Tellegen's theorem

Tellegen's Theorem for electrical network

1. CIRCUIT THEORY
TELLEGEN’S THEOREM
SYED HASAN SAEED
Sunday, August 18, 2019 1Syed Hasan Saeed

2. REFERENCE BOOKS
•Introductory Circuit Analysis, Robert L. Boylested, Pearson Education,
Prentice Hall.
•Networks And Systems, AshfaqHusain, KhannaBook Publishing Co (P)
Ltd. Delhi.
•Networks And Systems, A Sudhakr, ShyammohanS 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.
Sunday, August 18, 2019 syed hasan saeed 2

3. TELLEGEN‟S THEOREM
STATEMENT: This theorem states that “any time „t‟ the algebraic sum of
instantaneous power in „n‟ branches of any network is zero, if KCL and
KVL are satisfied.” Mathematically
PROOF: Consider the network shown in fig.1
Sunday, August 18, 2019 Syed Hasan Saeed 3
Fig. 10iv
k
n
1k
k

Z
2
Z
4
Z
3Z
1
i
1
i
3
i
2
i
4
v
1 v
3
v
4v
2v
0
v
1 = 6V, v
2 = 4V,
v
3 = 3V, v4 = 1V
i
1 = 5A. i
2 = 2A,
i
3 = 3A, i
4 = 3A
Where
Where v
k= instantaneous voltage drop in
each branch
i
k= instantaneous current in each branch

4. TELLEGEN‟S THEOREM
PROOF:
STEP 1 :Verification of KCL:
At node „a‟ : i
1= i
2+ i
3 (1)
5 = 2 +3 = 5
At node „b‟ : i
3=i
4 (2)
3 =3
STEP 2 :Verification of KVL:
In mesh “1” : -v
1–v
2+ v
0= 0
-6 -4 + 10 = 0
In mesh “2” : v
2–v
3–v
4= 0
4 –3 –1 = 0
Hence KVL and KCL are satisfied.
Sunday, August 18, 2019 Syed Hasan Saeed 4

5. TELLEGEN‟S THEOREM
STEP 3 : Calculation of Power in each branch
-v
1* i
1= -6 x 5 = -30 W -v
4* i
4= -1 * 3 = -3 W
-v
2* i
2= -4 * 2 = -8 W v
0 * i
1= 10 * 5 = 50 W
-v
3* i
3= -3 * (-3) = -9 W
Sunday, August 18, 2019 Syed Hasan Saeed 50 503-9-8-3- iv
k
n
1k
k 

PROVED
OR,
Power Supplied = 50 W
Power Dissipated = -50 W

6. Sunday, August 18, 2019 syed hasan saeed 6
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