Network Theorems for network solving and design

Network Theorems

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Network Theorems-1Network Theorems-1
Subodh Kumar SinghalSubodh Kumar Singhal

2. 14-09-24 04:06 AM Network Theorems-1 2
Thought of the DAY
Every man has faults.
It all depends on whether
he has
enough good qualities
to counterbalance them.

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Topics to be DiscussedTopics to be Discussed
•Network Theorems
-- their importance.
•Superposition Theorem.
•Linear Dependent Source.
• Thevenin’s Theorem.
•Problems.

4. 14-09-24 04:06 AM Network Theorems-1 4
Network Theorems
•Some special techniques, known as
network theorems and network
reduction methods, have been
developed.
•These drastically reduce the labour
needed to solve a network.
•These provide simple conclusions and
good insight into the problems.

5. 14-09-24 04:06 AM Network Theorems-1 5
Network Theorems
•The Superposition Theorem.
•Thevenin’s Theorem.
•Norton’s Theorem.
•Maximum Power Transfer
Theorem.
•Tellegen’s Theorem

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Superposition Theorem
•In a linear network, containing more than one
source (current and/or emf) (including
dependent sources),
• the resultant current (or voltage) in an element
may be found by considering one source at a
time,
• and all other sources made inoperative, that is
replaced ‘temporarily' by their internal
resistances;
• followed by adding the current (or voltages)
due to the individual sources.

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Linear Dependent Source
•It is a source whose output current or voltage
is proportional only to the first power of some
current or voltage variable in the network or
to the sum of such quantities.
•Examples :
linear. not is 6.0
6.0 but,
linear, is166.0
21
2
1
21
viv
oriv
viv
s
s
s




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Application
•Problem : Consider two 1-V batteries in
series with a 1-Ω resistor. Let us apply
the principle of superposition, and find
the power delivered by both the
batteries.
•Solutions : Power delivered by only one
source working at time is
P
1 = 1 W

9. 14-09-24 04:06 AM Network Theorems-1 9
•Therefore, the power delivered by
both the sources,
P = 2P
1 = 2 W
•The above answer is obviously
wrong, because it is a wrong
application of
the superposition theorem.

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Problem
1.Find the current I in the network given, using
the superposition theorem.

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Solution :
A0.375





4.0
15.0
3.01.0
3.05.0
1I

12. 14-09-24 04:06 AM Network Theorems-1 12
A0.175
A0.2






21
3
2
I
3.01.0
1080
II
I

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Problem
2.Using superposition theorem, find
current i
x
in the network given.

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Solution :
A05.0
15050
10
1 

i

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A30
15050
150
40
2


i

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A30
15050
50
120
3


i

17. 14-09-24 04:06 AM Network Theorems-1 17
A0.05


303005.0
321
iiii
x

18. 14-09-24 04:06 AM Network Theorems-1 18
Thevenin’s Theorem
•It was first proposed by a French
telegraph engineer, M.L. Thevenin in 1883.

•There also exists an earlier statement of
the theorem credited to Helmholtz.
•Hence it is also known as Helmholtz-
Thevenin Theorem.
•It is useful when we wish to find the
response only in a single resistance in a
big network.

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Thevenin’s Theorem
•Any two terminals AB of a network
composed of linear passive and
active elements may by replaced by
a simple equivalent circuit
consisting of
1.an equivalent voltage source V
oc,
,

and

2.an equivalent resistance R
thin series.

20. 14-09-24 04:06 AM Network Theorems-1 20
• The voltage V
oc
is equal to the
potential difference between
the two terminals AB caused by
the active network with no
external resistance connected
to these terminals.

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• The series resistance R
th
is the
equivalent resistance looking
back into the network at the
terminals AB with all the
sources within the network
made inactive, or dead.

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Problem
•Using Thevenin’s theorem, find the
current and voltage in the 2-Ω resistor
connected across points A and B in the
network given.

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Solution
V10


IV
IorI
V
oc
AB
212
A1)22(812
current, thefindFirst
. find then and
resistor, -2 theRemove

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


 1
22
22
thR

25. 14-09-24 04:06 AM Network Theorems-1 25
V6.67


12
2
10
LV

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Problem
•Using Thevenin’s Theorem, find the
current in the ammeter A of resistance
1.5 Ω connected in an unbalanced
Wheatstone bridge shown.

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Solution :

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V6







65.1475.0
A5.1
62
12
andA75.0
412
12
2
1
BDADABoc
VVVV
I
I

30. 14-09-24 04:06 AM Network Theorems-1 30
Ans. -1 A

31. 14-09-24 04:06 AM Network Theorems-1 31
ReviewReview
•Network Theorems
-- their importance.
•Superposition Theorem.
•Linear Dependent Source.
• Thevenin’s Theorem.
•Problems.

32. 14-09-24 04:06 AM Network Theorems-1 32
In the Next ClassIn the Next Class
•Norton’s Theorem.
•Maximum Power Transfer
Theorem.
•Problems.