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Short Notes Circuit Theorems - Network Theory (Electric Circuits) - Electrical Engineering
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Page 2
Superposition
It states that, in any linear circuit containing multiple independent sources, the total current
through or voltage across an element can be determined by algebraically adding the voltage or
current due to each independent source acting alone with all other independent source set to
zero.
Source Transformation
It states that as independent voltage source
S
V in series with a resistance R is equivalent to
independent current source ?
Ss
I V / R in parallel with a resistance R.
Or
An independent current source
S
I in parallel with a resistance R is equivalent to a dependent
source
SS
V I R ? in series with a resistance R.
Thevenin’s Theorem
It states that any network composed of ideal voltage and current source, and of linear resistor,
may be represented by an equivalent circuit consisting of an ideal voltage source
TH
V in series
with an equivalent resistance
TH
R .
Methods to calculate thevein equivalent
The therein voltage ? ?
TH
V is equal to open circuit voltage across load terminals.
Therein resistance is input or equivalent resistance at open circuit terminals (load terminals) when
all independent source are set to zero (voltage sources replaced by short circuit & current source
by OC)
Case – 1 : Circuit with independent sources only
Page 3
Superposition
It states that, in any linear circuit containing multiple independent sources, the total current
through or voltage across an element can be determined by algebraically adding the voltage or
current due to each independent source acting alone with all other independent source set to
zero.
Source Transformation
It states that as independent voltage source
S
V in series with a resistance R is equivalent to
independent current source ?
Ss
I V / R in parallel with a resistance R.
Or
An independent current source
S
I in parallel with a resistance R is equivalent to a dependent
source
SS
V I R ? in series with a resistance R.
Thevenin’s Theorem
It states that any network composed of ideal voltage and current source, and of linear resistor,
may be represented by an equivalent circuit consisting of an ideal voltage source
TH
V in series
with an equivalent resistance
TH
R .
Methods to calculate thevein equivalent
The therein voltage ? ?
TH
V is equal to open circuit voltage across load terminals.
Therein resistance is input or equivalent resistance at open circuit terminals (load terminals) when
all independent source are set to zero (voltage sources replaced by short circuit & current source
by OC)
Case – 1 : Circuit with independent sources only
To calculate
TH
V , open circuit of RL
Using sources transformation
? ? ?
?
TH
2
V 24 12V
22
To calculate Rth
Short I & V sources & open 6mA source
? ?
? ? ? ? ?
th
R 1 2 1 1 2k
Page 4
Superposition
It states that, in any linear circuit containing multiple independent sources, the total current
through or voltage across an element can be determined by algebraically adding the voltage or
current due to each independent source acting alone with all other independent source set to
zero.
Source Transformation
It states that as independent voltage source
S
V in series with a resistance R is equivalent to
independent current source ?
Ss
I V / R in parallel with a resistance R.
Or
An independent current source
S
I in parallel with a resistance R is equivalent to a dependent
source
SS
V I R ? in series with a resistance R.
Thevenin’s Theorem
It states that any network composed of ideal voltage and current source, and of linear resistor,
may be represented by an equivalent circuit consisting of an ideal voltage source
TH
V in series
with an equivalent resistance
TH
R .
Methods to calculate thevein equivalent
The therein voltage ? ?
TH
V is equal to open circuit voltage across load terminals.
Therein resistance is input or equivalent resistance at open circuit terminals (load terminals) when
all independent source are set to zero (voltage sources replaced by short circuit & current source
by OC)
Case – 1 : Circuit with independent sources only
To calculate
TH
V , open circuit of RL
Using sources transformation
? ? ?
?
TH
2
V 24 12V
22
To calculate Rth
Short I & V sources & open 6mA source
? ?
? ? ? ? ?
th
R 1 2 1 1 2k
Case – 1 : Circuit with both dependent & independent sources
Methodology 1:
?
Th
V can be found in same way.
? For
TH
R set all independent sources to zero.
? Remove load & put a test source
test
V across its terminals, let current through test source is
test
I .
? ?
test
TH
test
Thevenin resistance ,
V
R
I
? This method is must if independent sources are absent.
Methodology 2:
?
TH
V is calculated in same way.
? For
TH
R short circuit load terminals & leave independent sources as it is
? Obtain
SC
I through load terminals.
?
TH OC SC
R V I ?
Norton’s Theorem
Any network composed ideal voltage & current sources, and of linear resistors, may be
represented by an equivalent circuit consisting of an ideal current source
N
I in parallel with an
equivalent resistance
N
R .
? ?
N TH
RR
? To calculate
N
I we short circuit load terminals & calculate short circuit current.
? Therein equivalent & Norton equivalent are dual of each other.
Page 5
Superposition
It states that, in any linear circuit containing multiple independent sources, the total current
through or voltage across an element can be determined by algebraically adding the voltage or
current due to each independent source acting alone with all other independent source set to
zero.
Source Transformation
It states that as independent voltage source
S
V in series with a resistance R is equivalent to
independent current source ?
Ss
I V / R in parallel with a resistance R.
Or
An independent current source
S
I in parallel with a resistance R is equivalent to a dependent
source
SS
V I R ? in series with a resistance R.
Thevenin’s Theorem
It states that any network composed of ideal voltage and current source, and of linear resistor,
may be represented by an equivalent circuit consisting of an ideal voltage source
TH
V in series
with an equivalent resistance
TH
R .
Methods to calculate thevein equivalent
The therein voltage ? ?
TH
V is equal to open circuit voltage across load terminals.
Therein resistance is input or equivalent resistance at open circuit terminals (load terminals) when
all independent source are set to zero (voltage sources replaced by short circuit & current source
by OC)
Case – 1 : Circuit with independent sources only
To calculate
TH
V , open circuit of RL
Using sources transformation
? ? ?
?
TH
2
V 24 12V
22
To calculate Rth
Short I & V sources & open 6mA source
? ?
? ? ? ? ?
th
R 1 2 1 1 2k
Case – 1 : Circuit with both dependent & independent sources
Methodology 1:
?
Th
V can be found in same way.
? For
TH
R set all independent sources to zero.
? Remove load & put a test source
test
V across its terminals, let current through test source is
test
I .
? ?
test
TH
test
Thevenin resistance ,
V
R
I
? This method is must if independent sources are absent.
Methodology 2:
?
TH
V is calculated in same way.
? For
TH
R short circuit load terminals & leave independent sources as it is
? Obtain
SC
I through load terminals.
?
TH OC SC
R V I ?
Norton’s Theorem
Any network composed ideal voltage & current sources, and of linear resistors, may be
represented by an equivalent circuit consisting of an ideal current source
N
I in parallel with an
equivalent resistance
N
R .
? ?
N TH
RR
? To calculate
N
I we short circuit load terminals & calculate short circuit current.
? Therein equivalent & Norton equivalent are dual of each other.
Maximum Power Transfer Theorem:
A load resistance
L
R will receive maximum power from a circuit when load resistance is equal to
Thevenin’s/ Norton’s resistance seen at load terminals.
?
L Th
RR
In case of AC circuit, this condition translates to
?
L
*
th
ZZ
? But if load is resistive in AC circuit then
?
L Th
RZ
?
For maximum power transfer
? ?
? ? ?
2
2
LL Th Th
R R X X
?
For maximum power transfer
L Th
X X 0 ??
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FAQs on Short Notes Circuit Theorems - Network Theory (Electric Circuits) - Electrical Engineering
| 1. What are circuit theorems? |  |
Ans. Circuit theorems are mathematical principles or rules that are used to analyze and solve electrical circuits. They provide a systematic approach to understanding the behavior and characteristics of circuits, allowing engineers and technicians to design and troubleshoot electrical systems effectively.
| 2. What is the importance of circuit theorems in electrical engineering? | |
Ans. Circuit theorems play a crucial role in electrical engineering as they provide a set of tools and techniques to simplify complex circuits and calculate various parameters such as voltage, current, power, and resistance. They enable engineers to analyze circuit performance, identify faults, optimize designs, and ensure the safe and efficient operation of electrical systems.
| 3. What are some commonly used circuit theorems? | |
Ans. Some commonly used circuit theorems include Ohm's Law, Kirchhoff's Laws (Kirchhoff's Current Law and Kirchhoff's Voltage Law), Thevenin's Theorem, Norton's Theorem, Superposition Theorem, Maximum Power Transfer Theorem, and Millman's Theorem. These theorems provide different approaches to solving circuit problems and offer valuable insights into circuit behavior.
| 4. How does Thevenin's Theorem simplify circuit analysis? | |
Ans. Thevenin's Theorem states that any linear electrical network with voltage and current sources can be replaced by an equivalent circuit containing a single voltage source and a single resistance connected in series. This theorem simplifies circuit analysis by reducing complex networks into simpler circuits and allows engineers to determine the behavior of a circuit at a specific load without having to analyze the entire original network.
| 5. How is the Maximum Power Transfer Theorem useful in practical applications? | |
Ans. The Maximum Power Transfer Theorem states that the maximum power transfer between a source and a load occurs when the load resistance is equal to the internal resistance of the source. This theorem is useful in practical applications because it helps engineers determine the optimal load resistance to extract the maximum power from a source. It is commonly applied in power transmission systems, audio amplifiers, and other electrical devices where power efficiency is crucial.
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