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LECTURE #
Theveninโs Theorem is a network analysis
procedure meant to simplify the computations of a
complex network (with several sources and
resistances).
It does so by reducing a complex network to simple
equivalent circuit (Theveninโs Equivalent
Circuit) containing a Single Voltage Source in
series with a two Resistances.
Whereby:
The voltage source is the open circuit voltage
measured between terminals where its required
to determine the current
One of the resistors is the Theveninโs
equivalent resistance, measured between
terminals (where its required to compute
current) in a passive circuit
While the other resistance represents the load
resistance (connected between terminals where
its required to find current).
Theveninโ
s Theorem
Active Network
with linear
Sources and
Resistances
resistance R th
Equivalent Source, then its possible to determine the Load current, i.e.
current between terminals A & B
๐ธ ๐กhh โ๐h๐๐ฃ๐๐๐ ๐
โฒ ๐ ๐๐๐๐กh๐๐๐
๐h๐๐ฃ๐๐๐ ๐
โฒ ๐ ๐ธ๐๐ข๐๐ฃ๐๐๐๐๐กh ๐๐๐ข๐๐๐
Example # [Prove that I
1
=10A]
E
R 1 R 2
I 1 ?
E
R 1 R 2
A
B
R R 1 2
I L ? I L ?
๐ฌ = ๐๐ ๐ฝ ฮฉ^ ๐น^ ๐ = ๐ ฮฉ^ ๐^ = ๐ ฮฉ
E
A
B
E R 2
A
B
I 2 I ๐ฐ= ๐ฐ ๐
๐ (^) R 2
A
B
๐น ๐๐=
๐๐น ๐
๐ + ๐น ๐
๐ฌ ๐๐= ๐๐ ๐ฝ
๐น ๐๐= ๐. ๐๐๐ ฮฉ
A
B
๐ฐ ๐ณ=
๐ฌ ๐๐
๐น ๐๐+ ๐น๐ณ
=๐ฐ ๐
๐ฐ ๐ณ=
๐๐
๐. ๐๐๐ + ๐. ๐๐๐
= ๐๐ ๐จ
Example #
๐ท๐๐กh๐๐๐๐๐๐ ๐๐ข๐๐๐๐๐กh ๐กhh๐๐๐ข๐h ๐๐๐ ๐๐ ๐กh๐๐๐๐ ๐
2 ๐ข๐ ๐๐๐ ๐h๐๐ฃ๐๐๐๐
โฒ ๐ ๐h๐๐๐๐๐
๐ท๐๐กh๐๐๐๐๐๐ ๐๐ข๐๐๐๐๐กh ๐กhh๐๐๐ข๐h ๐๐๐ ๐๐ ๐กh๐๐๐๐ ๐
2 ๐ข๐ ๐๐๐ ๐h๐๐ฃ๐๐๐๐
โฒ ๐ ๐h๐๐๐๐๐
Example
V 3
=?
R 1
I A
E 1
R 3
R 2
R 4
This implies that any active network of linear sources and resistances can
be represented by a constant current source in parallel with a resistance.
Active Network
with linear
Sources and
Resistances
A current flowing in any portion (between any two terminals) of an active
network of linear sources and resistances can be determined through CDR
as the current from a constant current source in parallel with a resistance.
๐ฐ ๐บ๐ช
- referred to as Nortonโs equivalent resistance is the resistance measured between the
terminals A & B while all voltage sources are replaced by internal resistances or short
circuits and current sources by open circuit.
The constant current source is the short circuit current measured between the terminals
Nortonโs Equivalent Source
๐ฐ ๐จ๐ฉ= ๐ฐ ๐ณ=
๐ฐ ๐๐ โ ๐น๐ต
๐น ๐ต + ๐น ๐ณ
Example # 2
๐ท๐๐กh๐๐๐๐๐๐ ๐๐ข๐๐๐๐๐กh ๐กhh๐๐๐ข๐h ๐๐๐ ๐๐ ๐กh๐๐๐๐ ๐
2 ๐ข๐ ๐๐๐ ๐๐๐๐กh๐ ๐
โฒ ๐ ๐h๐๐๐๐๐
๐ท๐๐กh๐๐๐๐๐๐ ๐๐ข๐๐๐๐๐กh ๐กhh๐๐๐ข๐h ๐๐๐ ๐๐ ๐กh๐๐๐๐ ๐
2 ๐ข๐ ๐๐๐ ๐๐๐๐กh๐ ๐
โฒ ๐ ๐h๐๐๐๐๐
Example
R 1 R 4
R 3
R 2
E 1
V 4
=?
Example
V 4
=?
R 1
I A
E 1
R 3
R 2
R 4
๐ฐ ๐จ= ๐ ๐จ ๐^ = ๐ ฮฉ
