COURSE HANDOUT - Rajagiri School of Engineering & · PDF fileCOURSE HANDOUT Department of...

COURSE HANDOUT Department of Electrical & Electronics Engineering

SEMESTER 1

Period: August 2017 – December 2017

ii

INDEX

PAGE NO.

1 Assignment Schedule iii

2 MA101: Calculus 1

2.1 Course Information Sheet 8

2.2 Course Plan 6

2.3 Tutorials & Assignments 11

3 PH100 Engineering Physics 27


3.2 Course Plan 36

3.3 Tutorials 39

3.4 Assignments 40

4 BE100: Engineering Mechanics 42


4.2 Course Plan 47

4.3 Tutorials 51

4.4 Assignments 56

5 BE101 03: Introduction to Electrical Engineering 57


5.2 Course Plan 62

5.3 Tutorials 64

5.4 Assignments 82

6 BE103: Introduction to Sustainable Engineering 88


6.2 Course Plan 94

6.3 Assignments 97

6 CE100: Basics of Civil Engineering 98


6.2 Course Plan 104

6.3 Tutorials 107

6.4 Assignments 108

7 PH110: Engineering Physics Lab 109


7.2 Course Plan 111

8 EE 110: Electrical Engineering Workshop 112


8.2 Course Plan 114

8.3 Lab Cycle 115

8.4 Lab Questions 116

iii

ASSIGNMENT SCHEDULE

SUBJECT DATE

MA101: Calculus Week1

Week 7

PH100 Engineering Physics

Week 2

Week 8

BE100: Engineering Mechanics

Week 3

Week 9

BE101 03: Introduction to Electrical

Engineering

Week 4

Week 10

BE103: Introduction to Sustainable

Engineering

Week 5

Week 11

CE100: Basics of Civil Engineering

Week 6

Week 12

Course Handout

Department of Electrical & Electronics Engineering Page 1

2. MA101: CALCULUS

Course Handout


2.1 COURSE INFORMATION SHEET

PROGRAMME: ENGINEERING DEGREE: B.TECH

COURSE- CALCULUS SEMESTER-1 CREDITS-4

COURSE CODE- MA101

Year of introduction - 2016

COURSE TYPE - CORE

COURSE AREA/DOMAIN- MATHEMATICS CONTACT HOURS: 3-1-0

CORRESPONDING LAB COURSE CODE (IF

ANY): NIL

LAB COURSE NAME: NA

SYLLABUS:

MODULE DETAILS HOURS

I Basic ideas of infinite series and convergence.

Convergence tests-comparison, ratio, root and integral

tests (without proof). Geometric series and p-

series. Alternating series, absolute convergence,

Leibnitz test. Maclaurins series-Taylor series - radius of

convergence

9

II Partial derivatives - Partial derivatives of functions of

more than two variables - higher order partial

derivatives - differentiability, differentials and local

linearity

The chain rule - Maxima and Minima of functions of

two variables - extreme value theorem (without

proof)relative extrema.

9

III Introduction to vector valued functions - parametric

curves in 3-space. Limits and continuity - derivatives -

tangent lines - derivative of dot and cross

productdefinite integrals of vector valued functions.

unit tangent - normal - velocity - acceleration and speed

9

Course Handout


- Normal and tangential components of acceleration

Directional derivatives and gradients-tangent planes and

normal vectors.

IV Double integrals - Evaluation of double integrals -

Double integrals in non-rectangular coordinates -

reversing the order of integration.

Area calculated as double integral

Triple integrals - volume calculated as a triple integral

9

V Vector and scalar fields- Gradient fields – conservative

fields and potential functions – divergence and curl - the

Gradient operator , Laplacian

Line integrals - work as a line integral- independence of

path-conservative vector field.

8

VI Green’s Theorem (without proof- only for simply

connected region in plane), surface integrals –

Divergence Theorem (without proof) , Stokes’ Theorem

(without proof)

10

Total hours – 54

Text /Reference books

TEXT/REFERENCE BOOKS:

T/R BOOK TITLE/AUTHORS/PUBLICATION

T • Anton, Bivens and Davis, Calculus, John Wiley and Sons.

R Thomas Jr., G. B., Weir, M. D. and Hass, J. R., Thomas’ Calculus, Pearson.

R B.S Grewal-Higher Engineering mathematics,Khanna publishers,New Delhi

R Jordan, D. W. and Smith, P., Mathematical Techniques, Oxford University Press.

R Kreyszig, E., Advanced Engineering Mathematics, Wiley India edition.

Course Handout


Course Objectives

In this course the students are introduced to some basic tools in Mathematics which are useful in modelling and analysing

physical phenomena involving continuous changes of variables or parameters. The differential and integral calculus of functions of

one or more variables and of vector functions taught in this course have applications across all branches of engineering. This course

will also provide basic training in plotting and visualising graphs of functions and intuitively understanding their properties using

appropriate software packages.

Course Outcomes

1 Students are introduced to some basic tools which are useful in modelling and analysing

physical phenomena.

2 Students will get an awareness of phenomena involving continuous change of variables.

3 Students are introduced to differential and integral calculus of functions of one or more

variables and of vector functions.

4 Students are introduced finding areas and volumes using integrals.

5 Students will analyze the application of vector valued functions in physical applications.

6 Students will be introduced to plotting and visualising graphs of functions.

2) CO mapping with PO, PSO

PO1 PO2 PO3 PO4 PO

5

PO

6

PO

7

PO

8

PO

9 PO10

PO

11

PO

12

PSO

1

PSO

2

PS

O3

CO1 3

CO2 3

CO3 3 3

CO4 3 3

CO5 3

CO6 3 2 3

Mapping to be done based on extent of correlation between specific CO and PO. Refer SAR Format, June

2015 for details.

Course Handout


* Average of the correlation values of each CO mapped to the particular PO/PSO, corrected to the nearest whole number

3) Justification for the correlation level assigned in each cell of the table

above.

PO1 PO2 PO3 PO4

P

O

5

P

O

6

P

O

7

P

O

8

P

O

9

P

O

1

0

P

O

11

P

O

12

PSO

1

P

S

O

2

PS

O3

CO

1

fundamental

knowledge in

Calculus will

help in

analyzing

engineering

problems very

easily

CO

2

Basic

knowledge in

continuous

change in

variables will

help to model

various

engineering

problems

CO

3

basic

knowledge in

differential and

integral

calculus of

functions of

several

variableshelps

in solving

engineering

problems

differential

and integral

calculus will

help to design

solutions for

various

engineering

problems

CO

4

basic

knowledge in

finding areas

and volumes is

used for

solving

complex

engineering

problems

techniques of

finding areas

and volumes

using

integration is

used for

designing

solutions for

various

Course Handout


engineering

problems

CO

5

concept of

vector valued

functions will

give thorough

knowledge in

the application

problems

CO

6

plotting and

visualising

graphs and

surfaces will

help in

analysing

various

engineering

problems

visualisin

g of

graphs

will help

in easier

formulatio

n of

various

problems

plotting and

visualising

graphs and

surfaces will

help in

designing

solutions of

complex

problems

easily.

DELIVERY/INSTRUCTIONAL METHODOLOGIES

CHALK & TALK

WEB RESOURCES

STUDENT ASSIGNMENTS

ASSESMENT METHODOLOGIES – DIRECT

ASSIGNMENTS

SEMINARS

TESTS/ MODEL EXAMS

UNIVERSITY EXAMS

ASSESMENT METHODOLOGIES INDIRECT

ASSESMENT OF COURSE OUTCOMES( BY FEEDBACK, ONCE)

STUDENT FEEDBACK ON FACULTY

WEB SOURCES

Course Handout


Open source software packages such as gnuplot, maxima, scilab, geogebra or R may be used as appropriate

for practice and assignment problems

Course Handout


2.2 COURSE PLAN

Sl.No Module Planned Date Planned

1 1 7-Aug-17 SEQUENCE AND INFINITE SERIES

2 1 8-Aug-17 GEOMETRIC SERIES AND HARMONIC SERIES

3 1 10-Aug-17 CONVERGENCE TEST - COMPARISON TEST

4 1 11-Aug-17 SEQUENCE OF PARTIAL SUM

5 1 14-Aug-17 LIMIT COMPARISON TEST

6 1 17-Aug-17 RATIO TEST

7 1 22-Aug-17 ROOT TEST

8 1 24-Aug-17 ALTERNATING SERIES, LEIBNITZ'S TEST

9 1 25-Aug-17 ABSOLUTE CONVERGENCE

10 1 26-Aug-17 MACLAURIAN AND TAYLOR SERIES

11 1 29-Aug-17 RADIUS OF CONVERGENCE

12 1 11-Sep-17 PROBLEMS

13 1 14-Sep-17 PROBLEMS

14 2 15-Sep-17 PARTIAL DERIVATIVES OF FUNCTIONS OF

MORE THAN 2 VARIABLES.

Course Handout


15 2 16-Sep-17 HIGHER ORDER PARTIAL DERIVATIVES,

DIFFERENTIABILITY.

16 2 26-Sep-17 CHAIN RULE,LOCAL LINEARITY.

17 2 3-Oct-17 MAXIMA AND MINIMA OF FUNCTIONS OF TWO

VARIABLES.

18 2 5-Oct-17 EXTREME VALUE THEOREM.

19 2 6-Oct-17 RELATIVE EXTREMA

20 2 9-Oct-17 DIFFERENTIAL AND LOCAL LINEARITY

21 4 10-Oct-17 MULTIPLE INTEGRALS.

22 4 12-Oct-17 DOUBLE INTEGRALS, TRIPLE INTEGTRALS

23 4 13-Oct-17 REVERSING THE ORDER OF INTEGRATION

24 4 16-Oct-17 AREA BY DOUBLE INTEGRATION

25 4 17-Oct-17 VOLUME BY TRIPLE INTEGRATION.

26 4 24-Oct-17 VOLUME - PROBLEMS

27 4 26-Oct-17 PROBLEMS

28 4 27-Oct-17 PROBLEMS.

29 3 30-Oct-17 VECTOR CALCULUS.

30 3 31-Oct-17 INTRODUCTION TO VECTOR VALUED

FUNCTIONS

Course Handout


31 3 2-Nov-17 PARAMETRIC CURVES IN 3 DIMENSIONAL

SPACE

32 3 3-Nov-17 LIMIT AND CONTINUITY

33 3 6-Nov-17 DERIVATIVES, TANGENT LINES

34 3 7-Nov-17 DERIVATIVES OF DOT AND CROSS PRODUCT

35 3 9-Nov-17 DEFINITE INTEGRALS OF VECTOR VALUED

FUNCTION, UNIT TANGENT AND NORMAL

VECTORS.

36 3 10-Nov-17 DIRECTIONAL DERIVATIVES AND GRADIENT.

37 5 13-Nov-17 VECTORS AND SCALAR FIELD

38 5 14-Nov-17 GRADIENT FIELD, CONSERVATIVE FIELD &

POTENTIAL FUNCTION.

39 5 16-Nov-17 DIVERGENCE AND CURL, DEL OPERATOR,

LAPLACIAN OPERATOR

40 5 17-Nov-17 LINE INTEGRAL, WORK AS LINE INTEGRAL,

CONSERVATIVE VECTOR FIELD.

41 6 20-Nov-17 GREEN'S THEOREM

42 6 21-Nov-17 SURFACE INTEGRAL

43 6 23-Nov-17 DIVERGENCE THEOREM.

44 6 24-Nov-17 STOKE'S THEOREM.

Rajagiri School of Engineering and Technology, Kakkanad, Kochi

TUTORIAL/ASSIGNMENT RECORD BOOK

Course : CALCULUS

Code : MA101

Branch : Common for all Branches

Semester : I

Academic Year : 2017

University : APJ Abdul Kalam Technological University

Name of the Student: ………………………………………………….

Reg. No: ………………………… Branch: …………………………..

Faculty in charge: ……………………………………………………..


INDEX

Module I Single variable calculus and infinite series

Tutorial Questions

Qn. No: 1 2 3 4 5 6 7 8 9 10

Remarks

Assignment Questions Date of submission:

Qn. No: 1 2 3 4 5 6 7 8 9 10 Total

Remarks

Marks

Module II Partial derivatives and its applications

Tutorial Questions

Qn. No: 1 2 3 4 5 6 7 8 9 10

Remarks


Qn. No: 1 2 3 4 5 6 7 8 9 10 Total

Remarks

Marks

Module III Calculus of vector valued function

Tutorial Questions

Qn. No: 1 2 3 4 5 6 7 8 9 10

Remarks


Qn. No: 1 2 3 4 5 6 7 8 9 10 Total

Remarks

Marks


Module IV Multiple integrals

Tutorial Questions

Qn. No: 1 2 3 4 5 6 7 8 9 10

Remarks


Qn. No: 1 2 3 4 5 6 7 8 9 10 Total

Remarks

Marks

Module V Topics in vector calculus

Tutorial Questions

Qn. No: 1 2 3 4 5 6 7 8 9 10

Remarks


Qn. No: 1 2 3 4 5 6 7 8 9 10 Total

Remarks

Marks

Module VI Topics in vector calculus (continued)

Tutorial Questions

Qn. No: 1 2 3 4 5 6 7 8 9 10

Remarks


Qn. No: 1 2 3 4 5 6 7 8 9 10 Total

Remarks

Marks

Total Marks :

Signature of the faculty

Module I Single variable Calculusand Infinite Series

Tutorial Questions

1. Find the sum of the series

∑∞k=1

4k+2

7k−1a)∑∞

k=11

9k2+3k−2b)

2. In each part, find all values of x for which the series converges, and find the sum ofthe series for the values of x

x− x3 + x5 − x7 + x9 − · · ·a) 1x2 +

2x3 +

4x4 +

8x5 +

16x6 + · · ·b)

3. Use limit comparison test to determine whether the following series converges

13+

√25+

√37+ · · ·a)

∑∞k=1

√k4 + 1−

√k4 − 1b)

4. Test The convergence of the following series:

∑∞k=1

(k!)2

(2k)!a)

∑∞k=1

log k2k

b)

5. Classify each series as absolutely convergent, conditionally convergent or divergent

∑∞k=1(−1)k+1 k+7

k(k+4)a)

∑∞k=2

(−1)k+1(2k)!(3k−2)!

b)

6. Suppose that the function f is represented by the power series

f(x) = 1− x

2+

x2

4− x3

8+ · · ·+ (−1)k

xk

2k+ · · · .

Find (a) domain of f (b) f(0) and f(1).

7. Find the Taylor series about x0 = loge 3 of f(x) = e−x.

8. Find the Maclaurin series for the function f(x) = x sin x

9. Find the domain of the function f(x) =∑∞

k=11·3·5···(2k−1)

(2k−1)!xk.

10. Find the radius of convergence and the interval of convergence

∑∞k=1

xk

(2k+3)a)

∑∞k=0

100k

k!xkb)

∑∞k=1(

34)k(x+ 5)kc)

1

Tutorials & Assignments MA101 CALCULUS

Assignment questions

1. Find the sum of the series

∑∞k=1 5

3k61−ka)∑∞

k=11

4k2−1b)

∑∞k=1 5

−k − 1k(k+1)

c)

2. Find all values of x for which the series∑∞

k=1 e−kxconverges, and find the sum of

the series for the values of x.

3. Use limit comparison test to determine whether the following series converges

∑∞k=1

4k3−6k+58k7+k−8

a)∑∞

k=11√

k3+1b)

∑∞k=1

13√8k2−3k

c)

4. Test the convergence of the following series:

∑∞k=1

k2

2ka)

∑∞k=1

11+

√k

b)∑∞

k=1 e−k log kc)

5. Classify each series as absolutely convergent, conditionally convergent or divergent

∑∞k=1

(−1)k+1

7ka)

∑∞k=2

(−4)k

k3b)

∑∞k=2

(−π(k+1))k

kk+1c)

6. Use the ratio test for absolute convergence to determine whether the series convergesor diverges

∑∞k=1(−4

5)ka)

∑∞k=2

(−1)kk5

ekb)

7. Find the Maclaurin series for the function

log(1 + x)a) sinh xb)

8. Find the Taylor series about x0 = 1 of f(x) = 1x+2

.

9. Find the radius of convergence and the interval of convergence

∑∞k=1(−1)k+1 xk

k(log k)2a)

∑∞k=0

(2k+1)!(x−5)k

k4b)

∑∞k=1(−1)k x3k

(2k)!c)

10. Show that if p is a positive integer, then the power series∑∞

k=0(pk)!(k!)p

xk has a radius

of convergence of p−p.

Answers

Tutorial Questions

1. a) 448/3 b) 1/6

2. a) |x| < 1, S = x1+x2 b) |x| > 2;S =

1x(x+2)

3. a) Diverges b) Converges

4. a) Converges b) Converges

5. a) Conditionally converges b) Abso-lute Convergent

6. a) |x| < 2 b) f(0) = 1, f(1) = 2/3

7.∑∞

k=0(−1)k(x−ln 3)k

3k!

8.∑∞

k=0(−1)kx2x+2

(2k+1)!

Rajagiri School of Engineering & Technology 2


9. R = +∞

10. a) R = 1, [−1, 1) b) R = ∞, (−∞,∞)c) R = 4/3, (−19/3,−11/3)

Assignment Questions

1. a) Diverges b) 1/2 c) -3/2

2. x > 0;S = 1ex−1

3. a) Converges b) Converges c) Diverges

4. a) Converges b) Diverges c) Converges

5. a) Conditional b) Absolute c) Diver-gent

6. a) Absolute convergent b) AbsoluteConvergent

7. a)∑∞

k=1(−1)k+1xk

kb)

∑∞k=0

x2x+1

(2k+1)!

8.∑∞

k=0(−1)k(x−1)k

3k+1

9. a) R = 1, |x| < 1 b) R = 0, x = 5 c)R = ∞, |x| < ∞


Module II Partial Derivative and itsApplications

Tutorial Questions

1. Let z = e3x sin y. Find zx and zy at (x, 0), (0, y) and (ln 3, 0).

2. Find wx, wy and wz of a) w = x2−z2

y2+z2b) w =

√x2 + y2 + z2

3. Show that the function satisfies Laplace’s equation zxx + zyy = 0 wherea) z = x2 − y2 + 2xy b) z = ln(x2 + y2) + 2 tan−1 y

x

4. Confirm that the mixed second order partial derivatives of f are the samea) f(x, y) = ln(x2 + y2) b) f(x, y) = ex−y2 c) f(x, y) = x2−y2

x2+y2

5. Find zx and zy. a) x2 − 3yz2 + xyz − 2 = 0 b) yex − 5 sin 3z = 4z

6. Compute the differential dz or dw of the function a) z = 5x2y5 − 2x+ 6y + 7b) z = sec2(x− 4y) c) w = tan−1(xyz) d) w = 4x2y3z7 − 3xy + 7z + 5

7. Use appropriate form of the chain rule to find dwdt

a) w = 5x2y3z4; x = t2, y = t3, z = t4

b) w = 5 cosxy − sin xz; x = 1t; y = t; z = t2

8. Find the local linear approximation L to the specified function f at the designatedpoint P . Compare the error in approximating f by L at the specified point Q withthe distance between P and Qa) f(x, y) = x sin y;P (0, 0), Q(0.003, 0.004)b)f(x, y) = ln(xy);P (1, 2), Q(1.01, 2.01)c) f(x, y, z) = xyz;P (1, 2, 3), Q(1.001, 2.002, 3.003)

9. Use appropriate forms of the chain rule to find zu and zv a) z = ex2y; x =

√uv; y = 1

v

b) z = cosx sin y; x = u−v, y = u2+v2 c) z = 3x−2y; x = u+v ln u; y = u2−v ln v

10. Locate all relative maxima, relative minima and saddle points, if anya) f(x, y) = x2 + y2 + 32

xyb) f(x, y) = ex cos y c) f(x, y) = e−(x2+y2+4x)

4



1. (a) Let z = xe−y + 5y. Find the rate of change of z w.r.t. x and y at the point(3,1)

(b) Let z = sin(y2 − 4x). Find the rate of change of z w.r.t. x and y at the point(3,1).

2. Show that u(x, y) and v(x, y) satisfy the Cauchy - Riemann equations:

ux = vy; uy = −vx

where, a) u = x2 − y2, v = 2xy b) u = ex cos y; v = ex sin y

3. Find fx, fy and fz of a) f(x, y, z) = z ln(x3y cos z) b) f(x, y, z) = y−32 sec xz

y.

4. Compute the differential dw: a) w = x3y2z2 b) w =√x+

√y +

√z

5. Find the local linear approximation L to the specified function f at the designatedpoint P . Compute the error in approximating f by L at the specified point Q withthe distance between P and Q. a) f(x, y) = x0.5y0.3; P (1, 1), Q(1.05, 0.97). b)f(x, y, z) = ln(x+ yz); P (2, 1,−1), Q(2.02, 0.97,−1.02).

6. Suppose that w − x cos(yz2); x = cos t; y = t2; z = et. Find dwdt

at t = π, using chainrule and verify answer.

7. Let u = rs2 ln t, r = x2, s = 4y + 1, t = xy3. Find ux and uy.

8. (a) Let w = f(ρ), where ρ =√

x2 + y2 + z2. Show that w2x + w2

y + w2z = w2

ρ.

(b) Let w = f(x− y, y − z, z − x). Show that wx + wy + wz = 0.

9. (a) Find dydx, i) x3 − 3xy2 + y4 = 5 ii) exy + yex = 1

(b) Find zx and zy by implicit differentiation and verify with formulas, whereln(1 + z) + xy2 + 2z = 1.

10. Locate the relative maxima, relative minima and saddle points if any a) f(x, y) =y sin x b) f(x, y) = x2 + xy + y2 − 6x c) f(x, y) = xy + 2

x+ 4

y

Answers

Tutorial Questions

1. zx(x, 0) = 0, zx(0, y) = 3 sin y,zx(ln 3, 0) = 0, zy(x, 0) = 3e3x,zy(0, y) = 3 cos y, zy(ln 3, 0) = 27

2. a) wx = 2xy2+z2

, wy = −2y(x2−z2)(y2+z2)2

, wz =−2z(x2+y2)(y2+z2)2

b) wx = x√x2+y2+z2

, wy =

y√x2+y2+z2

, c) wz =z√

x2+y2+z2

3. verify

4. verify

5. a) zx = 2x+yz6yz−xy

, zy = xz+3z2

6yz−xyb) zx =

yex

15 cos 3z+4, zy =

ex

15 cos 3z+4



6. a) (10xy5 − 2)dx+ (25x2y4 + 6)dy b)2 sec2(x−4y) tan(x−4y)dx−8 sec2(x−4y) tan(x − 4y)dy c) yzdx

1+x2y2z2+

xzdy1+x2y2z2

+ xydz1+x2y2z2

d) (8xy3z7−3y)dx+

(12x2y2z7 − 3x)dy + (28x2y3z6 + 7)dz

7. a) 145t28 b) − cos t

8. a) 0, 0.0024 b) ln 2+(x−1)+0.5(y−2),0.0043931 c) 6+ 6(x− 1) + 3(y− 2)+2(z − 3), -0.000481

9. a) eu, 0 b) −sin(u − v) sin(u2 + v2) +2u cos(u − v) cos(u2 + v2), sin(u −v) sin(u2+ v2)+2v cos(u− v) cos(u2+v2) c) 3+ 3v/u− 4u, 2+ 3 lnu+2 ln v

10. a) (-2,-2), (2,2) relative minima b)nocritical points c) (-2,0); relative maxi-mum


1. a) 1, 1 b) −4 cos 11, 2 cos 11

2. Verify

3. a) fx = 3z/x, fy = z/y, fz =ln(x3y cos z) − z tan z b) fx =y−5/2z sec(xz/y) tan(xz/y), fy =−xy−7/2z sec(xz/y) tan(xz/y) −(3/2)y−5/2 sec(xz/y), fz =xy−5/2 sec(xz/y) tan(xz/y)

4. a) 3x2y2z2dx+ 2x3yz2dy + 2x3y2zdzb) dx/2

√x+ dy/2

√y + dz/2

√z

5. a) 1 + 0.5(x− 1) + 0.3(y − 1), 0.0107b) (x−2)−(y−1)+(z+1), 0.00342356

6. Verify

7. x(4y + 1)2(1 + 2 lnxy3), 8x2(4y +1) lnxy3 + 3x2(4y + 1)2/y

8. a) Verify b) Verify

9. a) i) − 3x2−3y2

−6xy+4y3ii) yexy

xexy+yey+eyb)

−y2(1+z)3+2z

, −−2xy(1+z)3+2z

10. a) (nπ, 0), saddle points b) (4,-2), rel-ative minimum c) (1,2), relative min-imum


Module III Vector Valued Function

Tutorial Questions

1. Find the limit : limt→∞

(t3+14t3+2

, 1t

).

2. Find the parametric equations of the line tangent to the graph of ~r(t) = e2ti−2 sin 5tjat t = 0.

3. Evaluate∫ π

2

0(cos 2t, sinh 2t) dta)

∫ 2

0

(√t, 1√

t

)dtb)

4. Find the unit tangent vector and the normal vector to the graph of

~r(t) = t2

2i+ t3

3j; t = 2a) ~r(t) = (t2 + 1)i+ tj; t = 1b)

5. Find the velocity, speed and acceleration at the given time t of a particle movingalong the curve:

~r(t) = ti+ t2

2j + t3

3k; t = 2a)

~r(t) = 2 cos t, y(t) = 2 sin(t), z = t; t = π2

b)

6. Find the scalar and vector tangential and normal component of acceleration of~r = e−ti+ etj at time t0 = 0.

7. Find Duf at P . f(x, y, z) = yex2

+ z3, P (0, 2, 3), u = 17(2i− 3j + 6k).

8. Find the unit vector in the direction in which f decreases most rapidly at P andfind the rate of change of f at P in that direction.

f(x, y) = 20− x2 − y2, P (−1,−3)a) f(x, y) = exy, P (1, 3)b)

9. Find the gradient of f(x, y, z) = yz + xz + xy at (1,1,1).

10. The temperature (in degree Celsius) at a point (x, y) on a metal plate on the xy-plane is T (x, y) = xy

1+x2+y2.

Find the rate of change of temperature at (1, 1) in the direction of ~a = 2i− j.a)

An ant at (1, 1) wants to walk in the direction in which the temperature dropsmost rapidly. Find a unit vector in that direction.

b)

7



1. Find the limit of limt→1

(3t2, ln tt2−1

, cos 3t).

2. Find the parametric equation of the line tangent to the graph ~r(t) = t2i+(2− ln t)jat t = e.

3. Evaluate∫ 1

0

(e2ti+ e−tj + 2tk

)dt.

4. Find ~T and ~N

~r(t) = 5 cos ti+ 5 sin tj, t = π3

a) ~r(t) = ln 2ti+ tj, t = eb)

5. Find the velocity, speed and acceleration at the given time t of a particle movingalong the curve: ~r(t) = et sin ti+ et cos tj + tk, t = π.

6. Find the scalar and vector tangential and normal component of acceleration at timet.

~r(t) = cos(t2)i+ sin(t2)j, t =√π2

a) ~r(t) = (t3 − 2t)i+ (t2 − 4)j, t = 1b)

7. Find Duf at P , f(x, y) = ln(1 + x2 + y2); P (0, 0); u = 1√10(−i− 3j).

8. Find the unit vector in the direction in which f decreases most rapidly at P andthe rate of change of f(x, y, z) =

√x− 3y + 4z at P (0, 0, 4) in that direction.

9. Find the gradient of f(x, y, z) = xy2z3 at (1, 1, 1).

10. The temperature (in degree Celsius) at a point (x, y, z) in a metal solid is T (x, y, z) =xyz

1+x2+y2+z2

Find the rate of change of temperature with respect to distance at (1, 1, 1) inthe direction of the origin.

a)

Find the direction in which the temperature rises most rapidly at the point(1,1,1).

b)

Answers

Tutorial Questions

1. (0.25, 0)

2. ~r(t) = (2i− 10j)t+ i

3. a) (0, cosh π − 1) b) (1.8856, 2.8284)

4. a)T (2) = 1√5(i+2j), N(2) = 1√

5(−2i+

1j) b) T (1) = 1√5(2i + j), N(1) =

1√5(i− 2j)

5. a) ~v = i + 2j + 4k,~a = j + 4k, ‖v‖ =√21. b) ~v = −2i+ k,~a = −2j, ‖v‖ =√5‖v‖ =

√21.

6. aT = 0, aN ~N = i+ j, aN =√2

7. 1717

8. a) −2√2 b) −

√10e3

9. (z + y)i+ (z + x)j + (y + x)k



10. a) 19√5b) −1√

2(i+ j)


1. (3, 0.5, cos 3)

2. ~r(e) = e2i+j, x = e2+2et, y = 1−te−1

3. 12(e2 − 1)i+ (1− e−1)j + k

4. a) (π/3) = −√3i + 0.5j; N(π/3) =

−0.5i−.5√3j b) T (e) = 1√

1+e2(i+ej),

N(e) = 1√1+e2

(−ei+ j)

5. ~v = −eπ i − eπ j + k, ‖v‖ = (1 +2e2π),~a = −2eπ i.

6. a) aT = 2, aN = π b) aTT = −√2(j −

j), aNN = (π/2)(i+ j)

7. 0

8.√268

9. (1,2,3)

10. a) −√3/8 b)(1, 1, 1)/

√3


Module IV Multiple integrals

Tutorial Questions

1. Evaluate∫∫

(x2+y2)dxdy over the region in the positive quadrant for which x+y ≤ 1.

2. Evaluate∫∫

xydxdy over the positive quadrant of the circle x2 + y2 = a2.

3. Evaluate∫ 4

0

∫ 4

yxdxdyx2+y2

by changing the order of integration.

4. Evaluate∫ 1

−1

∫ z

0

∫ x+z

x−z(x+ y + z)dydxdz.

5. Evaluate∫ 3

1

∫ 11

x

∫ √xy

0xyzdzdydx.

6. Find by double integration, the smaller of the areas bounded by the circles x2+y2 = 9and the line x+ y = 3.

7. Find the area enclosed by the curves y = 3xx2+2

and 4y = x2.

8. Evaluate∫ 1

0

∫ √1−x2

0

∫√1−x2−y2

0dzdydx√

1−x2−y2−z2.

9. Evaluate∫ e

0

∫ log y

1

∫ ex

1log zdzdxdy.

10. Find by triple integration, the volume in the positive octant bounded by the coor-dinate planes and the plane x+ 2y + 3z = 4.


1. Evaluate∫∫

S

√xy − y2dxdy, where S is a triangle with vertices (0, 0), (10, 1), and

(1, 1).

2. Evaluate∫∫

Axydxdy, where A is the domain bounded by the x-axis, ordinate x = 2a

and the curve x2 = 4ay.

3. Evaluate∫ a

0

∫ a√ax

y2√y4−a2x2

dydx, by changing the order of integration.

4. Evaluate∫ log 2

0

∫ x

0

∫ x+log y

0ex+y+zdzdydx.

5. Find the area bounded by the parabola y = x2 and the line y = 2x+ 3.

10


6. Find the areas bounded by the parabolas y2 = 4− x and y2 = 4− 4x.

7. Find by double integration, the area enclosed by the ellipse x2

a2+ y2

b2= 1.

8. Evaluate∫ 2

0

∫ √4−x2

0

∫ 3−x2−y2

−1+x2+y2xdzdydx.

9. Evaluate∫ 3

0

∫ √9−z2

0

∫ x

0xydydxdz.

10. Find by triple integration, the volume of the parabloid of revolution x2 + y2 = 4zcut off by the plane z = 4.

Answers

Tutorial Questions

1.∫ 1

0

∫ 1−x

0(x2 + y2)dydx = 1

6

2.∫ a

0

∫ √a2−x2

0xydydx = a4

8

3.∫ 4

0

∫ x

0x

x2+y2dydx = π

4. 0

5. 139− 1

6log 3

6.∫ 3

0

∫√9−y2

3−ydxdy = 9

4(π − 2)

7.∫ 2

0

∫ 3x

x2+2

x2

4

dydx = 32log 3− 2

3

8. π2

8

9. 14(e2 − 8e+ 13)

10.∫ 4

0

∫ 1

2(4−x)

00

1

3(4−x−2y)

dzdydx = 169


1.∫ 1

0

∫ 10y

y

√xy − y2dxdy = 6

2.∫ 2a

0

∫ x2

4a

0xydydx = a4

3

3.∫ a

0

∫ y2

a

0y2√

y4−a2x2dxdy = πa2

6

4. 83log 2− 19

9

5.∫ 3

−1

∫ 2x+3

x2 dydx = 323

6.∫ 2

−2

∫ 4−y2

4−y2

4

dxdy = 8

7. πab

8. −3215

9. 815

10. 4∫ 4

0

∫ √16−x2

0

∫ 4x2+y2

4

dzdydx = 32π


Module V Topics in vector calculus

Tutorial Questions

1. Compute the divergence and curl of the vector F = xyzi + 3x2yj + (xz2 − yz)k at(1,2,-1).

2. If a is a constant vector and ~r = xi+ yj + zk , show that ∇× (a× r) = 2a.

3. Find the value of a if F = (axy − z2)i+ (x2 + 2yz)j + (y2 − axz)k has curl zero.

4. Obtain a,b and c such that curlF = 0 where F = (x+ y + az)i + (bx + 2y − z)j +

(−x+ cy + 2z)k.

5. Let F = (y2 + 2xz2 − 1)i + 2xyj + 2x2zk. Show that curlF = 0. and find φ suchthat F = ∇φ.

6. If F = (3x2 +6y)i− 14yzj+20xz2k, evaluate∫CF.dr along the path C : x = t, y =

t2, z = t3

7. Find the work done by the force field F on a particle that moves along the curve Cwhere F (x, y, z) = (x+y)i+xyj− z2k and C: along the line segments from (0, 0, 0)to (1, 3, 1) to (2,−1, 5).

8. If F = (4xy − 3x2y2)i+ 2x2j − 2x3zk , show that∫CF cot d~r is independent of the

path C and find the potential φ .Hence find∫CF.dr where C is the path joining

(0, 0, 0) and (1, 1, 1).

9. Evaluate∫CF · d~r where F = (x− 3y)i+ (x− 2y)j and C is the closed curve in the

XY plane x = 2 cos t, y = 3 sin t from t = 0 to t = 2π.

10. Let C be the curve represented by the equation x = 2t,y = 3t2, (0 ≤ t ≤ 1).Evaluate∫C(x+ y)dy.


1. Prove that div r = 3 and curl r = 0 where r = xi+ yj + zk.

2. Determine the constant a so that the vector F = (x+ 3y)i+ (y − 2z)j + (x+ az)khas zero divergence.

12


3. A field F is of the form F = (6xy + z3)i+ (3x2 − z)j + (3xz2 − y)k, show that F isconservative field and find its potential.

4. Prove that ∇2(1r) = 0 where r =

√x2 + y2 + z2.

5. If F = 3xyi− y2j, evaluate∫CF.dr where C is the curve y = 2x2 in the XY plane

from (0, 0) to (1, 2).

6. Find the total work done in moving a particle in a force field given by F = 3xyi−5zj + 10xk along the curve x = t2 + 1,y = 2t2,z = t3 from t = 1 to t = 2.

7. Find the line integral of F around the curve C where F = yi + zj + xk and thecircle x2 + y2 = 1,z = 0.

8. Evaluate∫CF.dr where F = (x2 + y2)i− 2xyj where C is the rectangle in the XY

plane bounded by y = 0,x = a,y = b,x = 0.

9. Determine whether F (x, y) = (cos y + y cosx)i + (sin x− x sin y)j is a conservativevector field and if so find a potential function for it.

10. Show that∫ (−2,0)

(2,−2)2xy3dx+3x2y2dy is independent of path and use the fundamental

theorem of line integral to find its value.

Answers

Tutorial Questions

1. divF = 5at(1, 2,−1), curlF = 4i+ j+

13k

2.

3. a = 2

4. a = −1 = c, b = 1

5. φ = x2z2 + xy2 − x+ c

6. 5

7. −2336

8. φ = 2x2y + x3z2 and∫CF.dr = 0

9. 6π

10. 172


1.

2. a = −2

3. φ = 3x2 + xz3 − yz + c

4.

5. −76

6. 303

7. −π

8. −2ab2

9. conservative and φ = xcosy+ysinx+k

10. 32


Module VI Topics in Vector Calculus(contd.)

Tutorial Questions

1. Verify Green’s Theorem in the plane for∮C

(xy+y2)dx+x2dy where C is the closedcurve of the region bounded by y = x and y = x2.

2. Apply Green’s Theorem to evaluate∮C(y−sin x)dx+cosxdy where C is the triangle

C enclosed by the lines y = 0, x = π2and y = 2x

π.

3. Find the area of the ellipse using Green’s Theorem.

4. Evaluate the surface integral∫∫

σf(x, y, z)dS where f(x, y, z) = z2 and σ is the

portion of the cone z =√

x2 + y2 between the planes z = 1 and z = 3.

5. Find the flux of the vector field F across σ where F (x, y, z) = xi + yj + 2zk, σ isthe portion of the surface z = 4 − x2 − y2 above the XY plane oriented by upwardnormals.


σF · n dS where F = 6zi + 6j + 3yk and σ is the

portion of the plane 2x+ 3y + 4z = 12 which is in the first octant.

7. Let D be the region bounded by the closed cylinder x2 + y2 = 16,z = 0 and z =4.Verify the divergence theorem if F = 3x2i+ 6y2j + zk.

8. Verify the Stokes’s Theorem for the vector field F = zi+ (2x+ z)j + xk where C isthe boundary of the triangle with vertices (1, 0, 0), (0, 2, 0) and (0, 0, 3).

9. Show that∫∫

Sr.ndA = 3V where V is the volume of the bounded region and

r = xi+ yj + zk.

10. Verify Stokes’s Theorem. Assume that the surface S is oriented upward. V = x3i+x2yj.C is the boundary of the rectangle whose sides are x = 0, x = 3, y = 0, y = 4in the plane z = 0.

14




(2xy − x2)dx+ (x2 + y2)dy where C isthe boundary of the region enclosed by y = x2 and y2 = x.

2. Evaluate by Green’s Theorem∮C

e−x (sin ydx+ cos ydy) where C is the rectanglewith vertices (0, 0), (π, 0), (π, π

2) and (0, π

2).


(3x2 − 8y2)dx+ (4y − 6xy)dy where Cis the boundary of the region defined by x = 0, y = 0 and x+ y = 1.


σf(x, y, z)dS where f(x, y, z) = x + y + z and σ

is the surface of the cube defined by the inequalities 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 and0 ≤ z ≤ 1.

5. Let σ be the surface of the cube bounded by the planes x = ±1, y = ±1 and z = ±1,oriented by outward unit normals.Find the flux of F across σ where F (x, y, z) = xi.

6. Use Divergence Theorem to evaluate∫∫

σF.n dS where F = x2zi+yj−xz2k and σ

is the boundary of the region bounded by the paraboloid z = x2 + y2 and the planez = 4y.

7. Verify Stoke’s Theorem for the vector field F = (3x− y)i− 2yz2j − 2y2zk, where Sis the surface of the sphere x2 + y2 + z2 = 16,z > 0.

8. Evaluate∮C

V.dr using Stokes’s Theorem. Assume C is oriented in the counter

clockwise direction as viewed from above. V = (3x+ 2z)i+ (x+ 3y)j + (2y − 3z)kand C is the curve of intersection of the plane 6x+3y+4z = 12 with the coordinateplanes.

9. Show that∫∫

S(∇r2).ndA = 6V , where V is the volume of the bounded region and

r2 = x2 + y2 + z2.

10. Evaluate the integral∫∫

S(∇ × V ).ndA by Stoke’s Theorem where V = (x + y)i +

(y + z)j + (z + x)k and S is the portion of the cone z =√x2 + y2 for x2 + y2 ≤ 4.

Answers

Tutorial Questions

1.

2. −(π4+ 2

π)

3. πab

4. 40π√2

5. 32π

6. 138

7.

8. −1

9.

10. 72




1.

2. 2(e−π − 1)

3. 53

4. 9

5. 8

6. 8π

7. 16π

8. 22

9.

10. −4π


Date:___/___/_____

R a j a g i r i S c h o o l o f E n g i n e e r i n g a n d T e c h n o l o g y , K a k k a n a d

[Type text] Page 27

3. PH100 ENGINEERING PHYSICS

[Type text] Page 28


PROGRAMME: ELECTRICAL &

ELECTRONICS ENGINEERING

DEGREE: BTECH

COURSE: ENGINEERING

PHYSICS

SEMESTER: 1 AND 2 CREDITS: 4

COURSE CODE: PH100

REGULATION:2015

COURSE TYPE: CORE /ELECTIVE /

BREADTH/ S&H

COURSE AREA/DOMAIN: CONTACT HOURS: 3+1 (Tutorial)

hours/Week.

CORRESPONDING LAB COURSE CODE

: PH110

LAB COURSE NAME: Engineering

Physics Lab

SYLLABUS:

UNIT DETAILS HOUR

S

I OSCILLATIONS AND WAVES

Introduction Differential equation of damped harmonic oscillation

Forced harmonic oscillation and solutions Resonance, Q-Factor,

Sharpness of resonance LCR circuit as an electrical analogue of

mechanical oscillator Differential equation and solution of one

dimensional wave equation Transverse vibrations of stretched

string

9

II Interference in thin films and wedge shaped films for reflected system

Measurement of wavelength using Newton’s rings method

Refractive index of a liquid by Newton’s rings method

Interference filters and anti-reflection coatings

Fresnel and Fraunhofer diffraction

Fraunhofer diffraction at a single slit

Grating equation

Rayleigh criterion of resolution for a grating Resolving power and dispersive

power of a grating

9

III POLARISATION AND SUPERCONDUCTIVITY

Polarization and types of polarized light

Double refraction, Nicol prism, quarter and half wave plate

Production and detection of different types of polarized light

Induced refringence, Kerr cell and polaroid

Superconductivity and Meissner effect

Type I and type II superconductors

BCS theory and high temperature superconductors

9

IV QUANTUM MECHANICS AND STATISTICAL

MECHANICS

9

[Type text] Page 29

Uncertainty principle and its applications

Time dependent and time independent Schrodinger equations

Physical meaning of wave function.

Operators and Eigen value equation

One dimensional infinite square well potential.

Quantum mechanical tunneling

Microstates, macro states and phase space.

Distribution equations of three statistics and Fermi energy

significance

V ACOUSTICS AND ULTRASONICS Intensity and loudness of sound and absorption coefficient.

Reverberation and reverberation time

Sabine’s formula

Factors affecting the acoustics of a building.

Magnetostriction effect and Piezoelectric effect.

. Thermal and Piezoelectric method for the detection of ultrasonic

waves

NDT and medical applications of ultrasonic

7

VI LASER AND PHOTONICS

Properties of laser

Spontaneous and stimulated emission, Population inversion.

Einstein’s coefficients and working principle of laser

Ruby laser, semiconductor laser and Helium-Neon laser

Holography and its applications

Basics of solid state lighting

Photodetectors and I-V characteristics of a solar cell

Optical fiber communication system

Industrial and medical applications of fibers

Optical sensors

10

TOTAL HOURS 53



T Aruldhas G, engineering Physics, PHI Lt

T Beiser A, Concepts of Modern Physics, McGraw Hill India Ltd

T Bhattacharya and Tandon, Engineering Physics, Oxford India

R Brijlal and Subramanyam, A Text Book Of Optics, S. Chand & Co.

T Dominic and Nahari, A Text Book of Engineering Physics, Owl Books Publishers

T Hecht. E, Optics, Pearson Education

R Mehta N, Applied Physics for Engineers, PHI Ltd

R Palais J C, Fiber Optic Communications, Pearson Education

R Pandey B K and Chathurvedi S, Engineering Physics, Cengage Learning

R Philip J, A text book of Engineering Physics, Educational Publishers.

T Premlet B, Engineering Physics, McGraw Hill India Ltd

COURSE PRE-REQUISITES:

[Type text] Page 30

C.CODE COURSE NAME DESCRIPTION SEM

PH100 Higher secondary level physics To develop basic ideas on

electrochemistry, polymer chemistry,

fuels, water technology etc

1 &

2

COURSE OBJECTIVES:

1 To provide a bridge to the world of technology from the basics of science.

2 To equip the students with skills in scientific enquiry, problem solving and laboratory

techniques.

COURSE OUTCOMES:

SLNO DESCRIPTION

1 An ability to differentiate harmonic oscillations and waves and apply the

knowledge in mechanical and electrical systems

2 Ability to differentiate between interference and diffraction

3 Apply the knowledge of polarization in polaroids

4 Distinguish between different types of superconductors

5 Explain microscopic phenomenon using concepts of quantum mechanics

and statistical mechanics

6 Using the knowledge of acoustics in designing acoustically important

buildings

7 Explain the production of different types of lasers

CO-PO MAPPING

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PO13

CO1 3 3 2 2 2 2 2 2

CO2 3 3 2 2 2 2

CO3 3 3 2 2 2 2

CO4 2 2 2 2 2 2

CO5 2 2 2 2 2 2 2 2

CO6 3 3 3 3 3 3 3 2

CO7 2 2 1 1 1 2 3 2 2

JUSTIFICATION FOR CO-PO MAPPING

MAPPING JUSTIFICATION

[Type text] Page 31

CO1-PO2 Designing of instruments, structures and analysis using tools require

fundamentals of oscillation , resonance and waves

CO1-PO2 Applying the theoretical knowledge of resonance and waves to design

and conduct experiments for data interpretation

CO1-PO6 Selection of quality components for engineering design

CO1-PO7 Helps to achieve the skills through regular class discussion

/seminar/poster presentations

CO1-PO8 Applying the theoretical knowledge of resonance and waves to design

and conduct experiments for data interpretation

CO1-PO9 Helps to achieve the skills through poster presentation and thereby

stimulating them for lifelong learning

CO1-PO11 Enhanced lab experiments and creative questions

CO1-PO13 Physic is the basis of all engineering subjects

CO2-PO1 Designing of instruments, structures and analysis using tools require

fundamentals of interference and diffraction

CO2-PO2 Applying the theoretical knowledge of interference and diffraction to

design and conduct experiments for data interpretation

CO2-PO5 Knowledge of interference and diffraction for characterizing materials





CO2-PO13 Physic s the basis of all engineering subjects

CO3-PO1 Designing of polaroids require fundamentals of polarization

CO6-PO2 Applying the theoretical knowledge of polarization to design and

conduct experiments for data interpretation



CO3-PO 9 Helps to achieve the skills through regular class discussion


CO3-PO 11 Enhanced lab experiments and creative questions

[Type text] Page 32

CO3-PO 13 Physic s the basis of all engineering subjects

CO4-PO 1 Applying superconductivity in various branches of engineering

CO4-PO 2 Applying the theoretical knowledge of superconductivity for data

interpretation

CO4-PO 5 Knowledge of superconductors for characterizing materials






CO5-PO 1 Application of quantum and statistical mechanics in various branches

of engineering

CO5-PO 2 Applying the theoretical knowledge of quantum and statistical

mechanics for data interpretation

CO5-PO 3 Application of quantum and statistical mechanics fundamentals in

engineering design

CO5-PO 5 Knowledge of quantum and statistical mechanics fundamentals in

advanced engineering





CO5-PO 10 Application of quantum mechanics in advanced engineering fields


CO6-PO 1 Application of ultrasonics in various branches of engineering

CO6-PO 2 Applying the theoretical knowledge of ultrasonics in designing and

conducting experiments

CO6-PO 3 Application of ultrasonics fundamentals in engineering design

CO6-PO 5 Knowledge of ultrasonics fundamentals in advanced engineering

CO6-PO 6 Knowledge of ultrasonics for characterizing materials

[Type text] Page 33





CO6-PO 13 Application of ultrasonics in advanced engineering fields


CO7-PO 2 Application of laser in various branches o engineering

CO7-PO 3 Applying the theoretical knowledge of laser in designing and

conducting

CO7-PO 5 Application of laser fundamentals in engineering design

CO7-PO 6 Knowledge of laser fundamentals for designing materials

CO7-PO 7 Knowledge of laser for various application(following standards)





CO7-PO 13 Applications of laser in advanced engineering fields

GAPS IN THE SYLLABUS - TO MEET INDUSTRY/PROFESSION REQUIREMENTS:

SLNO DESCRIPTION PROPOSED

ACTIONS

1 Basic concepts on resonant electrical circuits & laws associated with it Reading,

Assignments

2 An introduction to advanced quantum computational techniques Reading,

Assignments

3 Important superconductivity applications and techniques Reading,

Assignments

4 Applications of optical fiber sensors Reading,

Assignments

TOPICS BEYOND SYLLABUS/ADVANCED TOPICS/DESIGN:

1 INTERFERENCE & DIFFRACTION

Anti-reflection coatings and its practical applications

Effect of interference filters and its practical applications

[Type text] Page 34

X-ray diffraction

Types of diffraction gratings

Holograms and its relation with diffraction

2 SUPERCONDUCTIVITY

Magnetic levitation techniques

Maglev trains

High temperature superconductors and its applications

Advanced superconducting technologies

3 QUANTUM MECHANICS & STATISTICAL MECHANICS

Quantum Superposition

Quantum Entanglement

Electron Spin

Photon polarization

Qubits and Quantum computing

An introduction to statistical thermodynamics

4 LASERS AND PHOTONICS

Laser induced spectroscopic techniques

Laser cooling

Laser guidance techniques

Different types of optical fibers

Propagation modes of optical fiber

WEB SOURCE REFERENCES:

1 http://www.animations.physics.unsw.edu.au/jw/oscillations.htm

2 http://www.itp.uni-hannover.de/~zawischa/ITP/diffraction.html

3 http://science.howstuffworks.com/environmental/energy/superconductivity.htm

4 http://plato.stanford.edu/entries/qm/

5 http://www.damtp.cam.ac.uk/user/tong/statphys.html

6 http://www.coherent.com/products/?834/Lasers

DELIVERY/INSTRUCTIONAL METHODOLOGIES:

CHALK &

TALK

STUD.

ASSIGNMENT

WEB

RESOURCES

LCD/SMART

BOARDS

STUD.

SEMINARS

ADD-ON

COURSES

ASSESSMENT METHODOLOGIES-DIRECT

ASSIGNMENTS STUD.

SEMINARS

TESTS/MODEL

EXAMS

UNIV.

EXAMINATION

STUD. LAB

PRACTICES

STUD. VIVA MINI/MAJOR

PROJECTS

CERTIFICATIONS

ADD-ON

COURSES

OTHERS POSTER

PRESENTATIONS

http://www.damtp.cam.ac.uk/user/tong/statphys.html

http://www.coherent.com/products/?834/Lasers

[Type text] Page 35

ASSESSMENT METHODOLOGIES-INDIRECT

ASSESSMENT OF COURSE OUTCOMES

(BY FEEDBACK, ONCE)

STUDENT FEEDBACK ON

FACULTY (TWICE)

ASSESSMENT OF MINI/MAJOR

PROJECTS BY EXT. EXPERTS

OTHERS

[Type text] Page 36

3.2. COURSE PLAN

Sl.No Module Planned

1 1 Differential Equation of SHM

2 1 Diff.eqn.of damped harmonic oscillations

3 1 Forced Harmonic Oscillations

4 1 Forced Harmonic Oscillation- solutions

5 1 Resonance,Q factor,Sharpness ofresonance

6 1 LCR circuit Electrical analogy,Problems

7 1 Waves ,one diamensional,Definitions

8 1 Differential Equations and solutions

9 1 Transverse vibrations of stretched strings

10 1 Three Diamensional waves -Solutions

11 1 Problems in Waves and Oscillations

12 2 Interference ,Coherence ,Basic Principles

13 2 Thin Films, Problems

14 2 Wedge Shaped films

15 2 Newton's rings-Derivations

16 2 Filters, Anti reflection coating

17 2 Diffraction -Fresnel and Fraunhoffer

18 2 Grating Equation ,Wavelength measurements

19 2 Rayleigh's criterion,D.P.,R.P.

20 3 Polarisation ,Different types

21 3 Double refraction, Nichol Prism

22 3 Quarter wave plate, Half wave plate,Production and detection

23 3 Birefriengence,kerr cell,Polaroids,Applications

24 3 Super conductivity, Meissner effect

25 3 Type I and Type II Super conductors.BCS theory

26 3 High Tc super conductors, Joseph'S junction

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27 3 Joseph's Junction ,Squid

28 3 Application of superconductivity,problems

29 4 Q.M.Basics,Uncertainity principle

30 4 Time dependent and independent Schrodinger equation

31 4 Wave function ,Operators

32 4 Eigen value functions, Square well potential

33 4 Q.M. tunnelling, Problems

34 4 Statistical Mechanics,Micro states,Macro states

35 4 Basic postulates of M.B, B.E.,F.D. statistics

36 4 Distribution equation,Fermi level

37 5 Accoustics, intensity, Loudness,Definitions,reverberrations

38 5 Sabines formula, Accoustics of a building

39 5 Ultrasonics, Magnetostriction,Oscillators

40 5 Detection of ultra sonics,NDT, Medical applications

41 6 Laser, properties,Basic principles, Einstein's coefficients

42 6 Ruby Laser ,He-Ne laser

43 6 Semi conductor Laser ,Laser applications

44 6 Holography

45 6 Photonics,Basics,L.E.D.

46 6 Photo detectors,Different types of photo diodes

47 6 Solar cells,I.V.characteristics

48 6 Optic fiber, N.A. O.F.C. basics, Various applications

49 6 O.F.sensors,Intensity modulated, phase modulated sensors

50 1 Revision of Module I

51 2 Revision of Module II

52 3 Revision of Module III

53 4 Revision of Module IV

54 5 Revision of Module V

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55 6 Revision of Module VI

56 6 Model Exam

57 6 Question Paper Discussion

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3.3 TUTORIALS

1. Determine the frequency of first and second modes of vibration for a quartz of piezo electric Oscillator.

The velocity of longitudinal waves in quartz crystal is 5.5 x 10 3 m/s. Thickness of Quartz Crystal is 0.05

m

2. A cinema hall has a volume of 8000m3

. It is required to have a reverberation time of 1.5 sec. What

should be the total absorption of the hall. Calculate the change in intensity level when the intensity

changes by 100 times and 10 6 times.

3. Calculate the thickness of half wave plate for sodium light

(λ=5893 A ). If μo =1.54 and ratio of velocity of ordinary and extra ordinary waves is 1.007. Is this

crystal a positive or negative?

4. A beam of linearly polarized light is changed into circularly polarized light by passing it through a slice

.003cm thick. Calculate the difference in the refractive indices for the two rays in the crystal assuming this

to be minimum thickness that will produce the effect and that the wavelength is 6x10 -7

m

5. Calculate the thickness of a (i) half wave plate (ii) quarter wave plate given that μe = 1.553 and μ o =1.544

and λ =5000A0

6. A given calcite plate behaves as a half wave plate for a particular wavelength λ .Assuming variation of

refractive index with λ to be negligible, how would the above plate behave for another light of wavelength

2λ.

7. Calculate the critical magnetic field for a super conducting wire of diameter 1.5 mm when a critical

current of 30 Amps is passing through it

8. Critical field of niobium is 1.75x105A/m at 10.5 K and 2.5x10

5A/m at 0 K. Calculate its critical

temperature.

9. What is the frequency of electromagnetic waves produced from a Josephson junction working at a d.c.

voltage of 650 μV?

10. At what angle the light should be incident on glass (μ = 1.5697) to get plane polarized light by reflection?

11. Tc for Hg with isotopic mass 199.5 is 4.185K. Calculate its critical temperature if the isotopic mass

changes to 203.4

[Type text] Page 40

.4 ASSIGNMENTS

ASSIGNMENT I

12. Define intensity and Loudness

13. Explain sound intensity level .What is its unit

14. Explain Sabine’s formula

15. Distinguish between reverberation and echo

16. Why in sound logarithmic scale is used

17. Explain reverberation time. Explain its significance

18. Explain magnetostriction effect

19. What are ultrasonics. Explain two methods of detecting ultrasonic waves

20. Explain NDT using ultrasonics

21. Explain sonar. What are their applications

22. What are the acoutic requirements of an auditorium.How they can be achieved.

23. Explain the piezo electric method of producing ultrasonic waves

24. Explain the various applications of ultrasonic waves

ASSIGNMENT II

Section A [ Answer all 2 marks each]

1. What is meant by Polarization?

2. What is the difference between ordinary light and plane polarized light?

3. State and explain Brewster’s law

4. What are the applications of polarized light?

5. Explain positive and negative crystals with examples

6. What is superconductivity?

7. Explain Meissner effect

8. Explain Isotope effect

9. Explain critical current and critical magnetic field

10. What are polariods?

11. Explain double refraction

12. Explain Kerr effect

Section B [Answer 10 questions, 4 marks each]

1. What are the uses of Polaroids?

2. Explain A.C. and D.C. Josephson effect

3. Write a note on high Tc super conductors

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Section C[ Answer 3 , 6 marks each]

1. Explain the construction and working of a Nichol prism

2. Explain BCS theory of super conductivity

3. Explain Type I and Type II super conductors. What are their differences?

4. Explain the various applications of super conductivity

Section D [Answer 3 , 6 marks each]

1. Explain the working of a squid. What are its applications?

2. With theory explain how we can produce different types of polarized light

3. How can we distinguish between circularly ,plane ,elliptically and un polarized light?

4. What are the various applications of polarization?

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4. BE100 ENGINEERING MECHANICS

[Type text] Page 43


PROGRAMME: EEE DEGREE: B. TECH.

COURSE: ENGINEERING MECHANICS SEMESTER: S1 CREDITS: 4

COURSE CODE:BE100REGULATION: 2015 COURSE TYPE: CORE

COURSE AREA/DOMAIN: CONTACT HOURS: 3+1 (Tutorial) hours/Week.

CORRESPONDING LAB COURSE CODE (IF

ANY): NIL LAB COURSE NAME: NIL

SYLLABUS:

UNIT DETAILS HOURS

I

Statics:Fundamentalconceptsandlawsofmechanics-Rigidbody-

Principleoftransmissibilityofforces. Coplanar force systems - Moment of a

force -Principle of moments. Resultantofforce and couple system.

Equilibriumofrigidbody-Freebodydiagram-Conditionsof equilibriumintwodimensions-Twoforceandthreeforce members.

11

II

Typesofsupports-Problemsinvolvingpointloadsanduniformly

distributedloads only. Forcesystemsinspace-Degreesoffreedom-

FreebodydiagramEquations of equilibrium -Simple resultant

andEquilibrium problems.

9

III

Propertiesofplanarsurfaces-Centroidandsecondmomentofarea

(Derivationsnotrequired)-Parallelandperpendicularaxistheorem-

CentroidandMomentofInertiaofcomposite area. PolarMomentofInertia-

Radiusofgyration-Massmomentofinertia of cylinder and thin disc (No

derivationsrequired). Product of inertia -Principal Moment of Inertia

(conceptual level). Theorems ofPappusand Guldinus.

9

IV

Friction-Characteristicsofdryfriction-Problemsinvolvingfrictionof

ladder,wedgesandconnectedbodies. Definitionofworkandvirtualwork-

Principleofvirtualworkfora system of connection bodies -Problems on

determinate beams only.

10

V

Dynamics:RectangularandCylindricalco-ordinatesystem. Combinedmotionofrotationandtranslation-Conceptofinstantaneous centre-Motionofconnectingrodofpistonandcrankofareciprocating pump. Rectilineartranslation-Newton'ssecondlaw-D'Alembert'sPrinciple Applicationtoconnectedbodies(Problemsonmotionofliftonly).

9

V1

Mechanical vibrations -Free and forced vibration - Degree of freedom. Simpleharmonicmotion-Spring-massmodel-Period-StiffnessFrequency - Simple numerical problems of single degree of freedom.

8

TOTAL HOURS 56



[Type text] Page 44

T1 Shames I.H.,EngineeringMechanics-StaticsandDynamics,Pearson Prentice

T2 Timoshenko S.&YoungD. H, Engineering Mechanics,

T4 BeerandJohnson,VectorMechanicsforEngineers-StaticsandDynamics,TataMc-

GrawHill PublishingCompanyLimited

T5 HibbelerR.C.,EngineeringMechanics:Statics and Dynamics.Pearson PrenticeHall

Pentex BookPublishers and Distributors

T6 KumarKL.,EngineeringMechanics,TataMc-GrawHillPublishingCompanyLimited

T7 TayalA.K.,EngineeringMechanics-StaticsandDynamics,UmeshPublications

T8 S.S.Bhavikkatti,EngineeringMechanics,NewAgeInternationalPublishers

T9 Jaget Babu, EngineeringMechanics, PearsonPrentice Hall



PHYSICS BASIC CONCEPTS OF FORCE

AND ITS EFFECT ON BODIES

HIGHER

SECONDARY

LEVEL

MATHEMATICS BASIC KNOWLEDGE OF

DIFFERENTIAL CALCULUS

HIGHER

SECONDARY

AND INTEGRAL CALCULUS LEVEL

COURSE OBJECTIVES:

1 Toapply the principles of mechanics to practical engineering problems. 2 Toidentifyappropriatestructuralsystemforstudyingagivenproblemandisolateitfromits

environment.

3 To develop simple mathematical model for engineering problemsand carry out static analysis.

4 To carry out kinematic and kinetic analyses for particlesand systems of particles.

COURSE OUTCOMES:

SL.NO. DESCRIPTION

[Type text] Page 45

www.nptel.com

1

Students will be able to identify all the forces associated with a frame work and to

calculate the resultant of the force system

2

Students will be able to construct free body diagrams and to calculate the

reactions necessary to ensure static equilibrium.

3 Students understand the different conditions of equilibrium of a body.

4

Students should be able to locate the centre of gravity and calculate the moment

of inertia of composite areas and physical objects.

5

Students will be able to determine the support reactions using the principle of

virtual work.

6

Students will be able to apply D’Alemberts principle to analyze the motion of

bodies.


SNO DESCRIPTION PROPOSED

ACTIONS

1 Derivation of moment of inertia and centroid of planar surfaces NPTEL

2 Rotational motion of rigid bodies NPTEL

PROPOSED ACTIONS: TOPICS BEYOND SYLLABUS/ASSIGNMENT/INDUSTRY VISIT/GUEST LECTURER/NPTEL ETC



CHALK & TALK STUD. ASSIGNMENT

WEB RESOURCES

LCD/SMART BOARDS STUD. SEMINARS ADD-ON COURSES


ASSIGNMENTS STUD. SEMINARS TESTS/MODEL EXAMS

UNIV. EXAMINATION

STUD. LAB PRACTICES STUD. VIVA MINI/MAJOR PROJECTS CERTIFICATIONS

ADD-ON COURSES OTHERS


ASSESSMENT OF COURSE OUTCOMES (BY FEEDBACK,

ONCE)

STUDENT FEEDBACK ON FACULTY (TWICE)

ASSESSMENT OF MINI/MAJOR PROJECTS BY EXT. EXPERTS OTHERS

[Type text] Page 46

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12

CO1 H M L L

CO2 H M L L

CO3 M M L L

CO4 M M L

CO5 M M

CO6 M M L L

PO MAPPING JUSTIFICATION

CO1 to 6 – PO1 It is the basic concept that is needed by an Engineering Professional to solve complex

engineering problems in the field of Electrical Engineering

CO1 to 6 – PO2 Basic concept used to understand the behavior of particles in a body and to analyze

any complex engineering problem.

CO1,2,3,6– PO4 Basic requirement used in research methods to analyze and interpret data for the

design the various machine components.

CO1 to 4,6 –

PO12

Any advanced learning in the field of Electrical Engineering is based fundamentally

on the concepts provided by the subject, without which it is not possible to engage in

any effort to improve technology

[Type text] Page 47

4.2 COURSE PLAN

Day

Module

1

1

Introduction to mechanics

2

Laws of mechanics

3

Force systems

4

Resultant , Equilibrant and Theorem of resolution

5

Determination of resultant of a system of forces

6

Tutorial

7

Free body diagram

8

Conditions of equilibrium for concurrent force system

9

Problems

10

Problems (contd)

11

Moment - Varignon's Theorem

12

Conditions of equilibrium for non-concurrent force system

13

Problems

14

Parallel forces in a plane - Force Couple system

[Type text] Page 48

15

Reduction of a system of forces into a single force and force couple

system

16

2

Types of supports,beams and loads

17

Determination of support reactions for different types of beams with

point loads and udl

18

Problems

19

Tutorials

20

Force systems in space

21

Resultant problems

22

Equilibrium Problems

23

Tutorials

24

3

Centroid - Theory

25

centroid of composite areas

26

Problems (Continued)

27 Moment of Inertia - Parallel Axis theorem and Perpendicular

axis theorem

28

Determination of moment of inertia of composite areas

29

Problems on moment of inertia

30

Problems

31

Tutorials

32

Mass moment of inertia, Product of inertia, Principal moment of inertia,

Pappus Guldinus theorem

[Type text] Page 49

33

4

Friction -Laws of friction, angle of friction, angle of repose, limiting

friction

34

Block Friction problems

35

Problems

36

Ladder friction problems

37

Problems

38

Wedge friction Problems

39

Problems

40

Tutorial

41

Principle of virtual work - Determination of support reactions for

statically determinate beams

42

Problems

43

Problems

44

5

Rectilinear translation: Newton's laws

45

Rectilinear motion with uniform acceleration

46

Rectilinear motion with variable acceleration

47

D'Alembert's Principle - Problems on lift motion

48

Problems on connected bodies

49

Combined motion of rotation and translation -Instantaneous centre

50 Motion of crank and piston of a reciprocating pump-Instantaneous

centre method

50

[Type text] Page 50

51

Problems

52

6

Mechanical Vibrations- Different types of vibrations

53

Simple harmonic Motion

54

Determination of velocity and acceleration of a body executing SHM at

different instants of time

55

Tutorial

56

Motion with single degree of freedom

57

Spring Mass Model-Natural frequency of vibration

58

Springs connected in series and parallel

59

Problems

60

Tutorial

51

[Type text] Page 51

4.3 TUTORIALS

Module 1

1. An electric-light fixture of weight Q = 178 N is supported as shown in Fig. A. Determine the tensile forces S1 and

S2 in the wires BA and BC if their angles of inclination are as shown.

(Ans. S1 = 130.3 N; S2 = 92.14 N)

Figure A

Figure B

2. A ball of weight Q = 53.4 N rests in a right-angled trough as shown in Fig. B. Determine the forces exerted on the

sides of the trough at D and E if all surfaces are perfectly smooth.

(Ans. Rd = 46.25 N; Re = 26.7 N)

3. A ball rests in a trough as shown in Fig. C. Determine the angle of tilt θ with the horizontal so that the reactive

force at B will be one-third at A if all surfaces are perfectly smooth.

(Ans. Θ =16.110)

Figure C

Figure D

4. What axial forces does the vertical load P induce in the members of the system shown in Fig. D. Neglect the

weights of the members themselves and assume an ideal hinge at A and a perfectly flexible string BC.

(Ans. S1 = P tanα, tension; S2 = P secα, compression)

52

[Type text] Page 52

5. A right circular roller of weight W rests on a smooth horizontal plane and is held in position by an inclined bar

AC as shown in Fig. E. Find the tension S in the bar AC and the vertical reaction Rb at B if there is also a

horizontal force P acting at.

(Ans. S = P secα; Rb = W + P tanα)

Figure E

Figure F

6. A pulley A is supported by two bars AB and AC which are hinged at points B and C to a vertical mast EF (Fig.

F). Over the pulley hangs a flexible cable DG which is fastened to the mast at D and carries at the other end G a

load Q = 20 kN. Neglecting friction in the pulley, determine the forces produced in the bars AB and AC. The

angles between the various members are shown in the figure.

(Ans. S2 = 34.64 kN; S1 = 0)

7. Two smooth circular cylinders, each of weight W = 445 N and radius r = 152 mm, are connected at their centers

by a string AB of length l = 406 mm and rest upon a horizontal plane, supporting above them a third cylinder of

weight Q = 890 N and radius r = 152 mm (Fig. G). Find the forces S in the string and the pressures produced on

the floor at the points of contact D and E.

(Ans. S = 398 N, tension; Rd = Re = 890 N)

53

[Type text] Page 53

Figure G

Figure H

8. A weight Q is suspended from a small ring C, supported by two cords AC and BC (Fig. H) The cord AC is

fastened at A while the cord BC passes over a frictionless pulley at B and carries the weight P as shown. If P = Q

and α = 500, find the value of the angle β.

(Ans. β = 800)

9. A force P is applied at point C as shown in (Fig. I). Determine the value of angle α for which the larger of the

string tension is as small as possible and the corresponding values of tension in the strings 1 and 2. (Ans. α

= 600, S1 = S2 = 0.577 P)

Figure I

Figure J

10. A system of coplanar parallel forces acting on a rigid bar as shown in Fig. J. Reduce this force system to (a) a

single force, (b) a single force and a couple at A and (c) a single force and a couple at B.

(Ans. (a) Ra = 60 N, down, from A = 0.75m; (b) Ra = 60 N, down Ma = -45 Nm; (c) 60 N, down, MB = 165

N)

11. The beam AB in Fig. K is hinged at A and supported at B by a vertical cord which passes over a frictionless

pulley at C and carries at its end a load P as shown. Determine the distance x from A at which a load Q must be

placed on the beam if it is to remain in equilibrium in a horizontal position. Neglect the weight of the beam.

(Ans. )

54

[Type text] Page 54

Figure K

Figure L

12. Using the method of projections, find the magnitude and direction of the resultant R of the four concurrent forces

shown in Fig. L and having the magnitudes F1 = 1500 N, F2 = 2000 N, F3 = 3500 N and F4 = 1000 N.

(Ans. R = 1842.6 N and α = 2270)

13. Forces of 2, 3, 4, 5 and 6 kN are acting at one of the angular points of a regular hexagon towards the other angular

points taken in order. Find the resultant of the system of forces.

(Ans. R = 15.6 kN; α = 76.70)

14. In Fig. M, weights P and Q are suspended in a vertical plane by strings 1, 2, 3, arranged as shown. Find the

tension induced in each string if P = 2225 N and Q = 4450 N.

(Ans. S1 = 4450 N; S2 = 4450 N; S3 = 596.2 N)

Figure M

Figure N

15. Two vertical masts AB and CD are guyed by the wires BF and DG, in the same vertical plane and connected by a

cable BD of length l, from the middle point E of which is suspended a load Q (Fig. N). Find the tensile force S in

each of the two guy wires BF and BG if the load Q = 445 N and the length l = 6.1 m and sag d = 0.305 m.

(Ans. S = 4450 N)

16. A ball of weight W rests upon a smooth horizontal plane and has attached to its centre two strings AB and AC

which pass over frictionless pulleys at B and C and carry loads P and Q, respectively, as shown in Fig. O. If the

string AB is horizontal, find the angle α that is string AC makes with horizontal when the ball is in a position of

equilibrium. Also find the pressure R between the ball and the plane.

55

[Type text] Page 55

(Ans. cosα = P/Q; √ )

Figure O

Figure P

17. Two cylinders of weights Q and R are interconnected by a bar of negligible weight hinged to each cylinder at its

geometric center by ideal pins. Determine the magnitude of P applied at the center of cylinder R to keep the

cylinders in equilibrium in the position shown in Fig. P. The following numerical data are given: Q = 2000 N and

R = 1000 N.

(Ans. P ≈ 258 N)

56

[Type text] Page 56

4.4 ASSIGNMENTS

57

[Type text] Page 57

5. BE101 03: INTRODUCTION TO ELECTRICAL

ENGINEERING

58

[Type text] Page 58

5.1. COURSE INFORMATION SHEET

PROGRAMME: EE DEGREE: BTECH

COURSE: Introduction to Electrical Engineering SEMESTER: 1 CREDITS: 3

COURSE CODE: BE 101-03 REGULATION:UG COURSE TYPE: CORE

COURSE AREA/DOMAIN: Electrical Engineering CONTACT HOURS: 2+1 (Tutorial) hours/Week.

CORRESPONDING LAB COURSE CODE (IF ANY):Yes LAB COURSE NAME: Electrical Engineering Workshop

SYLLABUS:

UNIT DETAILS HOURS

I

Fundamental Concepts of Circuit Elements and Circuit variables: Electromotive force,

potential and voltage. Resistors, Capacitors, Inductors- terminal V-I relations

Electromagnetic Induction: Faraday’s laws, Lenz’s law, statically and dynamically

induced EMF, self and mutual inductance, coupling coefficient-energy stored in

inductance

Real and Ideal independent voltage and current sources, V-I relations. Passive sign

convention. Numerical Problems

6

II Basic Circuit Laws: Kirchhoff's current and voltage laws, analysis of resistive circuits-

mesh analysis –super mesh analysis, Node analysis-super node analysis, star delta

transformation, Numerical problems

6

III

Magnetic Circuits: Magneto motive force, flux, reluctance, permeability -comparison of

electric and magnetic circuits, analysis of series magnetic circuits

Parallel magnetic circuits, magnetic circuits with air-gaps.

Numerical problems

6

IV

Alternating current fundamentals:-Generation of Alternating voltages-waveforms,

Frequency, Period, RMS and average values, peak factor and form factor of periodic

waveforms (pure sinusoidal) and composite waveforms

Phasor Concepts, Complex representation (exponential, polar and rectangular forms) of

sinusoidal voltages and currents phasor diagrams

Complex impedance - series and parallel impedances and admittances, Phasor analysis

of RL, RC, RLC circuits, Numerical problems

10

V

Complex Power : Concept of Power factor: active , reactive and apparent power

Resonance in series and parallel circuits, Energy, bandwidth and quality factor, variation

of impedance and admittance in series and parallel resonant circuits

Numerical problems

7

VI

Three phase systems: Star and delta connections, three-phase three wire and three phase

four-wire systems

Analysis of balanced and unbalanced star and delta connected loads

Power in three-phase circuits. Active and Reactive power measurement by one, two, and

three wattmeter methods, Numerical problems

8

TOTAL HOURS 43

59

[Type text] Page 59



R Bhattacharya, S. K., Basic Electrical & Electronics Engineering, Pearson

R Edminister, J., Electric Circuits, Schaum's Outline Series, Tata McGraw Hill

R Hayt, W. H., Kemmerly, J. E., and Durbin, S. M., Engineering Circuit Analysis, Tata McGraw Hill

R Hughes, Electrical and Electronic Technology, Pearson Education

R Parker and Smith, Problems in Electrical Engineering, CBS Publishers and Distributors

R Sudhakar and Syam Mohan, Circuits and Networks Analysis and Synthesis, Tata McGraw Hill

R Suresh Kumar, K. S, Electric Circuits and Networks, Pearson Education



11

th and 12

th Standard Physics and

Mathematics

A thorough knowledge of 11th

and 12th

standard

Physics and Mathematics

COURSE OBJECTIVES:

1 The objective of this course is to set a firm and solid foundation in Electrical Engineering

2 To equip the students with strong analytical skills and conceptual understanding of basic laws and analysis

methods in electrical and in electrical and magnetic circuits.

COURSE OUTCOMES:

SI.

No DESCRIPTION

1 Students will be able to acquire fundamental knowledge of Electrical circuits and can solve circuit related

problems.

2 Students will be able to recall and state ideas about magnetic circuits.

3 Students will be able to explain the fundamentals of AC circuits.

4 Students will be able to analyze three phase systems.

5 Students will be able to compare and contrast various types of resonance circuits

6 Students will be able to identify and differentiate between various methods of Power measurement

SI

No DESCRIPTION BLOOMS’ TAXONOMY LEVEL

1 Students will be able to acquire fundamental knowledge of

Electrical circuits and can solve circuit related problems.

Knowledge [Level 1]

2 Students will be able to recall and state ideas about

magnetic circuits.

Knowledge [Level 1]

3 Students will be able to explain the fundamentals of AC

circuits.

Comprehension [Level 2]

4 Students will be able to analyze three phase systems. Analysis [Level 4]

5 Students will be able to compare and contrast various

types of resonance circuits

Analysis [Level 4]

6 Students will be able to identify and differentiate between

various methods of Power measurement

Analysis [Level 4]

60

[Type text] Page 60

MAPPING COURSE OUTCOMES (COs) – PROGRAM OUTCOMES (POs) AND COURSE OUTCOMES (COs) –

PROGRAM SPECIFIC OUTCOMES (PSOs):

PO 1 PO 2 PO 3 PO 4 PO 5 PO 6 PO 7 PO 8 PO 9 PO 10 PO 11 PO 12 PSO 1 PSO 2 PSO 3

C101.03.1 3 1 1

C101.03.2 3 1 1

C101.03.3 1 1 1

C101.03.4 2 1 2

C101.03.5 1 2

C101.03.6 2 1

BE 101.03 3 1 1 1 1 1 1

JUSTIFATIONS FOR CO-PO MAPPING:

Mapping L/H/M Justification

C101.03.1-PO1 H Students will be apply the knowledge of mathematics and science to solve various

fundamental problems in electric circuits.

C101.03.1-PO5 L Students will be able to use modern tools to find solution for circuit related problems in

their higher semesters.

C101.03.2-PO1 H Students will be able to apply knowledge of magnetic circuits to solve engineering

problems.

C101.03.2-PO2 L Students will be able to analyze complex engineering problems using the first principles

of magnetic circuits.

C101.03.3-PO1 L Students will be apply the knowledge of engineering fundamentals to solve complex

problems in ac circuits.

C101.03.3-PO6 L Students will be apply the reasoning obtained from the context of ac circuit to access

societal and safety issues.

C101.03.4-PO1 M Students will be apply the knowledge of electrical engineering to analyze three phase

systems.

C101.03.4-PO7 L Students will be able to understand the need of three phase circuits for sustainable

development of society.

C101.03.4-

PO12 M

Students will be able to recognize the need for life long learning in the broadest context

of techonological change in the area of three phase systems.

C101.03.5-PO3 L Students will be able to design solutions with appropriate consideration for safety and

environmental issues.

C101.03.5-PO7 M Students will be able to undersatnd the impact of professional engineering solutions in

the context of environmental development by utilizing renewable energy sources.

C101.03.6-PO1 M Students will be able to apply the knowledge of science and engineering fundamentals

for identifying different resonance circuits.

C101.03.6-PO3 L Students will be able to develop solution using AC circuits for further development of

society.


SI

No. DESCRIPTION

PROPOSED

ACTIONS

RELEVANCE

WITH POs

RELEVANCE

WITH PSOs

1 Introduction to thumb rules for

magnetic circuits

Additional Class with

Tutorials

1,2,5 2

PROPOSED ACTIONS: TOPICS BEYOND SYLLABUS/ASSIGNMENT/INDUSTRY VISIT/GUEST LECTURER/NPTEL ETC

61

[Type text] Page 61


SI

No. DESCRIPTION

PROPOSE

D

ACTIONS

RELEVAN

CE WITH

POs

RELEVAN

CE WITH

PSOs

1 Applications of Resonance Circuits

Additional

Class

6,12


1 http://nptel.iitm.ac.in/


CHALK & TALK STUD. ASSIGNMENT WEB RESOURCES

LCD/SMART

BOARDS

STUD. SEMINARS ADD-ON COURSES


ASSIGNMENTS STUD. SEMINARS TESTS/MODEL

EXAMS

UNIV.

EXAMINATION

STUD. LAB

PRACTICES

STUD. VIVA MINI/MAJOR

PROJECTS

CERTIFICATIONS



ASSESSMENT OF COURSE OUTCOMES (BY

FEEDBACK, ONCE)

STUDENT FEEDBACK ON FACULTY

(TWICE)

ASSESSMENT OF MINI/MAJOR PROJECTS BY

EXT. EXPERTS

OTHERS

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5.2. COURSE PLAN

Module

I&II&III

Sub topics Hours

07/08/2017 Introduction to IEE + Basic concepts –W,P,E,I,V,R. 1

08/08/2017 Fundamental Concepts of Circuit Elements and

variables: Resistors, Capacitors, Inductors- terminal V-I relations

2

09/08/2017 Independent sources, Kirchoff’s Law - Theory 3

09/08/2017 Kirchoff’s Law - Tutorials 4

10/08/2017 Star Delta Transformation 5

14/08/2017 Kirchoff’s Law - Tutorials 6

14/08/2017 Star Delta Transformation- Tutorials 7

17/08/2017 Mesh Analysis –Independent Voltage sources + Tutorials 8

21/08/2017 Mesh Analysis –Independent Current sources + Tutorials 9

23/08/2017 Mesh Analysis –Dependent Current sources 10

23/08/2017 Mesh Analysis – Tutorials 11

23/08/2017 Nodal Analysis – Tutorials 12

29/08/2017 Nodal Analysis – Super Node, Tutorials 13

11/09/2017 Magnetic Ckts – Terms, comparison btwn Electric & Mag. Ckts 14

14/09/2017 Series Magnetic Circuits 15

25/09/2017 Magnetic Leakage+ Fringing + Tutorials 16

26/09/2017 Series Parallel Magnetic Circuits + Tutorials 17

28/09/2017 Tutorials on MC 18

03/10/2017 Electromagnetic Induction – Faraday’s laws, Lenz’s law 19

04/10/2017 Dynamically Induced e.m.f & Statically Induced e.m.f 20

04/10/2017 Mutually Induced e.m.f & Coefficient of Coupling 21

05/10/2017 Tutorials on MC & EMI 22

Module

IV& V

Sub topics Hours

12/10/2017 A.C. Introduction + Average Value - Derivation 1

23/10/2017 R.M. S. Value – Derivation & Tutorials, Form & Peak Factor 2

24/10/2017 Tutorials on Average, RMS, Form & Peak factor 3

26/10/2017 Phasor + Complex representations & j notation 4

30/10/2017 A.C. Circuits – Pure ‘R’ 5

31/10/2017 Tutorials – A.C. Circuits 6

02/11/2017 A.C. Circuits – Pure ‘L’, Pure ‘C’ 7

06/11/2017 A.C. Circuits – ‘RL’ + Tutorials 8

07/11/2017 A.C. Circuits – ‘RC’ + Tutorials 9

08/11/2017 A.C. Circuits – ‘RLC’ Series , Tutorials – Series circuit 10

08/11/2017 A.C. Circuits – Parallel Circuits, Admittance & Complex Methods 11

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09/11/2017 AC Circuits - Parallel Circuits - Tutorials 12

13/11/2017 Series Resonance –Expression for fr, Graphical, Resonance curve, Q

factor, BW, Exp. for f1 & f2

13

13/11/2017 Parallel Resonance – Pure R,L and C, Tank circuit + Tutorials 14

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5.3. TUTORIALS

MAGNETIC CIRCUITS

1. An iron ring of 200 mm mean diameter is made of 30 mm round iron of permeability 900, has an air gap 10 mm wide.

It has 800 turns. If the current flowing through this winding is 6.8A, determine

(i) m.m.f. (ii) total reluctance of the circuit (iii) flux in the ring (iv) flux density in the ring.

2. A magnetic circuit consists of an iron ring of mean circumference 80 cm with c.s.a of 12 cm2 throughout. A current of

1A in the magnetizing coil of 200 turns produces a total flux of 1.2 mWb in the iron. Calculate (i) flux density in the iron

(ii) the absolute and relative permeability of iron (iii) reluctance of the circuit.

3. An iron ring 100 cm mean circumference is made from cast iron of c.s.a. 10 cm2. Its relative permeability is 500. If it is

wound with 200 turns, what current will be required to produce a flux of 0.1x 10-2 Wb.

4. A flux density of 1.2 Wb/m2 is required in the 1mm air gap of an electromagnet having an iron path of 1.5m long.

Calculate the m.m.f. required. μr of iron = 1600. Neglect leakage.

5. A coil is wound uniformly over a wooden ring having a c.s.a of 600 mm2 and a mean circumference of 750 mm. If the

current through the coil is 5A and the no. of turns of the coil is 250 turns, calculate the magnetizing force, the flux

density and the total flux.

6. A magnetic circuit comprises three parts in series, each of different c.s.a. They are

(a) a length of 80 mm & c.s.a. 50 mm2

(b) a length of 60 mm & c.s.a. 90 mm2

(c) an airgap of length 0.5 mm & c.s.a. 150 mm2

A coil of 4000 turns is wound on part (b) and the flux density in the airgap is 0.3 T. Assuming that all the flux passes

through the given circuit and that the relative permeability is 1300, estimate the coil current to produce such a flux

density.

7. A ring has a mean diameter of 21 cm and c.s.a of 10 cm2. The ring is made of semicircular sections of cast iron and cast

steel, with each joint having a reluctance equal to an air gap of 0.2 mm. Find the Ampere turns required to establish a

flux of 8x10-4 Wb. The relative permeabilities of cast iron and cast steel are 166 and 800 respectively. Neglect leakage

and fringing.

8. The flux produced in the air gap of the two electromagnetic poles is 5x10-2 Wb. If the c.s.a. of the air gap is 0.2 m2, find

(i) the flux density in the air gap (ii) the magnetic field intensity (iii) reluctance of the air gap (iv) permeance of the

airgap (v) mmf dropped in the air gap. Length of the air gap is 1 cm.

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9. A magnetic core, in the form of a closed ring, has a mean length of 20 cm and a c.s.a. of 1 cm2. Given r of iron - 2400.

What direct current will be needed in a coil of 2000 turns uniformly wound around the ring to create a flux of 0.2 mWb

in the ring?

If an airgap of 1 mm is cut through the core perpendicular to the direction of this flux, what current will now be

needed round the ring to maintain the same flux in this gap?

10. A Steel ring of mean circumference 60 cm and having a cross sectional area of 4 cm2 is wound with a coil of 200 turns

around it. If it is required to produce a flux of 500 Wb in the ring, then calculate (i) Flux density (ii) Reluctance of the

ring (iii) the current in the coil. Given r of steel - 400.

11. A Cast steel electromagnet has an airgap of length 2 mm and a cast steel path of length 30 cm. Find the number of

ampere turns necessary to produce a flux density of 0.8 Tesla in the airgap. Neglect magnetic leakage and Fringing.

Assume that the cast steel requires 720 AT/m to produce a flux density of 0.8 Tesla.

12. A coil of insulated wire of 500 turns and of resistance 4 Ω is closely wound on an iron ring. The ring has a mean

diameter of 0.25m and a uniform c.s.a of 700 mm2. Calculate the total flux in the ring when a d.c supply of 6V is

applied to the ends of the winding. Assume a r - 550.

13. An iron ring of cross section area 6 cm2 is wound with a wire of 100 turns and the ring has a saw cut of 2 mm. Calculate

the magnetizing current required to produce a flux of 0.1 mWb if the mean length of the magnetic path is 30 cm and

the relative permeability of iron is 470. Neglect magnetic leakage and fringing.

14. Calculate the current required to be passed through the central limb winding so as to produce a flux of 1.6 mWb in this

limb. Length of the iron in the central limb is 15 cm. Cross sectional area of the central limb is 8 cm2 and that of the

outer limbs 4 cm2. The mean length of the iron of the outer limb is 32 cm each. Given that for iron, for a flux density of

2 Tesla, the value of H is 800 AT/m.

ELCTROMAGNETIC INDUCTION

15. An Iron ring 30 cm mean diameter is made up of square iron of 2cm x 2cm cross section and is uniformly wound

with 400 turns of wire of 2 mm2 cross section. Calculate the value of self inductance of the coil. μr = 800.

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16. Coils A and B having 100 and 150 turns respectively are wound side by side on a closed iron circuit of c.s.a 125 cm2

and mean length 2m. Determine (i) L of each coil (ii) M between them (iii) e.m.f induced in coil B when current changes

from 0 to 5A in coil A in 0.02sec. µr = 2000.

17. Two coils A and B each with 100 turns, are mounted so that part of the flux set up by one links the other. When

the current through coil A is changed from +2A to -2A in 0.5 sec, an e.m.f of 8mV is induced in coil B. Calculate (i) the

mutual inductance between the coils (ii) flux produced in coil B due to 2A in coil A.

18. Two coils A of 11,450 turns and B of 14,500 turns lie in parallel planes so that 65% of flux produced in A links coil B.

It is found that a current of 6A in A produces a flux of 0.7mWb, while the same current in B produces 0.9mWb. Determine

(i) Mutual Inductance (ii) Coupling coefficient.

19. An air cored solenoid has a length of 60 cm and a diameter of of 4 cm. Calculate its inductance, if it has 1000 turns

and also find the energy stored if the current rises from zero to 6A.

20. The no: of turns in a coil is 300. When a current of 2A flows in this coil, flux in the coil is 0.3 mWb. When this

current is reduced to zero in 1 ms, the voltage induced in a coil lying in the vicinity of coil is 70 Volts. If the coefficient of

coupling between the two coils is 0.75, find self inductances of the two coils, mutual inductance and the no: of turns in the

second coil.

21. Two long single layer solenoids have the same length and the same no. of turns, but are placed co-axially one

within the other. The diameter of the inner core is 60 mm and that of the other coil is 75 mm. Calculate the coefficient of

coupling between the coils.

22. Two coils A and B are wound side by side on a paper tube former. An e.m.f. of 0.25V is induced in coil A, when the

flux linking it changes at the rate of 1 mWb/sec. A current of 2A in coil B causes a flux of 10μWb to link coil A. Calculate the

Mutual Inductance between the coils.

23. Two identical 750 turn coils A and B lie in parallel planes. A current changing at the rate of 1500 A/s in A induces an

e.m.f. of 11.25 V in B. Calculate the mutual Inductance of the arrangement. If the self inductance of each coil is 15mH,

Calculate the flux produced in the coil A per ampere, and the percentage of this flux which links the turns of B.

24. A coil of 300 turns has a self inductance of 2.4 mH. If a second coil of 900 turns is positioned such that 25% of the

flux produced by the first coil links with the second coil, determine the mutual inductance between the coils.

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25. A 50 cm long conductor moves with a velocity of 2 m/s at right angles to itself and a uniform magnetic field of flux

density 1 Tesla. Calculate the voltage induced between the ends of the conductor. What will be the voltage if the

conductor is moving 300 from the direction of flux?

IEE Tutorial V – Answers

1. 68.3 mH

2. 0.157 H, 0.353 H, 0.2355 H, 58.87 V

3. 1 mH, 2x10-5

Wb

4. 1.1 H, 0.645

5. 2.63 mH, 0.0473 J

6. 45 mH, 48.4 mH, 35 mH, 233 turns

7. 0.8

8. 1.25 mH

9. 7.5 mH, 2x10-5

Wb/A, 50%

10. 1.8 mH

11. 1V, 0.5V

A.C. Circuits – SERIES CIRCUIT

1. Find the total current i1 + i 2 where i1 = 100 sin(100πt –(π/6)) A and i 2 = 100 cos (100πt –(π/3)) A. Also

calculate the r.m.s. value and average value.

2. A pure inductive coil allows a current of 12A to flow from a 220V, 50 Hz supply. Find (i) inductive

reactance (ii) inductance of the coil (iii) power absorbed (iv) voltage and current equations.

3. A 36 µF capacitor is connected across a 400V, 50 Hz supply. Calculate (i) reactance of the capacitor (ii)

the circuit current.

4. A 120V a.c. circuit contains 10 Ω resistance and 30 Ω inductive reactance in series. What would be the

average power in the circuit?

5. A voltage v = 200 sin(100πt) is applied to a coil having R = 200 Ω and L = 0.38 H. Find the expression for

the current, p.f. and power taken by the coil.

6. In a circuit containing a resistance of 5000 Ω and an inductance of 1H in series, a voltage of 150 V r.m.s.

at 400 Hz is applied. Determine the magnitude and phase of the current, the voltage across the

resistance and voltage across the inductance. Calculate the power taken from the supply.

7. A series circuit consists of a non-inductive resistance of 5 Ω and inductive reactance of 10 Ω. When

connected to a single phase supply, it draws a current i = 27.89 sin (628.3t – 450) A. Find (i) the voltage

applied to the series circuit (ii) inductance (iii) power drawn by the circuit.

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8. A non-inductive load takes 20A at 200V. Calculate the inductance of the reactance to be connected in

series to have the same current to be supplied from 230V, 50 Hz a.c. supply. Also determine the p.f. of

the circuit.

9. A current of 0.9 A flows through a series combination of a resistor of 120 Ω and a capacitor of reactance

250 Ω. Find (i) impedance (ii) p.f. (iii) supply voltage (iv) voltage across the resistor (v) voltage across the

capacitor (vi) apparent power (vii) active power (viii) reactive power.

10. A series circuit has R = 8 Ω and C = 30 µF. At what frequency will the current lead the voltage by 300?

11. A pure resistor in series with a pure capacitor is connected to a 200 V, 50 Hz supply. The current in the

circuit is 2 A and the power loss in the resistance is 100 W. Calculate the value of the resistance and

capacitance of the capacitor. Also draw the phasor diagram.

12. For the circuit shown,

calculate (i) impedance (ii) circuit current

(iii) phase angle (iv) voltage across each element (v) p.f. (vi) apparent power (vii) average power. Also

draw the phasor diagram.

13. A circuit consists of a resistance R in series with a capacitive reactance of 60 Ω. Determine the value of ‘R’

for which the p.f. of the circuit is 0.8 lead.

14. A choke takes 4 A current when connected to a 20 V d.c. supply. When connected to a 65 V, 50 Hz a.c.

supply, it takes 5 A current. Determine (i) the resistance and inductance of the coil (ii) p.f. (iii) the power

drawn by the coil.

15. A choke coil is connected to a 240 V a.c. supply. When the frequency of the supply is 50 Hz, an ammeter

connected in series with the choke reads 60A. On increasing the frequency of a.c. supply to 100 Hz, the

same ammeter reads 40 A. Calculate the resistance and inductance of the coil.

16. A coil having a resistance of 15 Ω and inductance of 0.2 H are connected in series with another coil

having a resistance of 25 Ω and inductance of 0.04 H to a 230V, 50 Hz supply. Determine (i) Voltage

across coils (ii) power dissipated in each coil (iii) p.f. of the whole circuit.

17. A non-inductive resistor of 10 ohm is connected in series with a choke coil having internal resistance of

1.2 ohm is fed from a 200V, 50 Hz supply. Current flowing through the circuit is 8 A. Calculate (i)

reactance of the coil (ii) its inductance (iii) voltage across the choke coil (iv) power absorbed by the choke

coil (v) power absorbed by the non-inductive resistor (vi) total power absorbed.

18. When a 100V, 50 Hz a.c. source is connected to a choke coil, the resulting current is 8 A and the power

delivered is 120 W. When the same source is connected to coil B, the resulting current is 10 A, and the

power absorbed is 500 W. What power and current will be taken from the source if the two coils are

joined in series and connected across the source?

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19. An a.c. sinusoidal voltage v= (160 + j120) V is applied to a circuit. The resulting current is i = (-4 + j10) A.

Find the impedance of the circuit and state whether it is inductive or capacitive. Also find the p.f., active

and reactive powers.

20. A sinusoidal voltage is given by v = 20 sin ωt V. (i) At what angle will the instantaneous value of voltage

be 10 V? (ii) What is the maximum value of the voltage and at what angle?

A.C. Circuits – Parallel Circuits

1. When a 2 element parallel circuit is connected across an a.c. source of frequency 50 Hz, it offers an impedance of Z = (10-j10) Ω. Determine the values of 2 elements.

2. A pure resistance of 25 Ω is connected in parallel with 79.62 mH inductive coil. The circuit is connected across 250 V, 50 Hz supply. Calculate (i) impedance (ii) total current (iii) p.f. of the circuit (iv) power consumed.

3. A capacitor of 100 µF is connected across a resistor of 100 Ω. The combination is connected across 250 V, 50 Hz supply. Calculate (i) impedance (ii) kVA of the circuit (iii) total power consumed.

4. A 100 Ω non-inductive resistance, 100 mH inductance and 101.5 µF capacitor are connected in parallel across 200 V, 50 Hz supply. Calculate the circuit current, p.f. of the circuit. Also draw the phasor diagram.

5. An impedance of (3+j5) Ω is connected in parallel with a reactance of (j4) Ω. The supply voltage is 50 V, 50 Hz. Calculate the circuit current and p.f. What value of parallel capacitor is to be connected to make the circuit p.f. unity?

6. Two impedances Z1 = 5 <-300 Ω and Z2 = 10 <450 Ω are connected in parallel. The combination draws (2+j4) A current from a voltage source. Determine the voltage source and the complex power of each branch.

7. A circuit is made of two branches in parallel, one having a resistance of 10 Ω in series with an inductive reactance of 20 Ω. The other having a resistance of 15 Ω in series with a capacitive reactance of 150 Ω. The supply voltage is 200 V. Find the total current, p.f. and power.

8. Using admittance method, find the current drawn by the circuit.

9. Two circuits having the same numerical ohmic impedances are joined in parallel. The p.f. of one circuit is 0.8

lag and the other is 0.6 lag. What is the p.f. of the combination? 10. For the circuit given, find the circuit current.

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TUTORIALS SHEET VII – A.C. Circuits – KTU Questions

1. An alternating current is represented by i(t) = 200 Sin (314t) A. Find RMS Value, frequency, time period and instantaneous value of current when t = 3 ms.

2. For the figure given below, evaluate ‘Í’ flowing through the circuit and draw the phasor diagram of current and voltage (take source voltage as reference quantity)

3. A choke coil takes 3 A which is lagging 600 with respect to applied voltage of 230 V, 50 Hz AC supply.

Determine impedance, resistance and inductance of coil. 4. The output voltage appearing across an electronic power converter is as shown in figure. Find rms and

average value of v(t) if Vm = 100 V and ‘α’ = 600.

5. Explain how sinusoidal voltage and current are represented in phasor form. 6. Prove that the instantaneous power consumed by a pure inductor is Zero. 7. Express the phasor in time domain ‘i(t)’ after carrying required computation in phasor form

/12 /8(4 3 )(15 1.2)

(2 25)(2 2)

j je eI j

j

8. A capacitor of capacitance 79.5 μF is connected in series with a non-inductive resistance of 30 Ω across 100 V, 50 Hz supply. Find Impedance, current, phase angle and equation for instantaneous value of current.

9. A voltage across 150 Ω resistor is 150 sin (2πx103t) V. At what value of ‘t’ does the current through the resistor equal to -0.26 A and what is instantaneous power at this time ‘t’?

10. Find the average and rms value of the given waveform.

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11. A coil of resistance 50 Ω and inductance 100 mH is connected in series with a capacitor of 500 μF is

connected across a 230 V, 50 Hz ac supply. Find (i) current through the coil (ii) power consumed (iii) reactive power and (iv) voltage across the coil. Also draw the phasor diagram with voltage as reference.

12. Prove the instantaneous power consumed by a pure capacitor is zero. 13. A capacitor and resistor are connected in series across a 120 V, 50 Hz supply. The circuit draws a current of

1.144 A. If power loss in the circuit is 130.8 W, find the values of resistance and capacitance.

14. For an ac circuit, if v(t) =160 sin (ωt + 100) and i(t) =5 sin (ωt - 200), find the power factor and active power

absorbed by the circuit. Draw the phasor diagram. 15. Find the average and rms value of the given waveform.

16. A non-inductive resistance is connected in series with a practical inductive coil. The circuit is supplied with

250 V, 50 Hz supply. When a current of 5 A flows through the circuit, the magnitude of voltage drop across the resistance and coil are 125 V and 200 V respectively. Calculate (i) the impedance, resistance and reactance of the coil (ii) power absorbed by the coil (iii) total power. Also draw the phasor diagram.

17. Two coils A and B are connected in series across a 240 V, 50 Hz supply. The resistance of A is 5 Ω and the inductance of B is 0.015 H. If the input from the supply is 3 kW and 2 kVAr, find the inductance of the coil A and resistance of the coil B. Calculate the voltage across each coil.

18. An RL series circuit is supplied from an ac voltage source v = 12 cos 4t V. The complex power delivered by the source is S = (3.6 + 7.2j) VA. Calculate the values of resistance R, inductance L. Evaluate the power factor.

19. Two impedances 10 L-300 and 20 L600 are connected in parallel. Evaluate the equivalent impedance. What is the nature of the equivalent impedance? If a current of 10 L 450 is passed through the parallel combination, calculate the voltage across the combination and express it in rectangular form. Evaluate the currents in each of the impedances. Draw the phasor diagram showing this voltage and all the three currents.

20. Define form factor and peak factor. Consider v(t) = 500 cos (100t), a sinusoidal voltage. Evaluate the rms and peak factor of the voltage waveform.

21. Define complex power. How is it related to ‘Apparent Power’?

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22. A pure inductance of 318 mH is connected in series with a pure resistance of 75 Ω. This circuit is supplied from a sinusoidal source and the voltage across the 75 Ω resistance is found to be 150 V. Calculate the supply voltage.

23. A current of 5A flows through a non-inductive resistance in series with a choke coil when supplied at 250 V, 50 Hz. If the voltage across the resistance is 125 V and across the coil is 200V, calculate (i) Z, R and L of the coil (ii) Power absorbed by the coil (iii) Total power. Draw the phasor diagram.

24. Two impedances (10+5j) Ω and (25-j10) Ω are connected in parallel across a 100V, 50 Hz supply. Find the total current, branch currents, pf, Power consumed.

25. The apparent power drawn by an AC circuit is 10 kVA and active power is 8kW. What is the reactive power and pf of the circuit?

RESONANCE

1. A coil having a resistance of 20 Ω and inductive reactance of 318 Ω at resonant frequency, is connected in series with

capacitor of capacitance 10 µF. Calculate (i) the value of resonant frequency (ii) quality factor of the circuit.

2. A coil having a resistance of 20 Ω and inductive reactance of 31.4 Ω at 50 Hz, is connected in series with capacitor of

capacitance 10 µF. Calculate (i) the value of resonant frequency (ii) quality factor of the circuit.

3. A resistance of 50 Ω is connected in series with capacitor of capacitance 100 µF and an unknown inductor. If the circuit is

under resonance for 220V, 50 Hz ac supply, Calculate (i) the value of the inductor (ii) impedance of the circuit (iii) current

in the circuit.

4. A resistor of 50 Ω, an inductor of internal resistance and a capacitor is connected in series with a variable frequency, 100 V

supply. At a frequency of 200 Hz, maximum current 0.7A flows through the circuit and the voltage across the capacitor is

200 V. Determine the circuit constants.

5. A coil of resistance 100 Ω and inductance of 100 µH is connected in series with capacitor of capacitance 100 pF. The circuit

is connected to a 10 V variable frequency supply. Calculate (i) the value of resonant frequency (ii) the current at resonance

(iii) voltage across L & C at resonance (iv) quality factor of the circuit (v) bandwidth.

6. An RLC series circuit consisting of resistance of 1000 Ω and inductance of 100 mH and a capacitor of capacitance 10 pF is

connected a voltage source of 100 V. Determine (i) the value of resonant frequency (ii) quality factor of the circuit (iii) half

power points.

7. An RLC series circuit is connected across v = 150 Sin 100πt Volts. The maximum current in the circuit is 25 A and at this

condition voltage across the capacitor is 600 V. Find the numerical values of the circuit elements.

8. A series RLC circuit has R = 5 Ω, L = 40 mH and C = 1 µF. Determine (i) the Q of the circuit (ii) separation between half

power frequencies (iii) the value of resonant frequency (iv) half power frequencies.

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9. Determine the impedance at resonant frequency 10 Hz above resonant frequency and 10 Hz below resonant frequency in

the series RLC circuit having R = 10 Ω, L = 0.1 H and C = 10 µF.

10. A coil having a resistance of 5 Ω and an inductance of 0.1H are connected in series with a 50 μF capacitor. A

constant alternating voltage of 200 V is applied to the circuit. At what value of frequency will current be

maximum? Calculate the current and voltage across the coil and across the capacitor for this frequency. Also

find the voltage magnification at resonance.

11. Find R1, so that the circuit is resonant.


power frequencies (iii) half power frequencies.

RESONANCE - Additional Questions

1. Find the resonant frequency of the two branch parallel circuit shown in figure.

2. Find R1, so that the circuit is resonant.

R1 j8

5 -j6

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3. A coil having a resistance of 20 Ω and an inductance of 10 mH are connected in series with a 10 μF capacitor

of negligible resistance across a variable frequency ac source which has a constant output of 4V. (a) At what

frequency will the current and applied voltage be in-phase (b) if the ac source is set to the frequency in (a),

determine (i) the current in the circuit (ii) voltage across the capacitance.

4. Compute the value of ‘C’ which results in resonance for the circuit shown in figure when f = (2500/π) Hz.

5. Determine the value of C for which the circuit is resonant at 6366 Hz.

6. A coil of 20 Ω resistances has an inductance of 0.2 H and is connected in parallel with a 100 µF capacitor. Calculate the

frequency at which the circuit will act as a non-inductive resistance. Also find the value of that resistance.

7. A resistance of 24 Ω, a capacitance of 150 µF and an inductance of 0.16 H are connected in series with each other. A

supply at 240 V, 50 Hz is applied to the ends of the combination. Calculate

(i) The current in the circuit

(ii) The potential difference across each element of the circuit

(iii) The frequency to which the supply would need to be changed so that the current would be at upf and find the current

at this frequency.


power frequencies (iii) half power frequencies.

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9. Show that in a series RLC circuit, the resonant frequency is the geometric mean of the lower and upper half

power frequencies.

10. In measurement on an inductor at a frequency of 1.59 MHz series resonance was obtained with a capacitor of

200 pF and magnification factor was 50. If the capacitor is assumed to have negligible resistance, determine

the inductance and effective series resistance of the inductor.

11. A coil of resistance 0.2 Ω and 10 mH is connected across a 100V, 50Hz sinusoidal supply. Calculate the

capacitance placed in parallel with the coil so that the resultant current is in phase with the voltage. Determine

the current under this condition.

12. An impedance of 3+j2 Ω is connected in parallel with a reactance of j4 Ω. The supply voltage is 50 V at 50

Hz. Calculate the circuit pf. What value of parallel capacitor is to be connected to make the circuit pf unity?

KTU – Questions

1. A series LC circuit is resonating at 150 kHz and has a Q factor of 50. Find the Upper and Lower cut off

frequencies.

2. A series RLC circuit which resonates at frequency 500 kHz has L = 100 µH, R = 25 Ω and C = 1000 pf.

Determine (i) Q factor of the circuit (ii) the new value of C to resonate at 500 kHz when the value of L is

doubled and the new Q factor.

3. A series RLC circuit with L = 25 mH and C = 70 µF has a lagging phase angle 300 at frequency 320 Hz. At what

frequency will the phase angle be 400 leading?

4. An RLC series circuit is connected to a variable frequency source of 230V. Parameter values are R = 22 Ω, L = 10 mH

and C = 30 µF. What will be the value of impedance at resonance, current through the circuit at resonance and

resonant frequency of the circuit?

5. A series RLC circuit has R = 10 Ω, L = 0.1 H and C = 8 µF. Calculate the following. (i) Resonant frequency (ii) Q

factor of the circuit at resonance (iii) Half power frequencies and bandwidth.

6. A resistance of 400 Ω and an inductance of 318 H are connected in parallel. Find the capacitance of a capacitor

which when connected in parallel with the combination will produce resonance with a supply frequency of 1

MHz. If a second capacitor of capacitance 23.5 pF is connected in parallel with the first capacitor, find the

frequency at which resonance will occur. What is the Q factor in each case?

7. The variation of current against frequency in a series RLC circuit is shown in figure. Obtain the resonant frequency of

the circuit from figure. If at resonance, the total voltage across the RLC series circuit is 100 V, evaluate the resistance in

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the circuit. What is the power factor at resonance? Calculate the power dissipated at resonance. The voltage, current etc.

are expressed in RMS values.

8. What is resonant frequency? Give a graphical representation of series resonance in series RLC circuits.

9. Show that the parameters of a series RLC circuit vary with frequency. Define Q factor and bandwidth of a series resonance

circuit. Give their expressions also.

10. Sketch the variation of impedance in series resonant circuit.

THREE PHASE SYSTEM Tutorial Sheet IX

1. In a balanced Y connected system, the value of the current in R phase is IR = 10 L200 A. Calculate the values of the 3

line currents.

2. Three star connected impedances (30+j40) per phase are connected across 398.36V, three phase supply. Find 1)

the line current 2) power factor 3) Power 4) Reactive Volt Amp. (Ans. IL= 4.6A, pf = 0.6 lag, P= 1904.28W, VAr =

2539 VAr)

3. A balanced three phase star connected load of 100kW takes a leading current of 100A, when connected to a three

phase, 1100V, 50 Hz supply. Calculate the circuit constants of the load per phase. (R = 3.333 and C = 588.9µF)

4. Three coils of inductance 0.1 H and resistance 10 each are connected in star and joined to a 3 phase 400 V, 50

Hz ac supply. Calculate (i) impedance / phase (ii) pf of the circuit (iii) phase current (iv) line current (v) total power.

5. Distinguish between star and delta connection. For a given balanced three-phase system with star-connected load

for which line voltage is 230 V, and impedance of each phase is (4 + j6) ohm. Find line current, p.f. & power

absorbed. (Ans. Il= 18.42A, p.f. = 0.555lag, P= 4072.6W).

6. Three similar inductive coils of resistance 20 and reactance 30 are connected in mesh across a three phase

400V supply. Calculate (i) Phase current (ii) Line current (iii) pf (iv) Power drawn from the supply. (Ans. IP = 11.1A,

IL= 19.22 A, pf = 0.554 lag, P = 7377W)

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7. A 3 phase delta connected load takes 100 kW at 0.9 pf lagging from a 415 V, 3 phase 50 Hz supply. Calculate (i) line

current (ii) phase current (iii) impedance/phase (iv) reactive voltamp.

8. Show that the power consumed by 3 identical 1 Φ loads connected in delta is equal to three times the power

consumed when the phase loads are connected in star.

9. Three resistors each of 100 are connected in (a) Star (b) Delta, across three phase 400V, 50Hz supply. Find in

each case (i) Line current (ii) Phase current (iii) Power absorbed.

(Ans. STAR: IL= 2.31A, IP = 2.31A, P = 1600W. DELTA: IL= 6.928A, IP = 4A, P = 4800W)

10. Three impedances each of value 25 L-600 are connected in delta across a 400V, three phase, 50 Hz supply. Find

the (i) current in each phase (ii) the line current (iii) total power consumed (iv) draw the phasor diagram for

currents. (Ans. IP = 16 A, IL= 27.72 A, P= 9602.49W)

11. A balanced star-connected load of (8+j6) ohm per phase is connected to a three phase 230 V supply. Find line

current, p.f. and power. (Ans. Il= 13.279A, p.f. = 0.8 lag, P= 4321.98W)

12. Three balanced impedances are connected in star, across a 3 phase, 415 V 50 Hz supply. The line current drawn is

20 A at a lagging pf of 0.4. Determine the parameters of the impedance in each phase.

13. The power input to a 3 phase circuit was measured by 2 wattmeter method. The readings are 3 kW and 1.5 kW.

Determine the total power consumed and pf of the balanced 3 phase circuit.

14. Two wattmeter method was used to determine the input power to a 3 phase motor. The readings are 5.2 kW and -

1.7 kW; and the line voltage was 415 V. Calculate (i) total power (ii) pf (iii) line current.

15. During the measurement of power by 2 wattmeter method, the total input power to a 3 phase 440 V motor

running at a pf of 0.8, was found to be 25 kW. Find the readings of the 2 wattmeters.

16. A single Wattmeter is connected to measure reactive power of a three phase three wire balanced load. The line

current is 17A and the line voltage is 440V. Calculate the p.f. of the load if the reading of the wattmeter is

4488VAr. Find also the total reactive power. ( pf = 0.8, 7773.44 VAr)

17. A star connected 3 phase load has a 6 resistance and 8 inductive reactance in each branch. It is connected to

a 220 V, 3 phase 4 wire supply. Write the phasor expression for (i) voltages across each phase (ii) line voltages (iii)

line currents. Also calculate the total power consumed.

18. A delta connected 3 phase load has a 6 resistance and 8 inductive reactance in each branch. It is connected to

a 220 V, 3 phase 4 wire supply. Write the phasor expression for (i) current through each phase (ii) line currents (iii)

line voltages. Also calculate the total power consumed.

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19. A 3-phase alternator produces a voltage of 6351 volts/phase and carry a current of 315 A/phase. Find the line

voltage, line current and the kVA capacity of the 3-phase alternator when it is (i) star connected; (ii) delta

connected. (Ans. STAR: VL= 11kV, IL= 315A, kVA capacity= 6001.74kVA

DELTA: VL= 6351V, IL= 545.6A, kVA capacity= 6001.74kVA)

20. Three impedances Z1 = 20 L300, Z2 = 40 L600 and Z3 = 10 L-900 are delta connected to a 400 V, 3 phase

system. Determine the (i) Phase currents (ii) Line currents (iii) Total power consumed by the load.

21. An unbalanced four-wire, star connected load has a balanced voltage of 400 V, the loads are Z1 = (4+j8) , Z2 =

(3+j4) and Z3 = (15+j20) . Calculate the (i) Line currents (ii) current in the neutral wire (iii) total power.

22. A 400 V, three phase supply feeds an unbalanced 3 wire, Y connected load. The branch impedances of the load are

ZR = (4+j8) , ZY = (3+j4) and ZB = (15+j20) . Find the line currents and the voltage across each phase

impedance. Assume RYB phase sequence.

23. An unbalanced star connected load has balanced voltages of 200 V and the load impedances are ZR = (1+j5) , ZY =

(3- j4) and ZB = (6+j10) . Find the line currents and the neutral currents. Assume RBY phase sequence.

24. An unbalanced delta connected load with impedances ZRY = 10 L-300, ZYB = 30 L600 and ZBR = 50 L1000 are

connected to a balanced line- to- line voltage of 440 V, in the positive sequence. Determine the (i) Line currents (ii)

Total power absorbed by the load.

25. The currents in the RY, YB and BR branches of a delta connected system with symmetrical voltages are 25 A at pf

0.8 lag, 30 A at pf 0.7 lead and 20 A at unity pf respectively. Determine the current in each line. Assume RYB phase

sequence.

26. During a power measurement using two wattmeter method, the wattmeter connected in R phase read -1000 W

and the one connected in Y phase, read 2000 W when connected to a 400 V supply. The load is balanced. Find the

line current and power factor. State whether the load is inductive or capacitive.

27. The power input to a 400 V 3 phase load is measured by two wattmeters which indicates 300 W and 100 W resp.

Determine the power input and the power factor.

28. Three delta connected impedances (80-j60) per phase are connected across 398.36V, three phase supply. Find

1) the line current 2) power factor 3) Power 4) reactive Volt Amp. (Ans. IL= 6.9A, pf = 0.8 lead, P= 3808.58W, VAr

= 2856.44 VAr)

29. A three phase 60 Hz generator in star generates a line voltage of 23,900V. Calculate (i) the line to neutral voltage

(ii) voltage induced in the individual windings (iii) the time interval between the positive peak voltages of phase R

and the positive peak voltages of phase Y (iv) Peak value of line voltage. (Ans. EP = 13,798.67 V, EP = 13,798.67 V,

t = 5.55ms, Em = 33,800V)

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30. A 3 ɸ delta connected load consumes a power of 100 kW taking a lagging current of 200A at a line voltage of 400V,

50 Hz. Calculate the parameters of each phase. (Ans. Rp= 2.5, LP=7.6mH)

KTU Questions

31. The load to a 3 phase power supply consists of 3 similar coils connected in star. The line currents are 25 A and the

kVA and kW inputs are 20 and 11 respectively. Find (i) Phase and Line voltages (ii) Reactive power input (iii)

resistance and reactance of each coil.

32. A three phase star connected load consumes a total of 12 kW at a pf of 0.8 lag when connected to a 3 phase 400 V

50 Hz supply. Calculate the resistance and inductance of load per phase.

33. Three impedances (10+j15) are connected in delta across 3 phase 400 V supply. Find the line current, pf and

active power.

34. The power input and line current of three phase induction motor is 15 kW and 25 A respectively. Find the readings

of the two wattmeters connected to measure the motor input power. Assume 3 phase supply voltage is 400 V.

35. Three identical coils having resistances of 10 and an inductance of 38.2 mH are connected in delta across 400 V,

3 phase 50 Hz supply. Find wattmeter reading if two wattmeter method is used to measure total power.

36. In the two wattmeter method of 3 phase power measurement, the load connected was 50 kW at 0.8 pf lagging.

Find the reading of each wattmeter.

37. Two single phase wattmeters are used to measure 3 phase power. The readings of the two wattmeters are 2500 W

and 450 W respectively. Calculate the pf of the circuit. What would be the pf if the reading of the second

wattmeter is negative?

38. The apparent power drawn by an AC circuit is 10 kVA and active power is 8 kW. What is the reactive power and

power factor of the circuit?

39. Two single phase wattmeter are used to measure 3 ɸ power. The readings of the 2 wattmeters are 2000 W and

400 W respectively. Calculate (i) p.f. of the circuit (ii) What would be the p.f. if the reading of the second

wattmeter is negative?

40. A 3 phase, 415 V supply is given to a balanced delta connected load of impedance (8+j6) Ω per phase. Find per

phase voltage, per phase current, line current, p.f. & total power.

41. A 3 phase 4 wire system has a balanced load in Y connection. The phase impedance of the load is ZP = 10 L300 Ω. If

the line to line voltage is 400 V rms, evaluate the phase currents in polar form. Evaluate the total active power.

42. A 3 phase (ABC system) delta connected balanced load is drawing a current of 10 L-300 in the AB arm of the delta.

If the A phase voltage is 230 L00 V, draw the phasor diagram showing all the 3 phase currents and 3 phase voltages.

Length of Voltages & currents may be shown at convenient scales. All angles have to be indicated.

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43. A 600 V rms 3 phase Y connected source has 2 balanced Delta loads connected to the lines. The load impedances

are 40 L300 Ω and 50 L-600 Ω respectively. Determine the rms line current and the total average power.

44. The 2 wattmeter method is used to determine the power drawn by a 3 phase 440 V rms motor that is a Y

connected balanced load. The motor draws a power of 20 kW. The magnitude of the line current is 52.5 A rms. The

wattmeters are connected in the A & C lines. Find the reading of each wattmeter.The motor has a lagging power

factor. Draw the phasor diagram showing all the voltages and currents measured.

ADDITIONAL QUESTIONS

1. Define line voltage, line current and phase current. A balanced delta connected load consists of (5+j3) ohms in

each branch. The line voltage is 3002 volts. Find line and phase currents, and real and apparent power. (Ans. Il=

126.04A, Ip= 72.77A, P= 79.47kW, S=92.62kVA)

2. A 3 phase, 400V supply is given to a balanced star connected load of impedance (8+j6) Ω per phase. Find line

current, p.f. & total power. (Ans. Il = 23.09A, p.f. = 0.8 lag, P= 12.798 kW)

3. A 3-phase alternator produces a voltage of 6351 volts/phase and carry a current of 262A / phase. Find the line

voltage, line current and the kVA capacity of the 3-phase alternator when it is (i) star connected; (ii) delta

connected.

(Ans. STAR: VL= 11kV, IL= 262A, kVA capacity= 4991.886kVA

DELTA: VL= 6351V, IL= 453.8A, kVA capacity= 4991.886kVA)

4. The load in each branch of a delta connected balanced 3 phase circuit consists of an inductance of 31.8mH in

series with a resistance of 10. The line voltage is 400V, 50Hz. Calculate (i) the line current (ii) total power in the

circuit. (Ans. IL= 49.03A, P= 24.036kW)

5. A balanced three phase, Y-connected load of 150kW is taking a leading current of 100A with a line voltage of

1100V, 50 Hz. Find the circuit parameters of the load per phase.

6. A balanced 3 phase load consists of 3 coils having reactance of 4 and resistance of 3 connected in delta. It is

connected across 250 V, 50 Hz, 3 phase supply. Calculate the line current, real and reactive power.

7. A delta connected load has the following impedances: ZRY = j10 , ZYB = 10 L00 and ZBR = -j10 . If the load is

connected across 100V balanced 3 phase supply, obtain the line currents.

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8. Three impedances ZR = 12 L00 , ZY = 12 L300 and ZBR = 10 L450 are connected in Y across a 3 phase 3 wire, 416

V supply system, the voltage being VRY = VL L-1200 V, VYB = VL L00 V, VBR = VL L1200 V. Determine all the line currents

and the voltage of common point of load impedance with respect to neutral of supply system.

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5.4 ASSIGNMENTS

ASSIGNMENT I (S1 EEE)

1. Determine the equivalent resistance of the network.

2. For the network shown, calculate the current through 150Ω resistor.

10

5

10

9

150

2

4

A

B

20V

3. In the network shown in figure, find the resistance between the points A and B.

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4

6

8

AB

C

8

8

6

4

4

6

4. Find the current through the 10 resistor using delta star transformation.

8

12

12

CB

AH

G F

10

D

30

E

17

+ -

180 V

5. Determine the current in each loop for the circuit shown below using mesh analysis

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3.25 0.23

+-

8.4 V

+-

1.3 V

+_ 1.5 V

6. Find the currents in the various branches of the given network shown in figure

80 A

100 A

80 A

90 A

150 A

120 A

0.010.02

0.02

0.030.02

0.01

F

A

B

C

D

E

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7. Find V0 using Mesh analysis.

Ia

4 mA

2 Ia

+

-

V0

8. Find the current I supplied by the battery in the circuit.

8V

10

2

2

3

5

4.4

3

I

1

9. Use the mesh current method to find the power delivered by the dependent voltage source in the circuit given below.

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660V

20 iaia

10. Convert the delta network into its equivalent star network.

21

3 4

R12

R31 R23

2

5 3

ASSIGNMENT II (S1 EEE)

26. A capacitor and resistor are connected in series across a 120 V, 50 Hz supply. The circuit draws a current of 1.144 A. If

power loss in the circuit is 130.8 W, find the values of resistance and capacitance.

27. Two impedances (10+5j) Ω and (25-j10) Ω are connected in parallel across a 100V, 50 Hz supply. Find the total current,

branch currents, pf, Power consumed.

28. The apparent power drawn by an AC circuit is 10 kVA and active power is 8kW. What is the reactive power and pf of

the circuit?

29. A series LC circuit is resonating at 150 kHz and has a Q factor of 50. Find the Upper and Lower cut off frequencies.

30. An RLC series circuit is connected to a variable frequency source of 230V. Parameter values are R = 22 Ω, L = 10 mH

and C = 30 µF. What will be the value of impedance at resonance, current through the circuit at resonance and

resonant frequency of the circuit?

31. A series RLC circuit has R = 10 Ω, L = 0.1 H and C = 8 µF. Calculate the following. (i) Resonant frequency (ii) Q factor of

the circuit at resonance (iii) Half power frequencies and bandwidth.

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BE103: INTRODUCTION TO SUSTAINABLE

ENGINEERING

89

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PROGRAMME: ELECTRICAL & ELECTRONICS ENGG DEGREE: BTECH

COURSE: INTRODUCTION TO SUSTAINABLE

ENGINEERING SEMESTER: S1 CREDITS: 3

COURSE CODE: BE 103

REGULATION: 2015 COURSE TYPE: CORE

COURSE AREA/DOMAIN: ENGINEERING (All Branches) CONTACT HOURS: 2(LECTURE) + 1(TUTORIAL)

HOUR/WEEK

CORRESPONDING LAB COURSE CODE (IF ANY): NIL LAB COURSE NAME: NIL

SYLLABUS:

MODULE

CONTENTS

HOURS

SEM.

EXAM

MARKS

I

Sustainability - Introduction, Need and concept of sustainability,

Social- environmental and economic sustainability concepts.

Sustainable development, Nexus between Technology and

Sustainable development, Challenges for Sustainable Development.

Multilateral environmental agreements and Protocols - Clean

Development Mechanism (CDM), Environmental legislations in

India - Water Act, Air Act.

L4

15%

Students may be assigned to do at least one project eg: a) Identifying/assessment of sustainability in your neighbourhood

in education, housing, water resources, energy resources, food

supplies, land use, environmental protection etc.

b) Identify the threats for sustainability in any selected area and

explore solutions for the same

P1

II

Air Pollution, Effects of Air Pollution; Water pollution- sources,

Sustainable wastewater treatment, Solid waste - sources, impacts of

solid waste, Zero waste concept, 3 R concept. Global

environmental issues- Resource degradation, Climate change,

Global warming, Ozone layer depletion, Regional and Local

Environmental Issues. Carbon credits and carbon trading, carbon foot print.

L6

15%

Students may be assigned to do at least one project for eg: a) Assessing the pollution status of a small area

b) Programmes for enhancing public environmental awareness

c) Observe a pond nearby and think about the different measures

that can be adopted for its conservation

P3

FIRST INTERNAL EXAM

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III

Environmental management standards, ISO 14000 series, Life

Cycle Analysis (LCA) - Scope and Goal, Bio-mimicking,

Environment Impact Assessment (EIA) – Procedures of EIA in India.

L4

15%

P2

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Students may be assigned to do at least one project eg: a) Conducting LCA of products (eg. Aluminium cans, PVC bottles,

cars etc. or activities (Comparison of land filling and open burning)

b) Conducting an EIA study of a small project (eg. Construction of

a building)

IV

Basic concepts of sustainable habitat, Green buildings, green

materials for building construction, material selection for

sustainable design, green building certification, Methods for

increasing energy efficiency of buildings. Sustainable cities, Sustainable transport.

L5

15%

Students may be assigned to do at least one project eg: a) Consider the design aspects of a sustainable building for your

campus

b) Explore the different methods that can be adopted for maintaining a sustainable transport system in your city..

P2

SECOND INTERNAL EXAM

V

Energy sources: Basic concepts-Conventional and non-

conventional, solar energy, Fuel cells, Wind energy, Small hydro plants, bio-fuels, Energy derived from oceans, Geothermal energy..

L5

20% Students may be assigned to do at least one project eg: a) Find out the energy savings that can be achieved by the

installation of a solar water heater

b) Conduct a feasibility study for the installation of wind mills in

Kerala

P2

VI

Green Engineering, Sustainable Urbanisation, industrialisation and poverty reduction; Social and technological change, Industrial Processes: Material selection, Pollution Prevention, Industrial Ecology, Industrial symbiosis.

L5

20%

Students may be assigned to do a group project eg: a) Collect details for instances of climate change in your locality b) Find out the carbon credits you can gain by using a sustainable transport system (travelling in a cycle or car pooling from college to home) c) Have a debate on the topics like: Industrial Ecology is a Boon or Bane for Industries?/Are we scaring the people on Climate Change unnecessarily?/Technology enables Development sustainable or the root cause of unsustainability?

P3

END SEMESTER EXAM

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T/R

T1

Allen, D. T. and Shonnard, D. R., Sustainability Engineering: Concepts, Design and Case Studies, Prentice Hall.

T2

Bradley. A.S; Adebayo,A.O., Maria, P. Engineering applications in sustainable design and development, Cengage learning

T3 Environment Impact Assessment Guidelines, Notification of Government of India, 2006

T4 Mackenthun, K.M., Basic Concepts in Environmental Management, Lewis Publication, London, 1998

T5 ECBC Code 2007, Bureau of Energy Efficiency, New Delhi Bureau of Energy Efficiency Publications-Rating System, TERI Publications - GRIHA Rating System

T6

Ni bin Chang, Systems Analysis for Sustainable Engineering: Theory and Applications, McGraw-Hill Professional.

T7 Twidell, J. W. and Weir, A. D., Renewable Energy Resources, English Language Book Society (ELBS).

T8 Purohit, S. S., Green Technology - An approach for sustainable environment, Agrobios

publication



SCIENCE BASIC KNOWLEDGE SCHOOL LEVEL

COURSE OBJECTIVES:

1 To have an increased awareness among students on issues in areas of sustainability

2 To understand the role of engineering and technology in sustainable development

3 To know the methods, tools, and incentives for sustainable product-service system development

To establish a clear understanding of the role and impact of various aspects of engineering and

engineering decisions on environmental, societal, and economic problems.

COURSE OUTCOMES:

Sl.

NO DESCRIPTION

PO

MAPPING

1 The student will be able to understand the different types of environmental pollution problems

and their sustainable solutions

(level1, 2)

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CO-PO AND CO-PSO MAPPING

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 PSO3

CO.1 1 1 2 _ _ 2 2 1 1 1 1 _ 1 - 1

CO.2 1 1 1 1 _ 2 2 _ _ 1 _ 1 1 1 1

CO.3 1 _ 2 _ 2 2 3 1 1 _ 1 _ 1 1 1


CHALK & TALK STUD. ASSIGNMENT WEB RESOURCES

LCD/SMART BOARDS STUD. SEMINARS DISCUSSIONS/ DEBATES

ASSESSMENT METHODOLOGIES-DIRECT:

ASSIGNMENTS √ STUD. SEMINARS √ TESTS/MODEL

EXAMS√

UNIV.

EXAMINATION√

STUD. LAB PRACTICES STUD. VIVA√ MINI/MAJOR PROJECTS CERTIFICATIONS


2 The student will be able to work in the area of sustainability for research and education (level 2, 3,

5)

3 The student will be having a broader perspective in thinking for sustainable practices by

utilizing the engineering knowledge and principles gained from this course

(level 3, 4)

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6.2 COURSE PLAN

Sl.No Module Planned

1

1

Introduction to syllabus & subject

2

1

SD-history,definition,concept

3

1

Multidimensional(3 pillar) concept-

social,economic,environment

4

1

Multilateral Envirn Agreements-principle-eg

5

1

Kyoto protocol- Clean Development mechanism

6

1

Challenges & Barriers to SD

7

1

Envi Legislation- Water Act

8

1

Envi Legislation- Air Act -penalties

9

2

Regional envi-issue -Air Pollution-sources & impact-

control methods

10

2

Regional envi-issue -Water Pollution-sources &

impact-control methods

11

2

sustainable-Sewage water treatment-Aerobic and

anaerobic oxidation-dissolved oxygen

12

2

Local Env-issue-Solid waste –source-impact-

Management

13

2

Solid Waste Management-3 R concept

14

2

Zero waste concept

15

2

Globalenvir -issue- Climatechange -Globalwarming

16

2

Global envir-issue-Ozone depletion-Resource

degradation

17

2

Carbon (credit-trading-foot print)

18

3

Environmental Management system/Standards(EMS)-

goals, Model, Key elements, benefits, manual

19

3

EMS- Key elements, benefits ,Cert, Document,

20

3

ISO 14000 series-scope, obj , principles, elements,

benefits

21

3

LCA-stages, limits, procedure, benefits-appl

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22

3

EIA-def, purpose ,benefit, limitation, procedures in

India

23

3

EIA-process& procedure in India-EIA-Guiding

principle-Flowchart-Sample EIA report-Stud Activity

24

3

Bio-mimicking-principle-Application

25

4

Basic concept of sustainable habitat -Green

buildings- green materials for construction

26

4

Material selection for sustainable design

27

4

Green building certification-(Stud activity-

discussion)-LEED,GRIHA

28

4

Methods of increasing energy efficiency of buildings-

sustainable-cities-transport-overview

29

4

Sustainable-cities-transport

30

5

Energy sources: Basic concept-Conventional & non-

Conventional

Course Handout


31

5

Solar energy -thermal-photovoltaic-systems-impact

on environment

32

5

Wind energy systems

33

5

Small hydro plants-Fuel cells

34

5

Bio mass-biofuels

35

5

Geothermal energy -Energy from oceans-Tidal, wave

36

5

Stud assign activity-presentation-environmental

impact-sustainable energy

37

6

Urbanization-sustainable urbanisation

38

6

Industrialization and poverty reduction

39

6

Green engineering-Social &technology change

40

6

Industrial Ecology

41

6

Industrial symbiosis

42

6

student activity-Group discussion-on Sustainable

Engineering solutions overview.

43

6

Subject review-univ exam-Discussion-Revision

Course Handout


6.3 ASSIGNMENTS

S. No Group/Batch Topic

1. Group A: B-I & Group B: B-I Design of standalone Solar PV-System

2. Group A: B-II & Group B: B-II Feasibility study of wind farms in Kerala

3. Group A: B-III & Group B: B-III Study on Energy from Ocean: Tidal Energy /wave

Energy potential in Kerala.

4. Group A: B-IV & Group B: B-IV Study on Bio-Fuels/Bio mass & its Impact on

Sustainability

5. Group A: B-V & Group B: B-V Study on Geo-Thermal Energy source& its Impact

on Sustainability

6. Group A: B-VI & Group B: B-VI Study on Fuel cell Technology & its Impact on

Sustainability

Course Handout


7. CE100: BASICS OF CIVIL

ENGINEERING

Course Handout



PROGRAMME: EC DEGREE: BTECH

COURSE: BASICS OF CIVIL

ENGINEERING

SEMESTER: S1 LTP CREDITS:

2-1-0-3

COURSE CODE: CE100

REGULATION: 2015 COURSE TYPE: BASIC

COURSE AREA/DOMAIN: CIVIL

ENGINEERING CONTACT HOURS: 2+1 hours/Week.

CORRESPONDING LAB COURSE

CODE (IF ANY): CE 110 BASIC CIVIL

ENGINEERING WORKSHOP

LAB COURSE NAME: BASIC CIVIL

ENGINEERING WORKSHOP

SYLLABUS:

UNI

T DETAILS

HOUR

S

I

General Introduction to Civil Engineering - Various disciplines of Civil

engineering, Relevance of Civil engineering in the overall infrastructural

development of the country. Introduction to types of buildings as per

NBC; Selection of site for buildings. Components of a residential

building and their functions. Introduction to industrial buildings – office /

factory / software

development office / power house /electronic equipment service centre

(any one related to the branch of study). Students have to visit one such

building and submit an assignment about the features of any one of the

listed building related to their branch (Not included for exam).

7

II

Building planning - Introduction to planning of residential buildings- Site

plan, Orientation of a building, Open space requirements, Position of

doors and windows, Size of rooms; Preparation of a scaled sketch of the

plan of a single storeyed residential building in a given site plan.

Introduction to the various building area terms - Computation of plinth

area / built up area, Floor area / carpet area - for a simple single storeyed

building; Setting out of a building.

7

Course Handout


III

Surveying - Principles and objectives of surveying; Horizontal

measurements – instruments used – tape, types of tapes; Ranging (direct

ranging only) – instruments used for ranging, Levelling - Definitions,

principles, Instruments (brief discussion only) - Level field book -

Reduction of levels - problems on levelling (height of collimation only).

Modern surveying instruments – Electronic distance meter, digital level,

total station, GPS (Brief discussion only).

8

IV

Building materials - Bricks, cement blocks - Properties and specifications,

Cement – OPC, properties, grades; other types of cement and its uses (in

brief). Cement mortar – constituents, preparation, Concrete – PCC and

RCC – grades, Steel - Use of steel in building construction, types and

market forms.

6

V

Building construction – Foundations; Bearing capacity of soil (definition

only); Functions of foundations, Types - shallow and deep (sketches

only). Brick masonry – header and stretcher bond, English bonds –

Elevation and plan (one brick thick walls only), Roofs – functions, types,

roofing materials (brief discussion only), Floors – functions, types;

flooring materials (brief discussion only), Decorative finishes – Plastering

– Purpose, procedure, Paints and Painting – Purpose, types, preparation of

surfaces for painting (brief discussion only).

9

VI

Basic infrastructure and services - Elevators, escalators, ramps, air

conditioning, sound proofing (Civil engineering aspects only), Towers,

Chimneys, Water tanks (brief discussion only), Concept of intelligent

buildings.

5

TOTAL HOURS 42



T1 Satheesh Gopi, Basic Civil Engineering, Pearson Publishers

T2 Rangwala, Essentials of Civil Engineering, Charotar Publishing House

T3 Anurag A. Kandya, Elements of Civil Engineering, Charotar Publishing house

T5 Rangwala S C and Ketki B Dalal, Engineering Materials, Charotar Publishing

house

T6 Rangwala S C and Ketki B Dalal, Building Construction, Charotar Publishing

house

T7 McKay, W. B. and McKay, J. K., Building Construction Volumes 1 to 4,

Pearson India Education Services

Course Handout




MATHEMATICS FUNDAMENTAL

KNOWLEDGE OF

TRIGONOMETRY

SECONDARY

SCHOOL

LEVEL

PHYSICS BASIC KNOWLEDGE

ABOUT FRICTION,

DENSITIES AND UNIT

WEIGHTS.

PLUS-TWO

CHEMISTRY FUNDAMENTAL

KNOWLEDGE ABOUT

MATERIAL PROPERTIES

PLUS-TWO

COURSE OBJECTIVES:

1 To inculcate the essentials of Civil Engineering field to the students of all

branches of Engineering.

2 To provide the students an illustration of the significance of the Civil Engineering

Profession in satisfying societal needs.

COURSE OUTCOMES:

SNO DESCRIPTION

1 The students should be able to illustrate the fundamental aspects of Civil

Engineering.

2 The students should be able to plan and set out a building.

3 The students should be able to differentiate the features and components of

Industrial

and Residential buildings by conducting field visits.

4 The students should be able to describe the different surveying methods used

in

Civil Engineering.

Course Handout


5 Students should be able to recognise the various building materials and explain

their applications.

6

Students should be able to understand the different components of a building

and

their purposes.

7 Students should be able to discuss about various services in a building.

8 Students should be able to explain the need of Intelligent buildings in modern

world.

GAPS IN THE SYLLABUS - TO MEET INDUSTRY/PROFESSION

REQUIREMENTS:

Sl

NO

DESCRIPTION PROPOSED

ACTIONS

1 Manufacture of concrete, Classifications of concrete.

2 Classifications of foundations (Description)

PROPOSED ACTIONS: TOPICS BEYOND

SYLLABUS/ASSIGNMENT/INDUSTRY VISIT/GUEST LECTURER/NPTEL ETC


1 Timber- Varieties, Uses, Defects, Seasoning

2 Aggregates- Qualities, classification, sources


1 www.nptel.ac.in


CHALK & TALK

√

STUD.

ASSIGNMENT √

WEB RESOURCES √

LCD/SMART

BOARDS√

STUD. SEMINARS

√

ADD-ON COURSES


http://www.nptel.ac.in/

Course Handout


ASSIGNMENTS √

STUD.

SEMINARS √

TESTS/MODEL

EXAMS√

UNIV.

EXAMINATION√

STUD. LAB

PRACTICES√

STUD.

VIVA√

MINI/MAJOR

PROJECTS

CERTIFICATIONS

ADD-ON

COURSES

OTHERS


ASSESSMENT OF COURSE

OUTCOMES (BY FEEDBACK, ONCE)

√

STUDENT FEEDBACK ON

FACULTY (TWICE) √

ASSESSMENT OF MINI/MAJOR

PROJECTS BY EXT. EXPERTS

OTHERS

Course Handout


7.2 COURSE PLAN

Module Days Topics

Module 1 Day 1 General Introduction to Civil Engineering

Day 2 Various disciplines of Civil engineering

Day 3 Relevance of Civil engineering in the overall infrastructural

development of the country

Day 4 Introduction to types of buildings as per NBC

Day 5 Introduction to types of buildings as per NBC

Day 6 Selection of site for buildings

Day 7 Components of a residential building and their functions

Day 8 Preparation of a scaled cross sectional sketch of a residential

building and marking the components

Module 2 Day 9 Building planning - Introduction to planning of residential

buildings- Site plan

Day 10 Orientation of a building, Open space requirements, Position

of doors and windows, Size of rooms

Day 11 Preparation of a sample site plan

Day 12 Preparation of a scaled sketch of the plan of a single

storeyed residential building in a given site plan

Day 13 Introduction to the various building area terms -

Computation of plinth area / built up area, Floor area / carpet

area - for a simple single storeyed building; Setting out of a

building

Day 14 Preparation of a line sketch of a single storeyed residential

Course Handout


building for given requirements

Module 3 Day 15 Surveying - Principles and objectives of surveying

Day 16 Horizontal measurements – instruments used – tape,

types of tapes; Ranging (direct ranging only) – instruments

used for ranging

Day 17 Test- surveying

Day 18 Levelling - Definitions, principles, Instruments

Day 19 Level field book - Reduction of levels -

Day 20 problems on levelling

Day 21 Modern surveying instruments – Electronic distance meter,

digital level, total station, GPS

Module 4 Day 22 Building materials - Bricks, cement blocks - Properties and

specifications

Day 23 problems on levelling

Day 24 Cement – OPC, properties, grades; other types of cement

and its uses

Day 25 Cement mortar – constituents, preparation,.Concrete – PCC

and RCC – grades.

Day 26 Quiz- cement, mortar, concrete

Day 27 Steel - Use of steel in building construction

Day 28 types and market forms of steel

Day 29 Test- Module 4

Module 5 Day 30 Building construction – Foundations; Bearing capacity of

Course Handout


soil

Day 31 Functions of foundations, Types - shallow and deep

Day 32 sketches of types of foundations

Day 33 Brick masonry – header and stretcher bond, English bonds –

Elevation and plan; Roofs – functions, types, roofing

materials

Day 34 Floors – functions, types; flooring materials ;Decorative

finishes – Plastering – Purpose, procedure; Paints and

Painting – Purpose, types, preparation of surfaces for

painting

Day 35 Powerpoint- types of brick masonry, floors, roofs, painting

Module 6 Day 36 Basic infrastructure and services - Elevators, escalators,

ramps

Day 37 air conditioning, sound proofing

Day 38 Tutorial 12- Basic infra structure and services

Day 39 Towers, Chimneys, water tanks

Day 40 Concept of intelligent buildings.

Day 41 Presentation by students - intelligent buildings

Day 42 Presentation by students - intelligent buildings

Course Handout


7.3 TUTORIALS

1. The following consecutive readings were taken with a level & four meter

leveling staff on a continuously sloping ground:

0.755,1.545,2.335,3.545,3.655, 0.525, 1.275, 2.650, 2.895, 3.565, 0.345,

1.525,1.850, 2.675, 3.775. The first reading on a BM whose reduced level is

200m from a page of level field book for continuously sloping ground. Find

the gradient between second & second last station (common interval is 20m).

2. Explain the functional requirements of industrial buildings.

3. Explain the role of civil engineer to the society.

4. Explain the general requirements of site and building for planning a residential

building.

5. What are the factors to be considered in the selection of site for a residential

building?

6. Explain in detail about the classification of buildings as per NBC.

7. With neat sketch explain the essential components of a residential building.

8. List out the various building components of your house.

(2 marks, ICE, Jan, 2016 - Regular) 9. Give the functions of any three building components.

(3 marks, ICE, Jan, 2016 - Regular) 10. Classify the types of buildings as per National Building Code of India.

(3 marks, ICE, Jan, 2016 - Regular) 11. Explain the relevance of Civil Engineering in the overall infrastructural

development of the country. (3 marks, BCE, Jan, 2016-Regular)

12. List out the types of building as per occupancy. Explain any two, each in about

five sentences. (6 marks, BCE, Jan, 2016-Regular)

13. Discuss the components of a building with a neat figure.

(6 marks, BCE, Jan, 2016-Regular) 14. Explain very briefly about the classification of buildings based on occupancy.

(3 marks, BCE, May, 2016-Regular) 15. Write a short note on various components of a residential building and their

functions.

(6 marks, BCE, May, 2016-Regular) 16. Write a note on the importance of civil engineering on infrastructural

development of India.

(6 marks, BCE, May, 2016-Regular)

Course Handout


7.4 ASSIGNMENTS

Assignment I

1. Students have to visit one industrial building related to their branch and submit

an assignment about the features of the particular building.

2. Assignment II

1. Write short notes on modern surveying instruments- electronic distance meter,

digital level, total station, GPS

Assignment III

1. Write about types of cement and its uses.

2. Discuss about painting (purpose, types and preparation of painting surface).

3. Write short notes on Towers, chimneys and water tanks.

4. Explain the concept of intelligent buildings.

Course Handout


8. PH110: ENGINEERING PHYSICS LAB

Course Handout



Course Handout


8.2 COURSE PLAN

Course Handout


8.3 LAB CYCLE

Course Handout


8.4 LAB QUESTIONS

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9. EE 110: ELECTRICAL ENGINEERING

WORKSHOP

Course Handout



Course Handout


9.2 COURSE PLAN

Course Handout


9.3 LAB CYCLE

Course Handout


9.4 LAB QUESTIONS

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