Electrical Network in term of linear algebra

1. 1Anas Anwar

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
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3. APPLICATIONS OF SYSTEM OF
LINEAR EQUATIONS
ELECTRICAL SYSTEM ANALYSIS
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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.
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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.
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6. Basic Components Of
Electric Circuit
1. CURRENT
2. VOLTAGE
3. RESISTANCE
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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.
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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”.
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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.
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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.
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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)
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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
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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
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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.
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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.
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16. SOLUTION
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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

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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
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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
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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
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









2.3100
4.3010
2.0001
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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
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REFRENCES
•https://www.youtube.com/watch?v=tSJnqt
nsuHY
•https://www.youtube.com/watch?v=vQ6iEZ
NB45o
•https://web.iit.edu/sites/web/files/depart
ments/academic-
•affairs/Academic%20Resource%20Center/
pdfs/Kirchhoff_s_Circuit_Laws.pdf
• https://www.student-
circuit.com/learning/year2/electronic-
circuits/kirchhoffs-law-application-circuits-
analysis/
•https://www.slideshare.net/BadruzzanJhon
/application-of-linear-algebra-in-electrical-
circuit
For any queries you may contact at
mailto:anasanwersaeed@gmail.com
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