witter is a microblogging and social networking service owned by American company Twitter, Inc., on which users post and interact with messages known as "tweets". Registered users can post, like, and retweet tweets, while unregistered users only have a limited ability to read public tweets. Users interact with Twitter through browser or mobile frontend software, or programmatically via its APIs. Prior to April 2020, services were accessible via SMS.[9] Tweets were originally restricted to 140 characters, but the limit was doubled to 280 for non-CJK languages in November 2017.[10] Audio and video tweets remain limited to 140 seconds for most accounts. Twitter was created by Jack Dorsey, Noah Glass, Biz Stone, and Evan Williams in March 2006 and launched in July of that year. Twitter, Inc. is based in San Francisco, California and has more than 25 offices around the world.[11] By 2012, more than 100 million users posted 340 million tweets a day,[12] and the service handled an average of 1.6 billion search queries per day.[13][14][15] In 2013, it was one of the ten most-visited websites and has been described as "the SMS of the Internet".[16] By the start of 2019, Twitter had more than 330 million monthly active users.[17] In practice, the vast majority of tweets are written by a minority of users.[18][19] On April 25, 2022, the Twitter board of directors agreed to a $44 billion buyout by Elon Musk, the CEO of SpaceX and Tesla, potentially making it one of the biggest deals to turn a company private.[20][21] Musk said on July 8, 2022, that he was terminating the deal, claiming that the social media company had failed to provide information about fake accounts on the platform.[22] Twitter board chair Bret Taylor subsequently pledged to pursue legal action against Musk, launching a lawsuit against him in the Chancery Court of Delaware on July 12.[23] In early October, 2022, Musk reversed his position, again -- saying he would go ahead with the deal at the originally agreed $44 billion price.witter is a microblogging and social networking service owned by American company Twitter, Inc., on which users post and interact with messages known as "tweets". Registered users can post, like, and retweet tweets, while unregistered users only have a limited ability to read public tweets. Users interact with Twitter through browser or mobile frontend software, or programmatically via its APIs. Prior to April 2020, services were accessible via SMS.[9] Tweets were originally restricted to 140 characters, but the limit was doubled to 280 for non-CJK languages in November 2017.[10] Audio and video tweets remain limited to 140 seconds for most awitter is a microblogging and social networking service owned by American company Twitter, Inc., on which users post and interact with messages known as "tweets". Registered users can post, like, and retweet tweets, while unregistered users only have a lim

1. LINEAR CIRCUIT ANALYSIS (LCA )
Associate Professor Dr. Attiq Ahamd
BETE - 58 A, B and C

2. Personnel Information
Name A/Prof Dr. Attiq Ahmad
Bachelor MCS, Nust
Masters Technical University of Denmark (DTU)
PhD Nust
Area of Specialty Digital Signal /Image Processing
Published Papers 30 (15x ISI indexed, 15xConference )
PhD students 4
UG Projects 2

3. OBJECTIVE: This course is intended to provide you with a understanding of
Basic Engineering Circuit analysis
INSTRUCTOR: Dr Attiq Ahmad
E-mail: attiq@mcs.edu.pk
Office: EE Dept (207)
OFFICE HOURS: Monday – Wednesday : 11:00 AM – 12:30 AM (may contact on whatapp/email)
I encourage you to make appointments if these times conflict with
your schedule.
REFERENCE TEXT: As indicated in the slides
LECTURES: Monday, Tuesday, Wednesday and Thursday (Class or MS Teams !)
LABS: Prog will be given by concerned Instr (Lab Engr Amir)
WEB Local Server lease check it periodically, as all the assigned
homework, together with the homework solutions, handouts,
etc will be posted there.
Linear Cct Analysis – Fall 2021- 2022(Nov - Feb)
Department of Electrical Engineering, MCS, Nust

4. GRADING: Assignments : 5% Due at the beginning of class on due date.
Quizzes : 15% Quizzes will be given at random dates.
hourly Test 1 : 15% No make up tests.
hourly Tests 2 : 15% No make up tests.
Final Exam : 50% Comprehensive.
QUIZZES: Quizzes will be given at random dates throughout the semester. Some of them (most of
them) will be pop quizzes.
HOMEWORK: Working in groups (or individual under Covid-19) is encouraged. Homework will
be due one week after the assigned date. Assignments are to be done neatly , with all pages stapled
together. Late homework will be penalized with 20% of the grade for each day it is late.
TESTS: There will be one midterm examinations. There will be no make-up tests.
FINAL EXAM: Final examination will be held for 2 hrs. It will be a comprehensive exam, covering
entire course. No make up on ANY circumstance.
ACADEMIC DISHONESTY:Violations of academic dishonesty will be sanctioned. Violations of
academic integrity involve the use of any method or technique enabling a student to misrepresent
the quality and integrity of his or her own academic work or the work of a fellow student. Students
committing academic dishonesty will be reported to the appropriate college official and an F grade
for this course will be recorded on the student’s transcript. In cases where a student has an existing
record of academic dishonesty, a more severe enalty, e.g. involving suspension or dismissal from the
college, may be sought.
TENTATIVE OUTLINE: Time as per assimilation of students will be given for each chapter !

5. Linear Circuit Analysis
Pre-Requisites: Nil Contact Hrs: 3+3
Course Code: EE111 Schedule
Credits: 3+1
Course Objective:
This course is meant to give a good understanding of the fundamentals of electrical engineering. Starting from Ohm’s law,
the kirchoffs laws and basic analysis techniques are taught. Important laws /theorems of circuit analysis are explained for
passive circuit elements .
Course Outline: Weeks
1 Basic Circuits Analysis. Basic electrical quantities, their units and circuit elements. Ohms Law.
Power rating and temp coefficient.
2
2 Kirchoff's Laws. Kirchhoff voltage law and Kirchhoff current law, voltage and current divider circuits. Single loop
circuits, single Node pair circuits, Parallel and series combinations of resistances, We and Delta transformations,
circuits with dependent sources.
2
3 Analysis Techniques. Mesh Analysis, including dependent and independent sources; Concept of super-mesh: Nodal
analysis, including dependent and independent sources; Concept of super-node.
2- 3
4 Network Theorems.Superposition; Thevenien and Norton theorems; source transformation Maximum power
transfer.
2- 3
5 Capacitance and Inductance. Capacitors and Inductors as energy storing devices, Combinations of Capacitors and
Inductors, energy storage, RLC circuits with DC excitation in steady state.
2- 3
6 Basic RL and RC circuits. Source free RL circuits (covering exponential response), source free RC circuits. Natural
and forced response
2
7 The RLC Circuits parallel RLC Circuits, differential equations. Over/under/critically damped circuits. Series RLC
circuits.
2
Text /Ref Book: Fundamentals of Electrical Circuits by Charles K Alexander, Sadiku (ISBN 13978-0-07-110582)
Basic Engineering Circuit analysis by J. David Irwin. 7e
Circuit Analysis- Theory and Practice by Robbins & Miller. 4e

6. OBE

7. Introduction
• An electrical circuit is a system of interconnected components
• The electrical behavior of these components is described by a
few basic experimental laws.
• Much of circuit theory deals with problem solving and
numerical analysis.
• Technology is rapidly changing (have computers in our
homes, electronic control systems in our cars, cellular phones).
• A first step to understanding these technologies is electric
circuit theory.
• Circuit theory provides us with the knowledge of basic
principles that we need to understand the behavior of electronic
devices, circuits, and systems.
In this course/book, we will develop and explore its basic
ideas !

8. Before We Begin

9. EXAMPLE 2

10. EXAMPLE 3

11. EXAMPLE 4
!!! All These thing are routed through ELECTRIC CIRCUIT THEORY

12. Alexander-Sadiku
Fundamentals of Electric Circuits
Chapter 1
Basic Concepts
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

13. Basic Concepts - Chapter 1
1.1 Systems of Units.
1.2 Electric Charge.
1.3 Current.
1.4 Voltage.
1.5 Power and Energy.
1.6 Circuit Elements.

14. 1.1 System of Units (1)
Quantity Basic unit Symbol
Length meter m
Mass kilogram Kg
Time second s
Electric current ampere A
Thermodynamic
temperature
kelvin K
Luminous intensity candela cd
Six basic units
Other are derived units

15. 1.1 System of Units (2)
The derived units commonly used in electric circuit theory
Decimal multiples and
submultiples of SI units

16. A few non-SI units are still in use. For example, electric motors are
commonly rated in horsepower, and wires are frequently specified in AWG
sizes (American Wire Gage, Section 3.2).
The SI System of Units

17. Electrical values vary tremendously in size. -- from a few millionths of a
volt to several thousand volts.
To handle this large range, the power of ten notation is used.
Thus, 247 000 = 2.47x105. (The number 10 is called the base, and its
power is called the exponent.)
Power of Ten Notation

19. The number of digits in a number that carry actual information are
termed significant digits.
3.57 meters long wire - three significant digits. (The number of
significant digits includes the first estimated digit.)
If we say that it is 3.570 m - we have four significant digits.
When determining significant digits, zeros used to locate the decimal
point are not counted.

22. 1.2 Electric Charges
• Charge is an electrical property of
the atomic particles of which matter
consists, measured in coulombs (C).
• The charge e on one electron is
negative and equal in magnitude to
1.602  10-19 C which is called as
electronic charge.

23. Atomic Theory
• The basic structure
• It consists of a nucleus of
protons and neutrons
surrounded by a group of
orbiting electrons.
• Each atom has an equal number
of electrons and protons, and the
atom is electrically neutral.
• The nucleus, however, has a net
positive charge, since it consists
of positively charged protons and
uncharged neutrons.

24. Cont..
• Hydrogen atom,
• Copper atom has 29
electrons and 29 protons,
and 35 neutrons (6
Isotopes).
• Silicon, which is important
because of its use in
transistors, has 14 electrons,
14 protons, and 14 neutrons.
• Electrons orbit the nucleus in
spherical orbits called
shells.

25. Electrical Charge
• Is an intrinsic property of matter that manifests itself in the
form of forces — electrons repel other electrons but attract
protons.
• The charge on the electron is negative while that on the proton
is positive, Charge on electrons and protons are equal and
opposite.
• If the atom acquires additional electrons (leaving it with more
electrons than protons), we say that it (the atom) is negatively
charged;
• conversely, if it loses electrons and is left with fewer electrons
than protons, we say that it is positively charged.
The term “charge” in this sense denotes an imbalance
between the number of electrons and protons present in the
atom, denoted by the letter Q, and is measured in coulomb.

26. Couloumbs Law
• Charles Coulomb (1736–1806).
• where Q1 and Q2 are the charges in coulombs, r
is the center-to-center spacing between them in
meters, and k is const = 9x109.
• Force decreases inversely as the square of
distance;
• Electrons in outer orbits are less strongly
attracted to the nucleus than those in inner
orbits(tightly bound).
• Valence electrons are the least tightly bound
and will escape from their parent atoms if they
acquire sufficient energy.

27. Free Electrons
• The amount of energy required to escape depends
on the number of electrons in the valence shell.
• Few valence electrons -- small amount of additional
energy is needed.
• Valence electrons can gain sufficient energy from
heat alone. They simply wander from the valence
shell and are called free electrons.
• In the presence of this large number of free
electrons in copper (1023) at room temperature
becomes such a good conductor of electric current.
• On the other hand, if the valence shell is full (or
nearly full), valence electrons are much more tightly
bound. Such materials have few (if any) free
electrons.

28. Ions !
When a neutral atom gains or loses an
electron, it acquires a net electrical
charge. The charged atom is referred
to as an ion. If the atom loses an
electron, it is called a positive ion; if it
gains an electron, it is called a
negative ion.

29. Conductors, Insulators, and Semiconductors
• Materials through which charges move easily are termed
conductors (metals. silver, copper, gold, and aluminum)
• Copper is the most widely used, it is inexpensive and easily
formed into wire, making it suitable for a broad spectrum of
applications.
• Aluminum, although it is only about 60% as good a conductor
as copper, is also used, mainly in applications where light
weight is important, such as in overhead power transmission
lines.
• Silver and gold are too expensive for general use.

30. Insulators
• Materials that do not conduct (e.g., glass, porcelain,
plastic, rubber, and so on) are termed insulators.
• It is used to prevent the wires from touching and to
protect us from electric shock.
• Insulators do not conduct because they have full or
nearly full valence shells and thus their electrons are
tightly bound.

31. Semiconductors
• Silicon and germanium (plus a few other materials) have half-
filled valence shells and are Known as semiconductors.
• They have unique electrical properties that make them
important to the electronics industry.
• Silicon etc is used to make transistors, diodes, integrated
circuits, and other electronic devices.
• Semiconductors have made possible personal computers,
VCRs, portable CD players, calculators, and a host of other
electronic products.

32. The coulomb
• The unit of electrical charge is the coulomb (C), defined as the
charge carried by 6.24x1018 electrons.
• Thus, if an electrically neutral (i.e., uncharged) body has
6.24x1018 electrons removed, it will be left with a net positive
charge of 1 coulomb, i.e., Q = 1 C.
• Conversely, if an uncharged body has 6.24x1018 electrons
added, it will have a net negative charge of 1 coulomb, i.e., Q
= 1 C.
• If 6.24x1018 electrons pass through a wire, we say that
the charge that passed through the wire is 1 C.

34. 1.3 Current (1)
• Electric current i = dq/dt. The unit
of ampere can be derived as 1 A =
1C/s.
• A direct current (dc) is a current
that remains constant with time.
• An alternating current (ac) is a
current that varies sinusoidally with
time. (reverse direction)

35. Current (2)
• The electrons move randomly throughout the material. The
movement of charge/electron is called an electric current.
• The more electrons per second that pass through the
circuit, the greater is the current.
• Thus, current is the rate of flow (or rate of movement) of
charge.

36. 1.3 Current (3)
• The direction of current flow
Positive ions Negative ions

37. 1.3 Current (3)
Example 1
A conductor has a constant current of
5 A.
How many electrons pass a fixed point
on the conductor in one minute?

38. 1.3 Current (4)
Solution
Total no. of charges pass in 1 min is given by
5 A = (5 C/s)(60 s/min) = 300 C/min
Total no. of electronics pass in 1 min is given
min
electrons/
10
87
.
1
C/electron
10
602
.
1
C/min
300 21
19
x
x



39. Ampere
• Since charge is measured in coulombs, its rate of flow is
coulombs per second.
• In the SI system, one coulomb per second is defined as one
ampere (commonly abbreviated A).
• From this, we get that one ampere is the current in a circuit
when one coulomb of charge passes a given point in one
second

40. Voltage
• When charges are detached
from one body and transferred
to another, a potential
difference or voltage results
between them.
• The voltage is entirely due to
the separation of positive and
negative charges.
• Hundreds of millions of volts
are created in this way. (This
is what causes the air to break
down and a lightning
discharge to occur).

41. Potential Energy
• The concept of voltage is tied into the concept of potential
energy.
• In mechanics, potential energy is the energy that a body
possesses because of its position.
• In a similar fashion, work is required to move positive and
negative charges apart. This gives them potential energy.

42. 1.4 Voltage (1)
• Voltage (or potential difference) is the energy required to
move a unit charge through an element, measured in volts
(V).
• Mathematically, (volt)
– w is energy in joules (J) and q is charge in coulomb (C).
• Electric voltage, vab, is always across the circuit element or
between two points in a circuit.
– vab > 0 means the potential of a is higher than potential of b.
– vab < 0 means the potential of a is lower than potential of b.
dq
dw
vab /

By definition, the voltage between two points is one volt if it
requires one joule of energy to move one coulomb of charge
from one point to the other.

43. • Note carefully that voltage is defined between points.
• For the case of the battery, for example, voltage appears
between its terminals.
• Thus, voltage does not exist at a point by itself; it is always
determined with respect to some other point. (For this reason,
voltage is also called potential difference. We often use the
terms interchangeably.).
• Working of Btys …., separated by chemical/mechanican means
in Bty/Gen.

44. 1.5 Power and Energy (1)
• Power is the time rate of expending or absorbing
energy, measured in watts (W).
• Mathematical expression: vi
dt
dq
dq
dw
dt
dw
p 



i
+
–
v
i
+
–
v
Passive sign convention
P = +vi p = –vi
absorbing power supplying power

45. 1.5 Power and Energy (2)
• The law of conservation of energy
  0
p
• Energy is the capacity to do work, measured
in joules (J).
• Mathematical expression  


t
t
t
t
vidt
pdt
w
0 0

46. 1.6 Circuit Elements (1)
Active Elements Passive Elements
Independent
sources
Dependant
sources
• A dependent source is an active
element in which the source quantity
is controlled by another voltage or
current.
• They have four different types: VCVS,
CCVS, VCCS, CCCS. Keep in minds the
signs of dependent sources.

47. 1.6 Circuit Elements (2)
Example 2
Obtain the voltage v in the branch shown in Figure 2.1.1P for i2 = 1A.
Figure 2.1.1P

48. 1.6 Circuit Elements (3)
Solution
Voltage v is the sum of the current-independent
10-V source and the current-dependent voltage
source vx.
Note that the factor 15 multiplying the control
current carries the units Ω.
Therefore, v = 10 + vx = 10 + 15(1) = 25 V

49. Practical DC Voltage
Sources
• Batteries
– Batteries are the most common dc source. They are made in a variety
of shapes, sizes, and ratings.
– Capable of delivering only a few microamps to large automotive
batteries capable of delivering hundreds of amps.
• Primary and Secondary Batteries
– Some types of batteries, can be “recharged.” Such batteries
are called secondary batteries.
– Other types, called primary batteries, cannot be recharged.
– A familiar example of a secondary battery is the automobile
battery.

50. Cells in Series and Parallel

51. Measuring Voltage and
Current

53. How to Measure Current !

54. PROBLEM 2

55. Resistance of Conductors
• The resistance of a material is dependent upon
several factors:
– Type of material
– Length of the conductor
– Cross-sectional area
– Temperature
The resistance of a conductor is dependent upon the type of
material.

58. Conductance
• Conductance, G, is defined as the measure of a
material’s ability to allow the flow of charge and is
assigned the SI unit the siemens (S).
• A large conductance indicates that a material is able
to conduct current well.
• Mathematically, conductance is defined as the
reciprocal of resistanc

59. Example