1. The document discusses the application of linear algebra in electrical network analysis. Kirchhoff's laws are used to write systems of linear equations relating the voltages and currents in a sample circuit.
2. The linear equations are represented using matrices and augmented matrices. Gaussian elimination is applied to solve for the unknown currents.
3. The currents are calculated to be I1 = 0.2 A, I2 = 3.4 A, and I3 = 3.2 A. Linear algebra allows the mathematical relationships in circuits to be modeled and solved efficiently.
Kirchhoff's Laws
Kirchhoff's laws quantify how current flows through a circuit and how voltage varies around a loop in a circuit
There are two laws
Kirchhoff’s Current Law (KCL) or First Law
Kirchhoff’s Voltage Law (KVL) or Second Law
Kirchhoff’s Current Law (KCL) or First Law
The total current entering a junction or a node is equal to the charge leaving the node as no charge is lost
Kirchhoff’s Voltage Law (KVL) or Second Law
According to Kirchhoff’s Voltage Law,
The voltage around ya loop equals to the sum of every voltage drop in the same loop for any closed network and also equals to zero.
Put differently, the algebraic sum of every voltage in the loop has to be equal to zero and this property of Kirchhoff’s law is called as conservation of energ.
Superposition Principle in Electric Circuit Fundamentals and Electrical Engin...Electrical Slides
Superposition principle is an important theorem in Electric Circuit fundamentals, It involves the calculation of current and voltage contributions separately from all sources in any circuit and then to sum up all these values for calculating overall voltage and current effects on any resistor or component. Superposition theorem is an important theorem which relieves problem of solving complex simultaneous problems. While, apply principle to any circuit, current sources are made open, whereas voltage sources are suppressed to short circuit.
Kirchhoff's Laws
Kirchhoff's laws quantify how current flows through a circuit and how voltage varies around a loop in a circuit
There are two laws
Kirchhoff’s Current Law (KCL) or First Law
Kirchhoff’s Voltage Law (KVL) or Second Law
Kirchhoff’s Current Law (KCL) or First Law
The total current entering a junction or a node is equal to the charge leaving the node as no charge is lost
Kirchhoff’s Voltage Law (KVL) or Second Law
According to Kirchhoff’s Voltage Law,
The voltage around ya loop equals to the sum of every voltage drop in the same loop for any closed network and also equals to zero.
Put differently, the algebraic sum of every voltage in the loop has to be equal to zero and this property of Kirchhoff’s law is called as conservation of energ.
Superposition Principle in Electric Circuit Fundamentals and Electrical Engin...Electrical Slides
Superposition principle is an important theorem in Electric Circuit fundamentals, It involves the calculation of current and voltage contributions separately from all sources in any circuit and then to sum up all these values for calculating overall voltage and current effects on any resistor or component. Superposition theorem is an important theorem which relieves problem of solving complex simultaneous problems. While, apply principle to any circuit, current sources are made open, whereas voltage sources are suppressed to short circuit.
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Electrical Engineering is the Branch of Engineering. Electrical Engineering field requires an understanding of core areas including Thermal and Hydraulics Prime Movers, Analog Electronic Circuits, Network Analysis and Synthesis, DC Machines and Transformers, Digital Electronic Circuits, Fundamentals of Power Electronics, Control System Engineering, Engineering Electromagnetics, Microprocessor and Microcontroller. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus.
This is a ppt of a college project of the topic kvl and kcl ..do read this..i have such interest in science projects and do maake aa lot of money by doing freelancing in embedded system so make sure to check this ppt for more updtes
Application of Linear Algebra in Electrical CircuitBadruzzman Jhon
Perhaps one of the most apparent uses of linear algebra is that which is used in
Electrical Engineering. As most students of mathematics have encountered, when the
subject of systems of equations is introduced, math class is temporarily converted into a
crash course in electrical components. There, the resistor, voltage source and capacitor
take the stage as well as their accompanying language consisting of Kirchoff and Ohm.
With the basic concepts down, math class is resumed and students can look forward to
playing with n number of equations with n number of unknowns. To solve for the
currents and voltages, students can use simplification and substitutions, but with many
equations, this task quickly becomes very time consuming and tedious.
However, using Gaussian Elimination along with computers, engineers are able to
efficiently calculate unknown values of extremely large and complex systems without
performing hundreds of calculations and exhaustive bookkeeping of values
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
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When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
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using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
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2. 2
NAME # MUHAMMAD ANAS ANWAR
Roll NO # 19CH44
DEPARTMENT # CHEMICAL
ENGINEERING
TOPIC # APPLCATIONS OF LINEAR
ALGEBRA
SUBMITTED TO # SIR MANSOOR ALI
BHAGAT
DATE # 7TH OF JLUY.2020
SUBJECT # LAAG
Anas Anwar
2
4. ELECTRICAL
NETWORK
An electrical network is
nothing but just a combination
of transistors, capacitors,
resistors and other electrical
parameters along with some
logic gates (Junction or Node).
Each electrical parameter has
its own specifications through
which we get to know about the
components of such electrical
parameter.
4
Anas Anwar
5. ELECTRICAL SYSTEM ANALYSIS
Electrical Network Analysis is a
procedure by which we can
compute distinctive electrical
components of an electric circuit
like voltage, current, resistance ,
impedance, reactance, inductance,
capacitance, frequency, electric
power, electrical energy and other
electric parameters.
5
Anas Anwar
7. CURRENT
The continuous flow of
electrons in an electric
circuit is called Current, In
other words we can add
that the movement of
charges from one place to
another is called Current.
It is represented by “I”
and it’s unit is Ampere.
7
Anas Anwar
8. RESISTANCE
Resistance is produced due to
the resistors injected in the
electric network . Resistance
is a measure of the opposition
to current flow in an electrical
circuit. Simply, resistance is
the property which controls
the variability in voltage of an
electric path. It is measured
in ohms, which is represented
as “Ω”.
8
Anas Anwar
9. VOLTAGE
Voltage is a difference in
electric potential that
makes electrons flow. It is
measured in volts and is
represented by “V”.
Greater the voltage will
increase in the flow of
current and vice versa.
9
Anas Anwar
10. OHM’S
LAW
In 1876 George Simon Ohm prepared
a relationship between potential
difference (V) and electric current
(I).
He stated that;
Potential difference (V) applied to a
conductor is directly proportional to
the amount of electric current (I)
passing through it.
V = IR
R is the constant , it is the
resistance of the conductor.
10
Anas Anwar
11. KIRCHHOFF’S LAWS
Kirchhoff’s laws govern the conservation of charge
and energy in electrical circuits.
There are two basic laws of Kirchhoff :
1. Kirchhoff’s Current Law(KCL)
2. Kirchhoff’s Voltage Law(KVL)
11
Anas Anwar
12. 12
KIRCHHOFF’S FIRST LAW
KIRCHHOFF’S CURRENT LAW (KCL):
It states that
“current flowing into a node (or a junction) must be equal to
current flowing out of it. This is a consequence of charge
conservation”.
Current flow into = Current flow out of
the node the node
Anas Anwar
12
13. 13
KIRCHHOFF’S SECOND LAW
KIRCHOFFS’S VOLTAGE LAW (KVL):
It states that
“The sum of all voltages around any closed loop in any circuit
must be equal to zero”.
In any closed loop;
(voltage gain) – (voltage drop) = 0
Anas Anwar
13
14. USES OF
LINEAR
ALGEBRA IN
ELECTRIC
NETWORK:
Linear Algebra is used for
exploration of electric circuit. We
can organize and simplify
mathematical calculations related
to current, voltage and resistance
of an electric circuit via using
Matrices and Linear Algebra.
Although electric circuits with
linear equations can be described
by using Gauss Elimination method
and Gauss-Jordan Elimination
method.
14
Anas Anwar
15. Problem# In the given
figure the values of
voltages and
resistances are given.
Compute the values of
current i.e. I1, I2 and
I3.
15
Anas Anwar
16. SOLUTION
16
Firstly, To calculate the current
passing through this electric network,
we must have to know the paths of
the flowing current
Here we apply Kirchhoff’s first law
which says that
Current flow inside junction =
current flow outside junction
For Junction A :
I1 + I3 = I2
For Junction B :
I2 = I1 + I3
Regret one of the above equation as
both are finely same,
I1+I3=I2----- ( equation 1) Anas Anwar
17. 17
I1 + I3 = I2 ( from first law)
OHM’S LAW
Volts drop = I.R
Now, If we talk about Kirchhoff’s Second
law that is Kirchhoff’s Voltage Law
For any loop;
(volt. Gain) – (volt. Drop) = 0
Here are two loops in the figure,
For loop 1:
(15) – (2I1 + 4I2 + 5I1) =0
15 – 7I1 -4I2 = 0 -----
For loop 2:
20-4I2 -2I3= 0 -------
2I1
4I2
5I1
4I2
2I3
Anas Anwar
18. 18
System of linear equations which I1 + I3 -I2 = 0
are obtained by Kirchhoff’s laws 7I1 +4I2 = 15
4I2 +2I3= 20
Now convert it into matrix form
=
After that convert into augmented matrix
20240
15047
0111
3
2
1
I
I
I
20
15
0
240
047
111
Anas Anwar
19. Reduced Echelon form of
augmented matrix is,
So we can simply conclude
that
I1 =0.2 A
I2=3.4 A
I3 =3.2 A
19
2.3100
4.3010
2.0001
Anas Anwar
20. 20
SHORLTLY WE CAN CONCLUDE WHOLE
PROCESS IN THREE STEPS
Kirchhoff’s 1st Law
Kirchhoff’s 2nd Law
I1 + I3 -I2 = 0
7I1 +4I2 = 15
. 4I2 +2I3= 20
Solve
I1 =0.2 A
I2=3.4 A
I3 =3.2 A
Electrical Network
System of Linear
Equations
Required Values of
current
Anas Anwar