Subsitution Theorem for AC Network

1. CIRCUIT THEORY
SUBSITUTION THEOREM
SYED HASAN SAEED
Monday, August 05, 2019 1Syed Hasan Saeed

2. REFERENCE BOOKS
• Introductory Circuit Analysis, Robert L. Boylested, Pearson Education,
Prentice Hall.
• Networks And Systems, Ashfaq Husain, Khanna Book Publishing Co (P)
Ltd. Delhi.
• Networks And Systems, A Sudhakr, Shyammohan S Palli, Tata McGraw
Hill, New Delhi.
• Network Analysis, M.E. Van Valkenburg, PHI Learning Private limited,
New Delhi.
• Circuit Analysis Principle and Applications, Allan H. Robbins &Wilhelm
C. Miller, DELMAR CENGAGE Learning, Indian Reprint.
Monday, August 05, 2019 syed hasan saeed 2

3. SUBSITUTION THEOREM
STATEMENT: This theorem states that any branch in a network can be replaced
or substituted by an independent voltage source without affecting the current
through that branch or by an independent current source without affecting the
voltage across that branch.
Monday, August 05, 2019 3Syed Hasan Saeed
a
b
Vab
Iab
Z
Iab
Vab
a
b
IabVab
a
b
Fig.1

4. EXAMPLE: Replace the impedance Zab by an independent source by
another branch.
Monday, August 05, 2019 Syed Hasan Saeed 4
SUBSITUTION THEOREM
5 ohm
-j2 ohm
6 ohm j8 ohm
5 ohm
j4 ohm
4 ohm
+
-
V0100 0

Fig.2
a
b

5. Monday, August 05, 2019 Syed Hasan Saeed 5
V1.3218.4(5)1.323.68RIV
A1.323.68j0.08493.6847II
Aj0.08493.6847
j1215j4)(4-
j4)(4-j29
0j4)(4-
0100j29
I
0
0100
I
I
j1215j4)(4-
j4)(4-j29
00
ababab
0
ab2
0
2
0
2
1

























 














SUBSITUTION THEOREM
SOLUTION :

6. SUBSITUTION THEOREM
Monday, August 05, 2019 6Syed Hasan Saeed
5 ohm
-j2 ohm
6 ohm
j8 ohm
j4 ohm
4 ohm
+
-
V0100 0
 A1.323.68 0

Fig.3
a
b
Zab is replaced by current source

7. SUBSITUTION THEOREM
Monday, August 05, 2019 7Syed Hasan Saeed
5 ohm
+
-
V0100 0

+
-
-j2 ohm 6 ohm
j8 ohm
j4 ohm
4 ohm
V1.3218.4
Fig.4
a
b
Zab is replaced by voltage source

8. Monday, August 05, 2019 syed hasan saeed 8
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