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Title: Verification of Some Network Theorems
1.
Superposition Theorem
2.
Thevenin’s Theorem
FIRST
EXPERIMENT
(Superposition
Theorem)
Aim:
To Verify Superposition theorem
Apparatus: (Same Apparatus For Both First and Second
Experiments)
1. Two DC Power Sources
2. Four Decade Resistance
Boxes
3. An AVO Meter
For
Circuit Diagram, See page 13 on your Electrical Lab Manual
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THEORY:
Superposition
theorem states that:
“In
a linear circuit with several sources the voltage and current responses in any
branch is the algebraic sum of the voltage and current responses due to each
source acting independently with all other sources replaced by their internal
impedance.”
Suppose
an electrical circuit having several branches and or loads and also several
source some being current source and some being voltage source. Then
Superposition theorem suggests that:
If
we find the branch responses (Voltage drop and Current through it) on a branch
due to only of those source by ignoring effect of all other sources or
replacing all other sources by their corresponding internal impedance , and
repeat the process for every source on the circuit. Then the Combined responses
(Voltage drop and Current through it) on a branch due to all the sources
combined is the algebraic sum of responses on the branches due to each
individual sources.
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If a number of voltage or current
source are acting simultanously in a linear network, the resultant current
in any branch is the algebraic sum of the currents that would be produced
in it, when each source acts alone replacing all other independent sources
by their internal resistances.
Circuit Diagram:
In a given figure apply
superposition theorem , let us first take the sources V1 alone at
first replacing V2 by short circuit
Here,
Next, removing V1 by
short circuit, let the circuit be energized by V2 only
Here,
As per superposition theorem,
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For
procedures, see your Electrical Laboratory Manual on page 14
SECOND
EXPERIMENT
(Thevenins
Theorem)
Apparatus:
(See in First Experiment above)
For
Circuit Diagram, See your Electrical Laboratory Manual on page 15
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THEORY:
In electrical circuit theory, Thevenin’s
theorem for linear electrical networks states that any combination of
voltage sources, current sources and resistors with two terminals is
electrically equivalent to a single voltage source V and a single series
resistor R. For single frequency AC systems, the theorem can also be
applied to general impedances, not just resistors. Any complex network can
be reduced to a Thevenin's equivalent circuit consist of a single voltage
source and series resistance connected to a load.
To calculate the equivalent circuit,
one needs a resistance and some voltage - two unknowns. Thus two equations
are needed. These two equations are usually obtained by using the following
steps, but any conditions one places on the terminals of the circuit should
also work:
1.
Calculate the
output voltage, VAB, when in open circuit condition (no load resistor -
meaning infinite resistance). This is VTh.
2.
Calculate the
output current, IAB, when the output terminals are short circuited (load
resistance is 0). RTh equals VTh divided by IAB.
The Thevenin-equivalent voltage is
the voltage at the output terminals of the original circuit. When
calculating a Thévenin-equivalent voltage, the voltage divider principle is
useful, by declaring one terminal to be Vout and the other terminal to
be at the ground point.
The Thevenin-equivalent resistance is the
resistance measured across points A and B "looking back" into the
circuit. It is important to first replace all voltage- and current-sources
with their internal resistances. For an ideal voltage source, this means
replace the voltage source with a short circuit. For an ideal current
source, this means replace the current source with an open circuit.
Resistance can then be calculated across the terminals using the formulae
for series and parallel circuits.
In
short the steps are,
•
Find
the Thevenin source voltage by removing the load resistor from the original
circuit and calculating voltage across the
open
connection points where the load resistor used to be.
•
Find
the Thevenin resistance by removing all power sources in the original circuit
(voltage sources shorted and current sources open) and calculating total
resistance between the open connection points.
•
Draw
the Thevenin equivalent circuit, with the Thevenin voltage source in series
with the Thevenin resistance. The load resistor re-attaches between the two
open points of the equivalent circuit.
•
Analyze
voltage and current for the load resistor following the rules for series
circuits.
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For Procedures, See
Page 16 on your electrical lab manual.
PRECAUTIONS:
For Precautions, See General Electrical Lab
Precautions
Answers
to Questions:
No Questions On This Experiment
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Stephen Djes is a passionate Graduate of Engineering from the University of Benin, and he is geared towards helping fellow engineering students in the great institution of UNIBEN to do better at academics.
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