rhe circuit shown in Fig. \] I (b) by Mesh analysis. (05 Marks)

c. For the network given in F,g. Qi(.:), finj '19' usi;rg ni,dal analysis. (10 Marks)

UD

4tx- To ln +t24V7-r\-

(10

.Joo!

q)

()!

4o

d97r)-*1troo

nboYO-o:e

(.) =

aX

o()

;6

iaOE

6Xtrp.o'!o-j

ai= -!l>- (Fuo"io0.-c6=a:\:oYl

U<-i ..i

ooZ

1rl

2a.

b.

Write the tie - set s:hedule fbr the,retwork shorvl in Fig. Q2(a), and using the tie setschedule determine all brarch currents. {Take inner resistors as tree branch elements).

(10 Marks)For the network shown in Fig. Q2(b). draw the dual circuit. Also write the nodal equationsfor the dual circuit.

Fig. Q2(a) '+

Find the voltage 'V' across

the Fig. Q3(a).

3f) resistor using superposition theorems for the circui3a.

b.

(10 Marks)load resistor Rr-

(I0 Marks)State Millman's theorem. Using Millman's theorem tlnd current through thefbr the circuit shown in Fig .Q3(b).

:l$-rr-

a. Find the Thevenin's equivalent of the network shown in Fig. Q4(a). (10 Marks)b. State maximum power transfbr theorem. For the circuit shown in Fig. Q4(b), what should be

the value of 'R' sucir that maximum power transfbr can take place from the rest of the

Fig. Q3(a)

network to 'R'. Obtain rhe amount of this power,33- 5)_

Fig. 3(b)

(10 Marks)

Fig. Q1(a)

ldlL

Irig. Ql(b) Fig. Q1(c)

m*"{ l<

./g

(.*zt;l (

w

\*

ti ?Yt'

Fig.Qa(a) Fig.Qa(b)

10ES34

PART - B

5 a. A220 V, 100 Hz AC souice supplies a series RLC cil'cuit with a capacitor and a coil. If thecoil has 50 m O resistance and 5 mH inductance, find at a resonance frequency of 100 Hzwhat is the value of capacitor. Also cal,:ulate the Q factor and half power frequencies of thecircuit.Find the value of Rr such that the circuit given in Fig. Q5(b) is resonant.

(10 Marks)(06 Marks)

(10 Marks)

(10 Marks)

(10 Marks)(10 Marks)

5rt

iu's=En* Fig.e7(b)

(10 Marks)

c.

6a.

la.

b.

Fig. Qs(b) Fig. Qs(c)Determine Rl and Rc- that causes the circuit to be resonant at all frequencies for the circuitshown in Fig. Q5(c). (04 Marks)

In the network shown in Fig. Q6(a) the switch is closed at t : 0. Determine

b. For the circuit shown in Fig. Q6(b), the switch 'K' is changed from position - I to position -2 at t: 0 steady - state condition having been reached at position - 1. Find the values of i,

. di ,d2it, Jand-;at t:o.dt dt'

d, d2i -+-r-.-at t:0dt'6,2

Fig. Q6(a) Fie. Q6(b)

Inthe Fig. Q7(a), the battery voltage'10'V is applied fbr a steady state period with switch'K' open. Obtain the cornplete expression lbr the current after closing the switch K. UseLaplace transforms.Referring to the Fig. Q7(b), solve lbr i;(t ). using Laplace transtbrmation.

ig ta^AA

Io-a-

2 su.(*-4

Fig.Q7(a)

8 a. Find the 'z' parameters of the circuit shown in Fig. Q8(a).T ILJL-\ .-

lbr a network

network.the

r(a)

lme

fbr

Q8(paral

ers fi

Following are the nrbl,T

[n, ' n,rl: [, 21

Lt , rrrr]-L3 6]

Determine the Y paramet

4-

(10 Marks)

USN 10IT35

Third Semester B.E. Degree Examination, Dec.2013 / Jan.2Ol4 :: ::

Electronic lnstrumentation . ',

Time: 3 hrs. Max. Markg:100

Note: .4nswer any FIVEfull questions, selecting atleast TWO questionsfrdmeach part.:::.

PART-A ."t"".'.,,

11 rr,rt

11,, ,

I a. Define the following terms as applied to an instrument : i) Accuracy and Precisionii) Random error iiil Absolute and relative error ir) ,Gxoss error v) Systematicerror. ,,

' (06 Marks)b. Determine the vaiue of the multiplier resistance on the 50V range of a dc voltmeter that uses

a250pA meter movement with an internal resistance of 100Q. (06 Marks)c. Explain in detail the working of true RMS volt rrrcter and give the difference between peak

(08 Marks)

2 a. Explain in detail the working of successive approximation tlpe digital voltmeter and givethe O/P for 4 bit control word. (08 Marks)

b. A 4% digit DUM is used for voltage measurements, i) Find its resolution ii) How would67.50Y be displayed on a 5V range iii) How would 0.716V be displayed on lV and10V ranges.

()oo

a)

oLoX

6e

trca.=NcB+hbnY()og:

_c()

;!

oO

o0ccB69=

-6!s=

5oOE

o- 6.

oj

a=AE!o

>,}trD0o=*otr>:o5Lo<:

.j(}a:z

oa

3a.b.c.

d.

re sponding and average resp,,qnding vo ltmet ers.

c. Explain in detail the working of digital multimetet.

Explain in detail the generation of time base signal for the horizontal deflecting plates.(05 Marks)

What is an electroflrd'*n.n and explain in detail lt, *.iAi..*odes of operation? (05 Marks)List the various control knobs on the front panel of CRO. (04 Marks)

(06 Marks)(06 Marks)

Marks)Marks)Marks)

An electrically deflected CRT has a final anode voltage of 2000V and parallel deflectingplates 1.59m apart. If the screen is 50cm from the center of t'h€ deflecting plates, findi) Beam speed ii) Deflection sensitivity of the tube iiD Deflection factor. (06 Marks)

4 a. ,,E4plain in detail the working of sampling oscilloscope, with necessary waveforms.' ''' (10 Marks)Explain in detail the working of digital storage oscilloscope and list the advantages of DSO.

(10 klarks)

PART _ B

Explain in detail the working of function generator.

b,

5a.b.c.

Explain in detail the working of square and pulse generator.Explain in detail the working of sine and square wave generator. (04

a. Explain in detail the working of wien bridge oscillator and find the parallel 'R' and 'C' thatcauses a wien bridge to null with the following components values. (12 Marks)R1 :2.7kC) , R2:22KA, Cl :5lrF , Rq: l00k0andtheoperating frequency is2.2KJ{2.

CEN{RALLIERARY t

10IT35

For the wheat stone bridge shown in fig. Q6(b), the galvanometer has a current sensitivity ofl2mmlpA. The internal resistance of galvanometer is 200Q. Calculate the deflection of thegalvanometer caused due to 5Q unbalance in the arm AD.

/i

tot *uru$,,,

t: ::'

.:.:::::.:

Fig.Q6(b)

*r;. 1 tOrt

Explain in detail the working of resistive position transducer afld f,i;o calculate the outputvoltage when,wjper is 10cm from extreme end for the applied voltage of 5V and if theresistive positid.tiansducer uses a shaft with a stroke

?{tOcm The total resistance of the

potentiometer is 5kQ. ,,,,, r,,,.. (10 Marks)Explain the construCtion principle and operation of LVDT. (10 Marks)

8a.b.c.

Write a short note on signal,eonditioning system.Explain the working of piezo eleCulc transdlmerwith circuit diagram.Compare LED displays and LCDdip,plafs.

(06 Marks)(10 Marks)(04 Marks)

.W",,;rtllil't'

ii,\1"."t

,,,:: :::, ,:

J'lgtt

2 of2

10ES36USN

2a.

Third Semester B.E. Degree Examination, Dec.2013 /Jan.2O14

Max. Marks: I00

Note: Answer FIVEfull questions, selectingat least TWO questions from each part.

hrs.

rks)

findo

c.

oiooLa

q

oo

ox

-*tcoo(d$itOYo)oE-o-ro>o2

a:

oo)(do

00i

-6

-.()OE

o.Etrp.(.) j

o=

A,i!o5.vx!bovio0o=soF>=ov!U.

\J<-i c'i

C)

oz

o

PART _ A

I a. State and -qxplain the Coulomb's law of force between the two po,]at charges. (05 Marks)b. Four 10nc positive charges are located in the Z:0 plane at thd coiners of a square of side

8cm. A fifth 10nc positive charge is located at a point 8cm distant from the other charges.Calculate the magnifude ofthe force on the fifth charge in free space. (07 Marks)A 100nc point charge is located at A(-1, 1, 3) in free space.i) Find the locus of all points P(x, y, z) at whichtr*:500 V/m.ii) Find yl it P(-2. y1. 3) lies on that locus. (08 Marks)

Determine the work done in carrying a charge of 2C from B(1, 0, 1) to A(0.8, 0.6, l) in

an-electric field E = yd, +xa, + 26,Ylmtalong the short arc of circl. *'+ y': l"Z:7.

b. Show that electric field intensity,, j'ni",Oue potential gradient.c. Derive an expression for continuit, equation in point form.c. The Z: 0 defines the boundary between free Space and dielectric medium

constant 20. The electric field intensity in free space is E,=106. +20Q

3a.b.

c.

4 .,..&

b.

c.

Determine the electrio field intensity in the dielectric medium.

Derive Poisson's and Laplace's equation.

In free space the volume charge density o,=ryC/mr,r'the potential V(r).

(06 Marks)(04 Marks)(04 Marks)

with dielectric

+40e,V/mt.

itor.(06 Marks)

Marks)Usmg Laplace's equation derive an expression for capacitance of

State and explain Biot-Savart law. (06 Marks)

Prove that Ampere's circular law V-x fr = i. i07 Marks)

Determine the magnetic field intensity fr at point P(0.4, 0.3, 0). If the 8A curreni: in aconductor inward from co to orgin on the x-axis and outward to .o along y-axis. (07 Marks)

PART _ B

5 a. Deduce the expression for force between the differential current elements. (10 Marks)b. A loop has a dimension of lmt x 2mt and lies in the uniform magnetic field

Eo = -0.6i, + 0.86, T. The loop current is 4mA. Calculate the torque on the loop. (10 Marks)

ffi

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10E536

a. Using Faraday's law derive an expression for emf induced in a stationary conductor placedin a time varying magnetic field. (04 Marks)

b. In a certain dielectric media the relative permittivity e, : 5, conductivity o : 0, the

displacement current density ia = 20cos(l.5 x 108t-bx)6y pNm'. Determine the electric

flux density and electric field intensity. (06 Marks)c. Show that, in a capacitor the conduction current density is equal to displacement current

" density for the applied voltage of v(t) : vs cos wt. (10 Marks)

a ' tlsing Maxwell's equation derive an expression for uniform plane wave in fre. rpug^.: _ _

b. Derive an expression for propagation constant, intrinsic impedance, and, ,*r" #r:"Y#\?

8 a. Derive an expression for reflection and transmission coefficient if the uniform plane wave

good confuting media if the uniform plane wave is propagating. "',, '

c. The fr fteiOi" t.e space is given by fr1*,t; = 10cos(10't -B*iay A/mt .

E(x, t) at P(0.1, A.2,0.3) and t: lns.

incident normally at tiie'boundary with different dielertric.b. Write a short note on Poyn(ipg theorem.

(06 Marks)

Find B, )" and

(06 Marks)

(10 Marks)(10 Marks)

,,'11. ",,, , ,,. ,i'

. , *.,0 *. ,I'.'*

..:

,, ,,,""' 1,,,,

:':: '

, .,. i

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