Download Thevenin, Norton and Tellegen Theorems - GATE Study

Thevenin, Norton and Tellegen Theorems GATE Study Material in PDF
In our study of Network Theorems, we come across certain important ones time and time
again. These free GATE notes will cover Thevenin, Norton, Tellegen Theorems. We will also
learn about Reciprocity Theorem. These GATE Study Material is designed to explain the
concepts of Thevenin’s Theorem, Norton’s Theorem, Reciprocity Theorem and Tellegen’s
Theorem.
You can download these GATE Study Notes in PDF. Useful for GATE EC, EE, BARC, BSNL,
DRDO, IES. But before you can start with Thevenin, Norton and Tellegen Theorems, you will
need to get familiar with other concepts first.
Recommended Reading –
Basic Network Theory Concepts
Source Transformation & Reciprocity Theorem
KCL and KVL in Electrical Networks
Nodal and Mesh Analysis
Voltage and Current Division, Star to Delta Conversion
Why do we need these Theorems?
i. Complex circuits could be analyzed using Ohm’s Law and Kirchhoff’s Law directly but
the calculations would be tedious.
ii. To handle complexity, some theorems have been developed to simplify the analysis
iii. In this article we will discuss four important network theorems
a. Thevenin’s theorem
b. Norton’s theorem
c. Reciprocity theorem
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d. Tellegen’s theorem
The rest of the theorems will be discussed in subsequent articles.
Thevenin’s Theorem
Any two terminal bilateral linear dc circuits can be replaced by an equivalent circuit
consisting of a voltage source and a series resistor.
Note:
i. This voltage is known as Thevenin’s voltage (or) open circuit voltage.
ii. The resistance is known as Thevenin’s resistance.
iii. Thevenin’s resistance is independent of input voltage.
Steps to be followed:
i. Remove the load and assume the voltage across load terminal is Voc.
ii. Use KCL and KVL to obtain the open circuit voltage Voc which is equal to VTh.
iii. To calculate RTh, replace all independent sources with their equivalent circuits i.e.
voltage source by Short circuit and current sources by open circuit.
iv. Do not disturb dependent sources present in the circuit.
Example 1:
Find the current through 10 Ω resistor using Thevenin’s theorem
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Solution:
We need to find current through 10Ω resistor so replace 10Ω by open circuit with Voc.
Apply nodal analysis we get
(Voc −10)
2
+
(Voc +12)
5
+0+
Voc −20
1
=0
5Voc − 50 + 2 Voc + 24 + 10Voc − 200 = 0
17Voc = 226
Voc = 13.3V
Procedure to find RTh
Replace all voltage sources by short circuit and current sources by open circuit then circuit
becomes
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1
∴R
Th
1
1
=2+5+1
10
R Th = 17 Ω
Then Thevenin’s circuit becomes
13.29
∴ I = 10
17
+10
= 1.26A
Example 2:
Find the Thevenin voltage and Thevenin resistance of the given circuit
Solution:
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Here there is no independent source hence VTh = 0V
So, the given circuit is a dead network which needs to be a separate source for energization.
i.e.
So given dead network acts like a resistor with R Th =
(V′ −3i)
6
+
V′
4
+i=0
5V ′ − 6i + 12i = 0
6i
V ′ = − 5 ------ (1)
And i = −I − − − − − (2)
(V′−V)
1
=I
∴ V ′ = V + i − − − − − (3)
From (1) and (2) and (3) we get
6i
−5 = V+I
6i
V=−5 −i=−
∴ R Th =
V
I
=
11
5
11i
5
=
11
5
I
Ω
Norton Theorem
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V
I
A linear active network consists of more number of sources and more elements can be
replaced by an equivalent circuit consisting of a current source in parallel with a resistance.
The current source being the short circuited current through the load and the resistance
being the internal resistance of source network looking through the open circuited load
terminals.
Note:
Always RTh = RN
Steps to be followed:
i. Short circuit load terminal and assume current through it is Isc.
ii. Compute the value if Isc using KCL and KVL i.e. IN = Isc.
iii. Find RNorton as calculated in RThevinin.
Example 3:
For the network find IN across a and b
Solution:
Short circuit the a and b we get
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Apply nodal analysis we get
0−10√2∠45°
−
(1+j)
5∠45° + Isc = 0
10√2
Isc = (1+j) ∠90° + 5∠45°
Isc =
10√2 ∠90°
√2 ∠45°
+ 5∠45° = 15∠45°
Note:
R Th =
VTh
IN
Reciprocity Theorem
In a network if we interchange the position of response and excitation then the ratio of
response to excitation is constant.
I
I
Then, VL = VS
S
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L
Example 4:
Find the value of I in the given network
Solution:
By reciprocity theorem
5
I
= − 30
10
I = - 15A
Tellegen’s Theorem:
In any network the algebraic sum of power at any given point is zero.
We can say that, Power delivered by some elements = Power absorb by the remaining
elements.
Note:
i. It depends on voltage and current product of an element but not on the type of element.
ii. While verifying Tellegen’s theorem do not disturb original network.
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Example 5:
Verify the Tellegen’s theorem for the given circuit.
Solution:
If current flows from + to – then treat it as power absorption
If current flow from – to + then treat it as power delivering
∴ P10V = V. I = 10 × 1 = 10 watt (Pabsorbed )
P2A = V. I = 10 × 2 = 20 watt (Pdelivered )
P10Ω = I2 . R = 1 × 10 = 10 watt (Pabsorbed )
∴ Pdelivered = Pabsorbed = 20 watt
Hence Tellegen’s theorem is verified.
Liked this article on Thevenin, Norton and Tellegen Theorems? Let us know in the
comments. You may also like some more articles in our series to help you ace your exam
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