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Circuit Theorem

The document explains key electrical engineering concepts including Superposition, Source Transformation, Thevenin's Theorem, Norton’s Theorem, and the Maximum Power Transfer Theorem. It details methods for calculating Thevenin and Norton equivalents, emphasizing the importance of independent and dependent sources. The document also outlines conditions for maximum power transfer in both DC and AC circuits.

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6 views5 pages

Circuit Theorem

The document explains key electrical engineering concepts including Superposition, Source Transformation, Thevenin's Theorem, Norton’s Theorem, and the Maximum Power Transfer Theorem. It details methods for calculating Thevenin and Norton equivalents, emphasizing the importance of independent and dependent sources. The document also outlines conditions for maximum power transfer in both DC and AC circuits.

Uploaded by

21bee539
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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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 VS in series with a resistance R is equivalent to
independent current source IS  Vs / R in parallel with a resistance R.
Or
An independent current source IS in parallel with a resistance R is equivalent to a dependent
source VS  ISR 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 VTH in series
with an equivalent resistance R TH .

Methods to calculate thevein equivalent


The therein voltage  VTH  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 VTH , open circuit of RL

Using sources transformation

2
VTH   24  12V
22

To calculate Rth
Short I & V sources & open 6mA source

R th  1  2 1  1  2k
Case – 1 : Circuit with both dependent & independent sources

Methodology 1:
 VTh can be found in same way.
 For R TH set all independent sources to zero.
 Remove load & put a test source Vtest across its terminals, let current through test source is Itest .
Vtest
 Thevenin resistance , R TH 
Itest
 This method is must if independent sources are absent.

Methodology 2:
 VTH is calculated in same way.
 For R TH short circuit load terminals & leave independent sources as it is
 Obtain ISC through load terminals.
 R TH  VOC ISC

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 IN in parallel with an
equivalent resistance R N .

 RN  R TH
 To calculate IN 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 RL will receive maximum power from a circuit when load resistance is equal to
Thevenin’s/ Norton’s resistance seen at load terminals.
RL  R Th
In case of AC circuit, this condition translates to
ZL  Z*th
 But if load is resistive in AC circuit then

RL  Z Th


For maximum power transfer

2
RL  R2Th   XL  X Th 


For maximum power transfer

XL  XTh  0

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