Verification Of Norton
Theorem And
Thevenin’s Theorem
Network Theory
Group no.- 07
Presented By:
Joydeep Das- 11500321107
INDEX
02
01
03
SOME EXAMPLES OF
NORTON’S THEOREM
NORTON’S THEOREM
INTRODUCTION
04
THEVENIN’S THEOREM
05
SOME EXAMPLES OF
THEVENIN’S THEOREM
01
Introduction
Thevenin’s and Norton's resistances are equal. Thevenin’s
voltage is equal to Norton's current times Norton resistance.
Norton current is equal to Thevenin voltage divided by Thevenin
resistance.
02 Norton Theorem
Norton's theorem is an analytical method used to
change a complex circuit into a simple equivalent
circuit consisting of a single resistance in parallel with a
current source
Norton's Theorem states that “Any linear circuit
containing several energy sources and resistances can be
replaced by a single Constant Current generator in parallel
with a Single Resistor“.
EXAMPLES
03
Consider the circuit.
To find the Norton's equivalent of the above circuit we firstly have
to remove the center 40Ω load resistor and short out the
terminals A and B to give us the following circuit.
When the terminals A and B are shorted together the
two resistors are connected in parallel across their two
respective voltage sources and the currents flowing
through each resistor as well as the total short circuit
current can now be calculated as:
with A-B Shorted Out
If we short-out the two voltage sources and open circuit
terminals A and B, the two resistors are now effectively
connected together in parallel. The value of the internal
resistor Rs is found by calculating the total resistance at the
terminals A and B giving us the following circuit.
Find the Equivalent Resistance (Rs)
Having found both the short circuit current, Is and equivalent internal resistance, Rs this then gives
us the following Norton's equivalent circuit.
Norton's equivalent circuit:
Ok, so far so good, but we now have to solve with
the original 40Ω load resistor connected across
terminals A and B as shown below.
Again, the two resistors are connected in parallel across the terminals A and B which gives us a total
resistance of:
The voltage across the terminals A and B with the load resistor connected is given as:
Then the current flowing in the 40Ω load resistor can be
found as:
Once again and using Norton's theorem, the value of
current for I3 is still calculated as 0.286 amps, which we
found using Kirchhoff´s circuit law
04
Thevenin’s Theorem
Thevenin theorem is an analytical method used to
change a complex circuit into a simple equivalent
circuit consisting of a single resistance in series with a
source voltage
Thevenin's Theorem states that “Any linear circuit
containing several voltages and resistances can be replaced
by just one single voltage in series with a single resistance
connected across the load“.
Thevenin's equivalent circuit:
As far as the load resistor RL is concerned, any complex “one-port” network consisting
of multiple resistive circuit elements and energy sources can be replaced by one single
equivalent resistance Rs and one single equivalent voltage Vs. Rs is the source
resistance value looking back into the circuit and Vs is the open circuit voltage at the
terminals.
You can obtain the Thevenin equivalent circuit by
applying the following sequential steps:
•
•
Find the Thevenin source voltage by removing
the load resistor from the original circuit and
calculating the 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
EXAMPLES:
Step 1: For the analysis of the above circuit using Thevenin’s theorem, firstly remove the load resistance at the center, in
this case, 40 Ω.
Step 2: Remove the voltage sources’ internal resistance by shorting all the voltage sources connected to the circuit, i.e. v =
0. If current sources are present in the circuit, then remove the internal resistance by open circuiting the sources. This step
is done to have an ideal voltage source or an ideal current source for the analysis.
Step 3: Find the equivalent resistance. In the example, the equivalent resistance of the circuit is calculated as follows:
With the load resistance removed and the voltage sources shorted, the equivalent
resistance of the circuit is calculated as follows:
The resistor 10 Ω is parallel to 20 Ω, therefore the equivalent resistance of the circuit is:
Step 4: Find the equivalent voltage.
To calculate the equivalent voltage, reconnect the
voltage sources back into the circuit. Vs = VAB, therefore
the current flowing around the loop is calculated as
follows:
The calculated current is common to both resistors, so the voltage drop across the resistors can be
calculated as follows:
VAB = 20 – (20 Ω x 0.33 A) = 13.33 V
or,
VAB = 10 + (10 Ω x 0.33 A) = 13.33 V
The voltage drop across both resistors is the same.
Step 5: Draw the Thevenin’s equivalent circuit. The Thevenin’s equivalent circuit consists of a series resistance of 6.67
Ω and a voltage source of 13.33 V.
The current flowing in the circuit is calculated using the formula below:
Thevenin’s theorem can be applied to both AC and DC circuits. But it should be noted that
this method can only be applied to AC circuits consisting of linear elements like resistors,
inductors, capacitors. Like Thevenin’s equivalent resistance, Thevenin’s equivalent
impedance is obtained by replacing all voltage sources with their internal impedances.
Example: If I = 33∠ -13o A, find the Thevenin’s equivalent circuit to the left of terminals x-y in
the network of figure 1.
Solution:
Let us first find the equivalent impedance across the current source. However, assuming the equivalent admittance to be Yeq, we find that
where Y1, Y2, Y3 and Y4 is the branch admittance of each branch.
Obviously,
Then,
and
To find Zin(= ZTh), the current source is deactivated and by inspection it is observed that
Figure 2 represents the Thevenin’s equivalent circuit where
References
 https://www.electronicstutorials.ws/dccircuits/dcp_8.html#:~:text=Nortons%20Theorem%20states%20that
%20%E2%80%9CAny,parallel%20with%20a%20Single%20Resistor%E2%80%9C.
 https://courses.engr.illinois.edu/ece110/sp2021/content/coursenotes/files/?Theveni
nAndNortonEquivalents
 https://practicalee.com/theveninequivalent/#:~:text=Steps%20to%20Find%20the%20Thevenin,to%20calculate%20t
he%20equivalent%20circuit.&text=Combine%20impedances%20using%20parallel
%20and,Thevenin%20and%20Norton%20Equivalent%20Impedance.
 https://www.differencebetween.com/difference-between-thevenin-and-vsnorton/#:~:text=What%20is%20the%20difference%20between,in%20parallel%20wi
th%20the%20source.
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